Lab 5 template
%% Lab 5 - Your Name - MAT 275 Lab
% The Mass-Spring System
%% EX 1 10 pts
%A) 1 pts | short comment
%
%B) 2 pts | short comment
%
%C) 1 pts | short comment
%
%D) 1 pts
%E) 2 pts | List the first 3-4 t values either in decimal format or as
%fractions involving pi
%F) 3 pts | comments. | (1 pts for including two distinct graphs, each with y(t) and v(t) plotted)
%% EX 2 10 pts
%A) 5 pts
% add commands to LAB05ex1 to compute and plot E(t). Then use ylim([~,~]) to change the yaxis limits.
% You don't need to include this code but at least one plot of E(t) and a comment must be
% included!
%B) 2 pts | write out main steps here
% first differentiate E(t) with respect to t using the chain rule. Then
% make substitutions using the expression for omega0 and using the
% differential equation
%C) 3 pts | show plot and comment
%% EX 3 10 pts
%A) 3 pts | modify the system of equations in LAB05ex1a
% write the t value and either a) show correponding graph or b) explain given matlab
% commands
%B) 2 pts | write t value and max |V| value; include figure
%note: velocity magnitude is like absolute value!
%C) 3 pts | include 3 figures here + comments.
% use title('text') to attach a title to the figure
%D) 2 pts | What needs to happen (in terms of the characteristic equation)
%in order for there to be no oscillations? Impose a condition on the
%characteristic equation to find the critical c value. Write out main steps
%% EX4 10 pts
% A) 5 pts | include 1 figure and comment
%B) 2 pts
% again find dE/dt using the chain rule and make substitutions based on the
% differential equation. You should reach an expression for dE/dt which is
% in terms of y'
%C) 3 pts | include one figure and comment
Exercise (1):
function LAB05ex1
m = 1; % mass [kg]
k = 9; % spring constant [N/m]
omega0=sqrt(k/m);
y0=0.4; v0=0; % initial conditions
[t,Y]=ode45(@f,[0,10],[y0,v0],[],omega0); % solve for 0<t<10
y=Y(:,1); v=Y(:,2); % retrieve y, v from Y
figure(1); plot(t,y,'b+-',t,v,'ro-'); % time series for y and v
grid on;
%------------------------------------------------------
function dYdt= f(t,Y,omega0)
y = Y(1); v= Y(2);
dYdt = [v; -omega0^2*y];
Exercise (1a):
function LAB05ex1a
m = 1; % mass [kg]
k = 9; % spring constant [N/m]
c = 1; % friction coefficient [Ns/m]
omega0 = sqrt(k/m); p = c/(2*m);
y0 = 0.4; v0 = 0; % initial conditions
[t,Y]=ode45(@f,[0,10],[y0,v0],[],omega0,p); % solve for 0<t<10
y=Y(:,1); v=Y(:,2); % retrieve y, v from Y
figure(1); plot(t,y,'b+-',t,v,'ro-'); % time series for y and v
grid on
%------------------------------------------------------
function dYdt= f(t,Y,omega0,p)
y = Y(1); v= Y(2);
dYdt = [v; ?? ]; % fill-in dv/dt
More instructions for the l ...
SAMPLE QUESTIONExercise 1 Consider the functionf (x,C).docxanhlodge
SAMPLE QUESTION:
Exercise 1: Consider the function
f (x,C)=
sin(C x)
Cx
(a) Create a vector x with 100 elements from -3*pi to 3*pi. Write f as an inline or anonymous function
and generate the vectors y1 = f(x,C1), y2 = f(x,C2) and y3 = f(x,C3), where C1 = 1, C2 = 2 and
C3 = 3. Make sure you suppress the output of x and y's vectors. Plot the function f (for the three
C's above), name the axis, give a title to the plot and include a legend to identify the plots. Add a
grid to the plot.
(b) Without using inline or anonymous functions write a function+function structure m-file that does
the same job as in part (a)
SAMPLE LAB WRITEUP:
MAT 275 MATLAB LAB 1 NAME: __________________________
LAB DAY and TIME:______________
Instructor: _______________________
Exercise 1
(a)
x = linspace(-3*pi,3*pi); % generating x vector - default value for number
% of pts linspace is 100
f= @(x,C) sin(C*x)./(C*x) % C will be just a constant, no need for ".*"
C1 = 1, C2 = 2, C3 = 3 % Using commans to separate commands
y1 = f(x,C1); y2 = f(x,C2); y3 = f(x,C3); % supressing the y's
plot(x,y1,'b.-', x,y2,'ro-', x,y3,'ks-') % using different markers for
% black and white plots
xlabel('x'), ylabel('y') % labeling the axis
title('f(x,C) = sin(Cx)/(Cx)') % adding a title
legend('C = 1','C = 2','C = 3') % adding a legend
grid on
Command window output:
f =
@(x,C)sin(C*x)./(C*x)
C1 =
1
C2 =
2
C3 =
3
(b)
M-file of structure function+function
function ex1
x = linspace(-3*pi,3*pi); % generating x vector - default value for number
% of pts linspace is 100
C1 = 1, C2 = 2, C3 = 3 % Using commans to separate commands
y1 = f(x,C1); y2 = f(x,C2); y3 = f(x,C3); % function f is defined below
plot(x,y1,'b.-', x,y2,'ro-', x,y3,'ks-') % using different markers for
% black and white plots
xlabel('x'), ylabel('y') % labeling the axis
title('f(x,C) = sin(Cx)/(Cx)') % adding a title
legend('C = 1','C = 2','C = 3') % adding a legend
grid on
end
function y = f(x,C)
y = sin(C*x)./(C*x);
end
Command window output:
C1 =
1
C2 =
2
C3 =
3
More instructions for the lab write-up:
1) You are not obligated to use the 'diary' function. It was presented only for you convenience. You
should be copying and pasting your code, plots, and results into some sort of "Word" type editor that
will allow you to import graphs and such. Make sure you always include the commands to generate
what is been asked and include the outputs (from command window and plots), unless the pr.
SAMPLE QUESTIONExercise 1 Consider the functionf (x,C).docxagnesdcarey33086
SAMPLE QUESTION:
Exercise 1: Consider the function
f (x,C)=
sin(C x)
Cx
(a) Create a vector x with 100 elements from -3*pi to 3*pi. Write f as an inline or anonymous function
and generate the vectors y1 = f(x,C1), y2 = f(x,C2) and y3 = f(x,C3), where C1 = 1, C2 = 2 and
C3 = 3. Make sure you suppress the output of x and y's vectors. Plot the function f (for the three
C's above), name the axis, give a title to the plot and include a legend to identify the plots. Add a
grid to the plot.
(b) Without using inline or anonymous functions write a function+function structure m-file that does
the same job as in part (a)
SAMPLE LAB WRITEUP:
MAT 275 MATLAB LAB 1 NAME: __________________________
LAB DAY and TIME:______________
Instructor: _______________________
Exercise 1
(a)
x = linspace(-3*pi,3*pi); % generating x vector - default value for number
% of pts linspace is 100
f= @(x,C) sin(C*x)./(C*x) % C will be just a constant, no need for ".*"
C1 = 1, C2 = 2, C3 = 3 % Using commans to separate commands
y1 = f(x,C1); y2 = f(x,C2); y3 = f(x,C3); % supressing the y's
plot(x,y1,'b.-', x,y2,'ro-', x,y3,'ks-') % using different markers for
% black and white plots
xlabel('x'), ylabel('y') % labeling the axis
title('f(x,C) = sin(Cx)/(Cx)') % adding a title
legend('C = 1','C = 2','C = 3') % adding a legend
grid on
Command window output:
f =
@(x,C)sin(C*x)./(C*x)
C1 =
1
C2 =
2
C3 =
3
(b)
M-file of structure function+function
function ex1
x = linspace(-3*pi,3*pi); % generating x vector - default value for number
% of pts linspace is 100
C1 = 1, C2 = 2, C3 = 3 % Using commans to separate commands
y1 = f(x,C1); y2 = f(x,C2); y3 = f(x,C3); % function f is defined below
plot(x,y1,'b.-', x,y2,'ro-', x,y3,'ks-') % using different markers for
% black and white plots
xlabel('x'), ylabel('y') % labeling the axis
title('f(x,C) = sin(Cx)/(Cx)') % adding a title
legend('C = 1','C = 2','C = 3') % adding a legend
grid on
end
function y = f(x,C)
y = sin(C*x)./(C*x);
end
Command window output:
C1 =
1
C2 =
2
C3 =
3
Joe Bob
Mon lab: 4:30-6:50
Lab 3
Exercise 1
(a) Create function M-file for banded LU factorization
function [L,U] = luband(A,p)
% LUBAND Banded LU factorization
% Adaptation to LUFACT
% Input:
% A diagonally dominant square matrix
% Output:
% L,U unit lower triangular and upper triangular such that LU=A
n = length(A);
L = eye(n); % ones on diagonal
% Gaussian Elimination
for j = 1:n-1
a = min(j+p.
More instructions for the lab write-up1) You are not obli.docxgilpinleeanna
More instructions for the lab write-up:
1) You are not obligated to use the 'diary' function. It was presented only for you convenience. You
should be copying and pasting your code, plots, and results into some sort of "Word" type editor that
will allow you to import graphs and such. Make sure you always include the commands to generate
what is been asked and include the outputs (from command window and plots), unless the problem
says to suppress it.
2) Edit this document: there should be no code or MATLAB commands that do not pertain to the
exercises you are presenting in your final submission. For each exercise, only the relevant code that
performs the task should be included. Do not include error messages. So once you have determined
either the command line instructions or the appropriate script file that will perform the task you are
given for the exercise, you should only include that and the associated output. Copy/paste these into
your final submission document followed by the output (including plots) that these MATLAB
instructions generate.
3) All code, output and plots for an exercise are to be grouped together. Do not put them in appendix, at
the end of the writeup, etc. In particular, put any mfiles you write BEFORE you first call them.
Each exercise, as well as the part of the exercises, is to be clearly demarked. Do not blend them all
together into some sort of composition style paper, complimentary to this: do NOT double space.
You can have spacing that makes your lab report look nice, but do not double space sections of text
as you would in a literature paper.
4) You can suppress much of the MATLAB output. If you need to create a vector, "x = 0:0.1:10" for
example, for use, there is no need to include this as output in your writeup. Just make sure you
include whatever result you are asked to show. Plots also do not have to be a full, or even half page.
They just have to be large enough that the relevant structure can be seen.
5) Before you put down any code, plots, etc. answer whatever questions that the exercise asks first.
You will follow this with the results of your work that support your answer.
SAMPLE QUESTION:
Exercise 1: Consider the function
f (x,C)=
sin(C x)
Cx
(a) Create a vector x with 100 elements from -3*pi to 3*pi. Write f as an inline or anonymous function
and generate the vectors y1 = f(x,C1), y2 = f(x,C2) and y3 = f(x,C3), where C1 = 1, C2 = 2 and
C3 = 3. Make sure you suppress the output of x and y's vectors. Plot the function f (for the three
C's above), name the axis, give a title to the plot and include a legend to identify the plots. Add a
grid to the plot.
(b) Without using inline or anonymous functions write a function+function structure m-file that does
the same job as in part (a)
SAMPLE LAB WRITEUP:
MAT 275 MATLAB LAB 1 NAME: ...
MATLAB sessions: Laboratory 2
MAT 275 Laboratory 2
Matrix Computations and Programming in MATLAB
In this laboratory session we will learn how to
1. Create and manipulate matrices and vectors.
2. Write simple programs in MATLAB
NOTE: For your lab write-up, follow the instructions of LAB1.
Matrices and Linear Algebra
⋆ Matrices can be constructed in MATLAB in different ways. For example the 3 × 3 matrix
A =
8 1 63 5 7
4 9 2
can be entered as
>> A=[8,1,6;3,5,7;4,9,2]
A =
8 1 6
3 5 7
4 9 2
or
>> A=[8,1,6;
3,5,7;
4,9,2]
A =
8 1 6
3 5 7
4 9 2
or defined as the concatenation of 3 rows
>> row1=[8,1,6]; row2=[3,5,7]; row3=[4,9,2]; A=[row1;row2;row3]
A =
8 1 6
3 5 7
4 9 2
or 3 columns
>> col1=[8;3;4]; col2=[1;5;9]; col3=[6;7;2]; A=[col1,col2,col3]
A =
8 1 6
3 5 7
4 9 2
Note the use of , and ;. Concatenated rows/columns must have the same length. Larger matrices can
be created from smaller ones in the same way:
c⃝2011 Stefania Tracogna, SoMSS, ASU
MATLAB sessions: Laboratory 2
>> C=[A,A] % Same as C=[A A]
C =
8 1 6 8 1 6
3 5 7 3 5 7
4 9 2 4 9 2
The matrix C has dimension 3 × 6 (“3 by 6”). On the other hand smaller matrices (submatrices) can
be extracted from any given matrix:
>> A(2,3) % coefficient of A in 2nd row, 3rd column
ans =
7
>> A(1,:) % 1st row of A
ans =
8 1 6
>> A(:,3) % 3rd column of A
ans =
6
7
2
>> A([1,3],[2,3]) % keep coefficients in rows 1 & 3 and columns 2 & 3
ans =
1 6
9 2
⋆ Some matrices are already predefined in MATLAB:
>> I=eye(3) % the Identity matrix
I =
1 0 0
0 1 0
0 0 1
>> magic(3)
ans =
8 1 6
3 5 7
4 9 2
(what is magic about this matrix?)
⋆ Matrices can be manipulated very easily in MATLAB (unlike Maple). Here are sample commands
to exercise with:
>> A=magic(3);
>> B=A’ % transpose of A, i.e, rows of B are columns of A
B =
8 3 4
1 5 9
6 7 2
>> A+B % sum of A and B
ans =
16 4 10
4 10 16
10 16 4
>> A*B % standard linear algebra matrix multiplication
ans =
101 71 53
c⃝2011 Stefania Tracogna, SoMSS, ASU
MATLAB sessions: Laboratory 2
71 83 71
53 71 101
>> A.*B % coefficient-wise multiplication
ans =
64 3 24
3 25 63
24 63 4
⋆ One MATLAB command is especially relevant when studying the solution of linear systems of dif-
ferentials equations: x=A\b determines the solution x = A−1b of the linear system Ax = b. Here is an
example:
>> A=magic(3);
>> z=[1,2,3]’ % same as z=[1;2;3]
z =
1
2
3
>> b=A*z
b =
28
34
28
>> x = A\b % solve the system Ax = b. Compare with the exact solution, z, defined above.
x =
1
2
3
>> y =inv(A)*b % solve the system using the inverse: less efficient and accurate
ans =
1.0000
2.0000
3.0000
Now let’s check for accuracy by evaluating the difference z − x and z − y. In exact arithmetic they
should both be zero since x, y and z all represent the solution to the system.
>> z - x % error for backslash command
ans =
0
0
0
>> z - y % error for inverse
ans =
1.0e-015 *
-0.4441
0
-0.88 ...
From the Front LinesOur robotic equipment and its maintenanc.docxhanneloremccaffery
From the Front Lines
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Source: Alemozaffar, Chang, Kacker, Sun, DeWolf, & Wagner (2013).
MATLAB sessions: Laboratory 5
MAT 275 Laboratory 5
The Mass-Spring System
In this laboratory we will examine harmonic oscillation. We will model the motion of a mass-spring
system with differential equations.
Our objectives are as follows:
1. Determine the effect of parameters on the solutions of differential equations.
2. Determine the behavior of the mass-spring system from the graph of the solution.
3. Determine the effect of the parameters on the behavior of the mass-spring.
The primary MATLAB command used is the ode45 function.
Mass-Spring System without Damping
The motion of a mass suspended to a vertical spring can be described as follows. When the spring is
not loaded it has length ℓ0 (situation (a)). When a mass m is attached to its lower end it has length ℓ
(situation (b)). From the first principle of mechanics we then obtain
mg︸︷︷︸
downward weight force
+ −k(ℓ − ℓ0)︸ ︷︷ ︸
upward tension force
= 0. (L5.1)
The term g measures the gravitational acceleration (g ≃ 9.8m/s2 ≃ 32ft/s2). The quantity k is a spring
constant measuring its stiffness. We now pull downwards on the mass by an amount y and let the mass
go (situation (c)). We expect the mass to oscillate around the position y = 0. The second principle of
mechanics yields
mg︸︷︷︸
weight
+ −k(ℓ + y − ℓ0)︸ ︷︷ ︸
upward tension force
= m
d2(ℓ + y)
dt2︸ ︷︷ ︸
acceleration of mass
, i.e., m
d2y
dt2
+ ky = 0 (L5.2)
using (L5.1). This ODE is second-order.
(a) (b) (c) (d)
y
ℓ
ℓ0
m
k
γ
Equation (L5.2) is rewritten
d2y
dt2
+ ω20y = 0 (L5.3)
c⃝2011 Stefania Tracogna, SoMSS, ASU
MATLAB sessions: Laboratory 5
where ω20 = k/m. Equation (L5.3) models simple harmonic motion. A numerical solution with ini-
tial conditions y(0) = 0.1 meter and y′(0) = 0 (i.e., the mass is initially stretched downward 10cms
and released, see setting (c) in figure) is obtained by first reducing the ODE to first-order ODEs (see
Laboratory 4).
Let v = y′. Then v′ = y′′ = −ω20y = −4y. Also v(0) = y′(0) = 0. The following MATLAB program
implements the problem (with ω0 = 2).
function LAB05ex1
m = 1; % mass [kg]
k = 4; % spring constant [N/m]
omega0 = sqrt(k/m);
y0 = 0.1; v0 = 0; % initial conditions
[t,Y] = ode45(@f,[0,10],[y0,v0],[],omega0); % solve for 0<t<10
y = Y(:,1); v = Y(:,2); % retrieve y, v from Y
figure(1); plot(t,y,’b+-’,t,v,’ro-’); % time series for y and v
grid on;
%-----------------------------------------
function dYdt = f(t,Y,omega0)
y = Y(1); v = Y(2);
dYdt = [ v ; -omega0^2*y ];
Note that the parameter ω0 was passed as an argument to ode45 rather than set to its value ω0 = 2
directly in the funct ...
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SAMPLE QUESTIONExercise 1 Consider the functionf (x,C).docxanhlodge
SAMPLE QUESTION:
Exercise 1: Consider the function
f (x,C)=
sin(C x)
Cx
(a) Create a vector x with 100 elements from -3*pi to 3*pi. Write f as an inline or anonymous function
and generate the vectors y1 = f(x,C1), y2 = f(x,C2) and y3 = f(x,C3), where C1 = 1, C2 = 2 and
C3 = 3. Make sure you suppress the output of x and y's vectors. Plot the function f (for the three
C's above), name the axis, give a title to the plot and include a legend to identify the plots. Add a
grid to the plot.
(b) Without using inline or anonymous functions write a function+function structure m-file that does
the same job as in part (a)
SAMPLE LAB WRITEUP:
MAT 275 MATLAB LAB 1 NAME: __________________________
LAB DAY and TIME:______________
Instructor: _______________________
Exercise 1
(a)
x = linspace(-3*pi,3*pi); % generating x vector - default value for number
% of pts linspace is 100
f= @(x,C) sin(C*x)./(C*x) % C will be just a constant, no need for ".*"
C1 = 1, C2 = 2, C3 = 3 % Using commans to separate commands
y1 = f(x,C1); y2 = f(x,C2); y3 = f(x,C3); % supressing the y's
plot(x,y1,'b.-', x,y2,'ro-', x,y3,'ks-') % using different markers for
% black and white plots
xlabel('x'), ylabel('y') % labeling the axis
title('f(x,C) = sin(Cx)/(Cx)') % adding a title
legend('C = 1','C = 2','C = 3') % adding a legend
grid on
Command window output:
f =
@(x,C)sin(C*x)./(C*x)
C1 =
1
C2 =
2
C3 =
3
(b)
M-file of structure function+function
function ex1
x = linspace(-3*pi,3*pi); % generating x vector - default value for number
% of pts linspace is 100
C1 = 1, C2 = 2, C3 = 3 % Using commans to separate commands
y1 = f(x,C1); y2 = f(x,C2); y3 = f(x,C3); % function f is defined below
plot(x,y1,'b.-', x,y2,'ro-', x,y3,'ks-') % using different markers for
% black and white plots
xlabel('x'), ylabel('y') % labeling the axis
title('f(x,C) = sin(Cx)/(Cx)') % adding a title
legend('C = 1','C = 2','C = 3') % adding a legend
grid on
end
function y = f(x,C)
y = sin(C*x)./(C*x);
end
Command window output:
C1 =
1
C2 =
2
C3 =
3
More instructions for the lab write-up:
1) You are not obligated to use the 'diary' function. It was presented only for you convenience. You
should be copying and pasting your code, plots, and results into some sort of "Word" type editor that
will allow you to import graphs and such. Make sure you always include the commands to generate
what is been asked and include the outputs (from command window and plots), unless the pr.
SAMPLE QUESTIONExercise 1 Consider the functionf (x,C).docxagnesdcarey33086
SAMPLE QUESTION:
Exercise 1: Consider the function
f (x,C)=
sin(C x)
Cx
(a) Create a vector x with 100 elements from -3*pi to 3*pi. Write f as an inline or anonymous function
and generate the vectors y1 = f(x,C1), y2 = f(x,C2) and y3 = f(x,C3), where C1 = 1, C2 = 2 and
C3 = 3. Make sure you suppress the output of x and y's vectors. Plot the function f (for the three
C's above), name the axis, give a title to the plot and include a legend to identify the plots. Add a
grid to the plot.
(b) Without using inline or anonymous functions write a function+function structure m-file that does
the same job as in part (a)
SAMPLE LAB WRITEUP:
MAT 275 MATLAB LAB 1 NAME: __________________________
LAB DAY and TIME:______________
Instructor: _______________________
Exercise 1
(a)
x = linspace(-3*pi,3*pi); % generating x vector - default value for number
% of pts linspace is 100
f= @(x,C) sin(C*x)./(C*x) % C will be just a constant, no need for ".*"
C1 = 1, C2 = 2, C3 = 3 % Using commans to separate commands
y1 = f(x,C1); y2 = f(x,C2); y3 = f(x,C3); % supressing the y's
plot(x,y1,'b.-', x,y2,'ro-', x,y3,'ks-') % using different markers for
% black and white plots
xlabel('x'), ylabel('y') % labeling the axis
title('f(x,C) = sin(Cx)/(Cx)') % adding a title
legend('C = 1','C = 2','C = 3') % adding a legend
grid on
Command window output:
f =
@(x,C)sin(C*x)./(C*x)
C1 =
1
C2 =
2
C3 =
3
(b)
M-file of structure function+function
function ex1
x = linspace(-3*pi,3*pi); % generating x vector - default value for number
% of pts linspace is 100
C1 = 1, C2 = 2, C3 = 3 % Using commans to separate commands
y1 = f(x,C1); y2 = f(x,C2); y3 = f(x,C3); % function f is defined below
plot(x,y1,'b.-', x,y2,'ro-', x,y3,'ks-') % using different markers for
% black and white plots
xlabel('x'), ylabel('y') % labeling the axis
title('f(x,C) = sin(Cx)/(Cx)') % adding a title
legend('C = 1','C = 2','C = 3') % adding a legend
grid on
end
function y = f(x,C)
y = sin(C*x)./(C*x);
end
Command window output:
C1 =
1
C2 =
2
C3 =
3
Joe Bob
Mon lab: 4:30-6:50
Lab 3
Exercise 1
(a) Create function M-file for banded LU factorization
function [L,U] = luband(A,p)
% LUBAND Banded LU factorization
% Adaptation to LUFACT
% Input:
% A diagonally dominant square matrix
% Output:
% L,U unit lower triangular and upper triangular such that LU=A
n = length(A);
L = eye(n); % ones on diagonal
% Gaussian Elimination
for j = 1:n-1
a = min(j+p.
More instructions for the lab write-up1) You are not obli.docxgilpinleeanna
More instructions for the lab write-up:
1) You are not obligated to use the 'diary' function. It was presented only for you convenience. You
should be copying and pasting your code, plots, and results into some sort of "Word" type editor that
will allow you to import graphs and such. Make sure you always include the commands to generate
what is been asked and include the outputs (from command window and plots), unless the problem
says to suppress it.
2) Edit this document: there should be no code or MATLAB commands that do not pertain to the
exercises you are presenting in your final submission. For each exercise, only the relevant code that
performs the task should be included. Do not include error messages. So once you have determined
either the command line instructions or the appropriate script file that will perform the task you are
given for the exercise, you should only include that and the associated output. Copy/paste these into
your final submission document followed by the output (including plots) that these MATLAB
instructions generate.
3) All code, output and plots for an exercise are to be grouped together. Do not put them in appendix, at
the end of the writeup, etc. In particular, put any mfiles you write BEFORE you first call them.
Each exercise, as well as the part of the exercises, is to be clearly demarked. Do not blend them all
together into some sort of composition style paper, complimentary to this: do NOT double space.
You can have spacing that makes your lab report look nice, but do not double space sections of text
as you would in a literature paper.
4) You can suppress much of the MATLAB output. If you need to create a vector, "x = 0:0.1:10" for
example, for use, there is no need to include this as output in your writeup. Just make sure you
include whatever result you are asked to show. Plots also do not have to be a full, or even half page.
They just have to be large enough that the relevant structure can be seen.
5) Before you put down any code, plots, etc. answer whatever questions that the exercise asks first.
You will follow this with the results of your work that support your answer.
SAMPLE QUESTION:
Exercise 1: Consider the function
f (x,C)=
sin(C x)
Cx
(a) Create a vector x with 100 elements from -3*pi to 3*pi. Write f as an inline or anonymous function
and generate the vectors y1 = f(x,C1), y2 = f(x,C2) and y3 = f(x,C3), where C1 = 1, C2 = 2 and
C3 = 3. Make sure you suppress the output of x and y's vectors. Plot the function f (for the three
C's above), name the axis, give a title to the plot and include a legend to identify the plots. Add a
grid to the plot.
(b) Without using inline or anonymous functions write a function+function structure m-file that does
the same job as in part (a)
SAMPLE LAB WRITEUP:
MAT 275 MATLAB LAB 1 NAME: ...
MATLAB sessions: Laboratory 2
MAT 275 Laboratory 2
Matrix Computations and Programming in MATLAB
In this laboratory session we will learn how to
1. Create and manipulate matrices and vectors.
2. Write simple programs in MATLAB
NOTE: For your lab write-up, follow the instructions of LAB1.
Matrices and Linear Algebra
⋆ Matrices can be constructed in MATLAB in different ways. For example the 3 × 3 matrix
A =
8 1 63 5 7
4 9 2
can be entered as
>> A=[8,1,6;3,5,7;4,9,2]
A =
8 1 6
3 5 7
4 9 2
or
>> A=[8,1,6;
3,5,7;
4,9,2]
A =
8 1 6
3 5 7
4 9 2
or defined as the concatenation of 3 rows
>> row1=[8,1,6]; row2=[3,5,7]; row3=[4,9,2]; A=[row1;row2;row3]
A =
8 1 6
3 5 7
4 9 2
or 3 columns
>> col1=[8;3;4]; col2=[1;5;9]; col3=[6;7;2]; A=[col1,col2,col3]
A =
8 1 6
3 5 7
4 9 2
Note the use of , and ;. Concatenated rows/columns must have the same length. Larger matrices can
be created from smaller ones in the same way:
c⃝2011 Stefania Tracogna, SoMSS, ASU
MATLAB sessions: Laboratory 2
>> C=[A,A] % Same as C=[A A]
C =
8 1 6 8 1 6
3 5 7 3 5 7
4 9 2 4 9 2
The matrix C has dimension 3 × 6 (“3 by 6”). On the other hand smaller matrices (submatrices) can
be extracted from any given matrix:
>> A(2,3) % coefficient of A in 2nd row, 3rd column
ans =
7
>> A(1,:) % 1st row of A
ans =
8 1 6
>> A(:,3) % 3rd column of A
ans =
6
7
2
>> A([1,3],[2,3]) % keep coefficients in rows 1 & 3 and columns 2 & 3
ans =
1 6
9 2
⋆ Some matrices are already predefined in MATLAB:
>> I=eye(3) % the Identity matrix
I =
1 0 0
0 1 0
0 0 1
>> magic(3)
ans =
8 1 6
3 5 7
4 9 2
(what is magic about this matrix?)
⋆ Matrices can be manipulated very easily in MATLAB (unlike Maple). Here are sample commands
to exercise with:
>> A=magic(3);
>> B=A’ % transpose of A, i.e, rows of B are columns of A
B =
8 3 4
1 5 9
6 7 2
>> A+B % sum of A and B
ans =
16 4 10
4 10 16
10 16 4
>> A*B % standard linear algebra matrix multiplication
ans =
101 71 53
c⃝2011 Stefania Tracogna, SoMSS, ASU
MATLAB sessions: Laboratory 2
71 83 71
53 71 101
>> A.*B % coefficient-wise multiplication
ans =
64 3 24
3 25 63
24 63 4
⋆ One MATLAB command is especially relevant when studying the solution of linear systems of dif-
ferentials equations: x=A\b determines the solution x = A−1b of the linear system Ax = b. Here is an
example:
>> A=magic(3);
>> z=[1,2,3]’ % same as z=[1;2;3]
z =
1
2
3
>> b=A*z
b =
28
34
28
>> x = A\b % solve the system Ax = b. Compare with the exact solution, z, defined above.
x =
1
2
3
>> y =inv(A)*b % solve the system using the inverse: less efficient and accurate
ans =
1.0000
2.0000
3.0000
Now let’s check for accuracy by evaluating the difference z − x and z − y. In exact arithmetic they
should both be zero since x, y and z all represent the solution to the system.
>> z - x % error for backslash command
ans =
0
0
0
>> z - y % error for inverse
ans =
1.0e-015 *
-0.4441
0
-0.88 ...
From the Front LinesOur robotic equipment and its maintenanc.docxhanneloremccaffery
From the Front Lines
Our robotic equipment and its maintenance represent a fixed cost of $23,320 per month. The cost-effectiveness of robotic-assisted surgery is related to patient volume: With only 10 cases, the fixed cost per case is $2,332, and with 40 cases, the fixed cost per case is $583.
Source: Alemozaffar, Chang, Kacker, Sun, DeWolf, & Wagner (2013).
MATLAB sessions: Laboratory 5
MAT 275 Laboratory 5
The Mass-Spring System
In this laboratory we will examine harmonic oscillation. We will model the motion of a mass-spring
system with differential equations.
Our objectives are as follows:
1. Determine the effect of parameters on the solutions of differential equations.
2. Determine the behavior of the mass-spring system from the graph of the solution.
3. Determine the effect of the parameters on the behavior of the mass-spring.
The primary MATLAB command used is the ode45 function.
Mass-Spring System without Damping
The motion of a mass suspended to a vertical spring can be described as follows. When the spring is
not loaded it has length ℓ0 (situation (a)). When a mass m is attached to its lower end it has length ℓ
(situation (b)). From the first principle of mechanics we then obtain
mg︸︷︷︸
downward weight force
+ −k(ℓ − ℓ0)︸ ︷︷ ︸
upward tension force
= 0. (L5.1)
The term g measures the gravitational acceleration (g ≃ 9.8m/s2 ≃ 32ft/s2). The quantity k is a spring
constant measuring its stiffness. We now pull downwards on the mass by an amount y and let the mass
go (situation (c)). We expect the mass to oscillate around the position y = 0. The second principle of
mechanics yields
mg︸︷︷︸
weight
+ −k(ℓ + y − ℓ0)︸ ︷︷ ︸
upward tension force
= m
d2(ℓ + y)
dt2︸ ︷︷ ︸
acceleration of mass
, i.e., m
d2y
dt2
+ ky = 0 (L5.2)
using (L5.1). This ODE is second-order.
(a) (b) (c) (d)
y
ℓ
ℓ0
m
k
γ
Equation (L5.2) is rewritten
d2y
dt2
+ ω20y = 0 (L5.3)
c⃝2011 Stefania Tracogna, SoMSS, ASU
MATLAB sessions: Laboratory 5
where ω20 = k/m. Equation (L5.3) models simple harmonic motion. A numerical solution with ini-
tial conditions y(0) = 0.1 meter and y′(0) = 0 (i.e., the mass is initially stretched downward 10cms
and released, see setting (c) in figure) is obtained by first reducing the ODE to first-order ODEs (see
Laboratory 4).
Let v = y′. Then v′ = y′′ = −ω20y = −4y. Also v(0) = y′(0) = 0. The following MATLAB program
implements the problem (with ω0 = 2).
function LAB05ex1
m = 1; % mass [kg]
k = 4; % spring constant [N/m]
omega0 = sqrt(k/m);
y0 = 0.1; v0 = 0; % initial conditions
[t,Y] = ode45(@f,[0,10],[y0,v0],[],omega0); % solve for 0<t<10
y = Y(:,1); v = Y(:,2); % retrieve y, v from Y
figure(1); plot(t,y,’b+-’,t,v,’ro-’); % time series for y and v
grid on;
%-----------------------------------------
function dYdt = f(t,Y,omega0)
y = Y(1); v = Y(2);
dYdt = [ v ; -omega0^2*y ];
Note that the parameter ω0 was passed as an argument to ode45 rather than set to its value ω0 = 2
directly in the funct ...
I am Paul G. I am a Mechanical Engineering Assignment Expert at matlabassignmentexperts.com. I hold a Ph.D. Matlab, University of Adelaide, Australia. I have been helping students with their homework for the past 10 years. I solve assignments related to Mechanical Engineering.
Visit matlabassignmentexperts.com or email info@matlabassignmentexperts.com.
You can also call on +1 678 648 4277 for any assistance with Mechanical Engineering Assignments.
MATLAB DOCUMENTATION ON SOME OF THE MODULES
A.Generate videos in which a skeleton of a person doing the following Gestures.
1.Tilting his head to right and left
2.Tilting his hand to right and left
3.Walking
in matlab.
B. Write a MATLAB program that converts a decimal number to Roman number and vice versa.
C.Using EZ plot & anonymous functions plot the following:
· Y=Sqrt(X)
· Y= X^2
· Y=e^(-XY)
D.Take your picture and
· Show R, G, B channels along with RGB Image in same figure using sub figure.
· Convert into HSV( Hue, saturation and value) and show the H,S,V channels along with HSV image
E.Record your name pronounced by yourself. Try to display the signal(name) in a plot vs Time, using matlab.
F.Write a script to open a new figure and plot five circles, all centered at the origin and with increasing radii. Set the line width for each circle to something thick (at least 2 points), and use the colors from a 5-color jet colormap (jet).
G. NEWTON RAPHSON AND SECANT METHOD
H.Write any one of the program to do following things using file concept.
1.Create or Open a file
2. Read data from the file and write data to another file
3. Append some text to already existed file
4. Close the file
I.Write a function to perform following set operations
1.Union of A and B
2. Intersection of A and B
3. Complement of A and B
(Assume A= {1, 2, 3, 4, 5, 6}, B= {2, 4, 6})
LAB05ex1.m
function LAB05ex1
m = 1; % mass [kg]
k = 4; % spring constant [N/m]
omega0=sqrt(k/m);
y0=0.1; v0=0; % initial conditions
[t,Y]=ode45(@f,[0,10],[y0,v0],[],omega0); % solve for 0<t<10
y=Y(:,1); v=Y(:,2); % retrieve y, v from Y
figure(1); plot(t,y,'b+-',t,v,'ro-'); % time series for y and v
grid on;
%------------------------------------------------------
function dYdt= f(t,Y,omega0)
y = Y(1); v= Y(2);
dYdt = [v; -omega0^2*y];
__MACOSX/._LAB05ex1.m
LAB05ex1a.m
function LAB05ex1a
m = 1; % mass [kg]
k = 4; % spring constant [N/m]
c = 1; % friction coefficient [Ns/m]
omega0 = sqrt(k/m); p = c/(2*m);
y0 = 0.1; v0 = 0; % initial conditions
[t,Y]=ode45(@f,[0,10],[y0,v0],[],omega0,p); % solve for 0<t<10
y=Y(:,1); v=Y(:,2); % retrieve y, v from Y
figure(1); plot(t,y,'b+-',t,v,'ro-'); % time series for y and v
grid on
%------------------------------------------------------
function dYdt= f(t,Y,omega0,p)
y = Y(1); v= Y(2);
dYdt = [v; ?? ]; % fill-in dv/dt
__MACOSX/._LAB05ex1a.m
MAT275_LAB05.pdf
MATLAB sessions: Laboratory 5
MAT 275 Laboratory 5
The Mass-Spring System
In this laboratory we will examine harmonic oscillation. We will model the motion of a mass-spring
system with differential equations.
Our objectives are as follows:
1. Determine the effect of parameters on the solutions of differential equations.
2. Determine the behavior of the mass-spring system from the graph of the solution.
3. Determine the effect of the parameters on the behavior of the mass-spring.
The primary MATLAB command used is the ode45 function.
Mass-Spring System without Damping
The motion of a mass suspended to a vertical spring can be described as follows. When the spring is
not loaded it has length ℓ0 (situation (a)). When a mass m is attached to its lower end it has length ℓ
(situation (b)). From the first principle of mechanics we then obtain
mg︸︷︷︸
downward weight force
+ −k(ℓ − ℓ0)︸ ︷︷ ︸
upward tension force
= 0. (L5.1)
The term g measures the gravitational acceleration (g ≃ 9.8m/s2 ≃ 32ft/s2). The quantity k is a spring
constant measuring its stiffness. We now pull downwards on the mass by an amount y and let the mass
go (situation (c)). We expect the mass to oscillate around the position y = 0. The second principle of
mechanics yields
mg︸︷︷︸
weight
+ −k(ℓ + y − ℓ0)︸ ︷︷ ︸
upward tension force
= m
d2(ℓ + y)
dt2︸ ︷︷ ︸
acceleration of mass
, i.e., m
d2y
dt2
+ ky = 0 (L5.2)
using (L5.1). This ODE is second-order.
(a) (b) (c) (d)
y
ℓ
ℓ0
m
k
γ
Equation (L5.2) is rewritten
d2y
dt2
+ ω20y = 0 (L5.3)
c⃝2011 Stefania Tracogna, SoMSS, ASU
MATLAB sessions: Laboratory 5
where ω20 = k/m. Equation (L5.3) models simple harmonic motion. A numerica ...
MATLAB sessions: Laboratory 3
MAT 275 Laboratory 3
Numerical
Solution
s by Euler and Improved Euler Methods
(scalar equations)
In this session we look at basic numerical methods to help us understand the fundamentals of numerical
approximations. Our objective is as follows.
1. Implement Euler’s method as well as an improved version to numerically solve an IVP.
2. Compare the accuracy and efficiency of the methods with methods readily available in MATLAB.
3. Apply the methods to specific problems and investigate potential pitfalls of the methods.
Instructions: For your lab write-up follow the instructions of LAB 1.
Euler’s Method
To derive Euler’s method start from y(t0) = y0 and consider a Taylor expansion at t1 = t0 + h:
y(t1) = y(t0) + y
′(t0)(t1 − t0) + . . .
= y0 + hf(t0, y(t0)) + . . .
= y0 + hf(t0, y0) + . . .
For small enough h we get an approximation y1 for y(t1) by suppressing the . . ., namely
y1 = y0 + hf(t0, y0) (L3.1)
The iteration (L3.1) is repeated to obtain y2 ≃ y(t2), . . . such that
yn+1 = yn + hf(tn, yn)
tn+1 = tn + h
Geometrically, the approximation made is equivalent to replacing the
solution curve by the tangent line at (t0, y0). From the figure we have
f(t0, y0) = f(t0, y(t0)) = y
′(t0) = tan θ =
y1 − y0
h
,
from which (L3.1) follows.
.
...........
...........
...........
..........s
s
y0
y1
y(t1)
t0 t1
θ
h
�
�
�
�
�
�
As an example consider the IVP
y′ = 2y = f(t, y) with y(0) = 3.
Note that here f does not explicitly depend on t (the ODE is called autonomous), but does implicitly
through y = y(t). To apply Euler’s method we start with the initial condition and select a step size h.
Since we are constructing arrays t and y without dimensionalizing them first it is best to clear these
names in case they have been used already in the same MATLAB work session.
>> clear t y % no comma between t and y! type help clear for more info
>> y(1)=3; t(1)=0; h=0.1;
c⃝2011 Stefania Tracogna, SoMSS, ASU
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MATLAB sessions: Laboratory 3
Since f is simple enough we may use the inline syntax:
>> f=inline(’2*y’,’t’,’y’)
f =
Inline function:
f(t,y) = 2*y
Note that the initialization y(1)=3 should not be interpreted as “the value of y at 1 is 3”, but rather “the
first value in the array y is 3”. In other words the 1 in y(1) is an index, not a time value! Unfortunately,
MATLAB indices in arrays must be positive (a legacy from Fortran...). The ...
The name MATLAB stands for MATrix LABoratory.MATLAB is a high-performance language for technical computing.
It integrates computation, visualization, and programming environment. Furthermore, MATLAB is a modern programming language environment: it has sophisticated data structures, contains built-in editing and debugging tools, and supports object-oriented programming.
These factor make MATLAB an excellent tool for teaching and research.
MATLAB sessions: Laboratory 1
MAT 275 Laboratory 1
Introduction to MATLAB
MATLAB is a computer software commonly used in both education and industry to solve a wide range
of problems.
This Laboratory provides a brief introduction to MATLAB, and the tools and functions that help
you to work with MATLAB variables and files.
The MATLAB Environment
⋆ To start MATLAB double-click on the MATLAB shortcut icon. The MATLAB desktop will open.
On the left side you will generally find the Current Folder window and on the right the Workspace
and Command History windows. The Command Window is where the MATLAB commands are entered
and executed. Note that windows within the MATLAB desktop can be resized by dragging the separator
bar(s).
If you have never used MATLAB before, we suggest you type demo at the MATLAB prompt. Click
on Getting Started with MATLAB and run the file.
Basics And Help
Commands are entered in the Command Window.
⋆ Basic operations are +, -, *, and /. The sequence
>> a=2; b=3; a+b, a*b
ans =
5
ans =
6
defines variables a and b and assigns values 2 and 3, respectively, then computes the sum a+b and product
ab. Each command ends with , (output is visible) or ; (output is suppressed). The last command on a
line does not require a ,.
⋆ Standard functions can be invoked using their usual mathematical notations. For example
>> theta=pi/5;
>> cos(theta)^2+sin(theta)^2
ans =
1
verifies the trigonometric identity sin2 θ + cos2 θ = 1 for θ = π
5
. A list of elementary math functions can
be obtained by typing
>> help elfun
⋆ To obtain a description of the use of a particular function type help followed by the name of the
function. For example
>> help cosh
gives help on the hyperbolic cosine function.
⋆ To get a list of other groups of MATLAB programs already available enter help:
>> help
c⃝2011 Stefania Tracogna, SoMSS, ASU
MATLAB sessions: Laboratory 1
⋆ Another way to obtain help is through the desktop Help menu, Help > Product Help.
⋆ MATLAB is case-sensitive. For example
>> theta=1e-3, Theta=2e-5, ratio=theta/Theta
theta =
1.0000e-003
Theta =
2.0000e-005
ratio =
50
⋆ The quantities Inf (∞) and NaN (Not a Number) also appear frequently. Compare
>> c=1/0
c =
Inf
with
>> d=0/0
d =
NaN
Plotting with MATLAB
⋆ To plot a function you have to create two arrays (vectors): one containing the abscissae, the other the
corresponding function values. Both arrays should have the same length. For example, consider plotting
the function
y = f(x) =
x2 − sin(πx) + ex
x − 1
for 0 ≤ x ≤ 2. First choose a sample of x values in this interval:
>> x=[0,.1,.2,.3,.4,.5,.6,.7,.8,.9,1, ...
1.1,1.2,1.3,1.4,1.5,1.6,1.7,1.8,1.9,2]
x =
Columns 1 through 7
0 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000
Columns 8 through 14
0.7000 0.8000 0.9000 1.0000 1.1000 1.2000 1.3000
Columns 15 through 21
1.4000 1.5000 1.6000 1.7000 1.8000 1.9000 2.0000
Note that an ellipsis ... was used to continue a command too long to fit in a sing ...
EE380-4 Course project Experimental determination of a Ser.docxjack60216
EE380-4 Course project
Experimental determination of a Servo-Motor State Space Model
Dr. A. Masoud, Course Project, Posted Thursday, October 8, 2015, Due a week before the end of the semester 151.
Objective: To determine experimentally the state space model and the transfer function of the
control laboratory servo-trainer using physical measurements instead of mathematical
derivations. In addition, to be familiarized with the mathematical tools needed for doing this task
Background: The servo-process you will be examining in the EE380 laboratory is the DC
motor (figure-1). By now, you are familiar with how to model theoretically this process. To do
this, you need to know beforehand all the parameters of the system. These parameters are
usually not readily available. Computing them may be difficult or not possible. Therefore, the
only other alternative is to determine the model of the servo-process experimentally.
Figure-1: Equivalent circuit of a DC motor
The motor used in the laboratory servo-trainer is a permanent magnet DC motor. The field is
generated by the permanent magnet is a constant. This makes the armature voltage (Va) the
only means of control available, i.e the motor is in an armature control mode.
The state of the overall system (X) consists of the state of the electrical part which is the current
in the inductor (the armature current Ia), the angular position ( )θ and the velocity of the
mechanical part (θ ). As for the output, it can be selected as anyone of these variables. This
makes writing the output equation of the state space model of the motor a simple and a
straightforward task. The state vector of the overall system is: X=[ Ia θ θ ]T. However, we are
going to use a simplified model that neglects the electrical component and focus only on the
mechanical one. The state vector of the simplified model is: X=[θ θ ]T. The state equation of
the simplified model in (1)
Va,
dc
ba
⎥
⎦
⎤
⎢
⎣
⎡
+⎥
⎦
⎤
⎢
⎣
⎡
⎥
⎦
⎤
⎢
⎣
⎡
=⎥
⎦
⎤
⎢
⎣
⎡
f
e
θ
θ
θ
θ (1)
Determining the model means that the input (Va(t)), the states (θ (t), θ (t)) and their derivatives
can be directly measured or reliably computed. The parameters (a,b,c,d,e,f) are the unknowns
that need to be determined from the measurements.
To determine the parameters, we first need to change the form of the state space equations into
the form in (2)
,
f
e
d
c
b
a
Va0(t)(t)00
0Va00(t)(t)
(t)
(t)
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎣
⎡
⎥
⎦
⎤
⎢
⎣
⎡
=⎥
⎦
⎤
⎢
⎣
⎡
θθ
θθ
θ
θ
(2)
Now take “n” measurements of the states, their derivatives and the input and form the equations
in (3). Determining the time instants (t1, t2,..,tn) at which measurements are to be taken are left
up to the student. However, one should make sure that the measurements are distinct, i.e. do
not take the same measurement more than once. ...
Computers and Programming , Programming Languages Types, Problem solving, Introduction to the MATLAB environment, Using MATLAB Documentation
Introduction to the course, Operating methodology-Installation Procedure
1. Compare a sample code in C with MATLAB
2. Trajectory of a particle in projectile motion ( solving quadratic equations)
3. Ideal gas law problem to find volume
PART B Please response to these two original posts below. Wh.docxsmile790243
PART B
Please response to these two original posts below. When
responding to these posts, please either expand the
thought, add additional insights, or respectfully disagree
and explain why. Remember that we are after reasons
and arguments, and not simply the statement of
opinions.
Original Post 1
Are human lives intrinsically valuable? If so, in virtue of what? (Is
it our uniqueness, perhaps, or our autonomy, or something else?)
To begin, I would like to remind us that being intrinsically valuable
means having values for just being us and nothing else. I believe
that human lives are intrinsically valuable in virtue of our
uniqueness. As a bio nerd, I would like to state the fact that there
are a lot of crossover events during meiosis, which create trillions
of different DNA combinations. Hence, from a biological
standpoint, without considering other aspects, being you is
already valuable because you are that one sperm that won the
race and got fertilized. On a larger scale, there are hardly two
people whose look and behaviors are the same in the same
family, unless they are identical twins. However, identical twins
still act differently and have differences (such as fingerprints).
Since we are raised in different families, we are taught different
things and have different cultures. In general, we all have
different genetic information, appearances, personalities, senses
of humor, ambitions, talents, interests and life experiences. These
characteristics make up our “unique individual value” and make
us so unique and irreplaceable.
I would also love to discuss how our diversities enrich and
contribute to society, but that would be a talk about our extrinsic
values.
Original Post 2
Are human lives intrinsically valuable? If so, in virtue of what? (Is
it our uniqueness, perhaps, or our autonomy, or something else?)
I believe that human lives are intrinsically valuable due to a
number of reasons. Firstly, human lives aren’t replaceable. You
can’t replace a human being with another just like you can
replace a broken laptop with brand new one. Part of the reason
why we tend to think this way is that we were nurtured with the
notion that there is, indeed, a special value to human life. This
could be in virtue of our uniqueness-- the fact that we are
sentient and capable of complex thoughts and emotions
separates us from any other species on this planet. From a
scientific standpoint, this is also one of the reasons as to why
humans became the dominant species in today’s age.
Moreover, human lives aren’t disposable. I think this is largely due
to us humans having the ability to empathize with others. We
understand that it’s morally inappropriate to take the life of
another individual even if they’re complete strangers because
they’re another human being like us who has their own thoughts,
values, memories, and stories. In a way, we have a strong
emotional connection to our own species. As .
Part C Developing Your Design SolutionThe Production Cycle.docxsmile790243
Part C Developing Your Design
Solution
The Production Cycle
Within the four stages of the design workflow there are two distinct parts.
The first three stages, as presented in Part B of this book, were described
as ‘The Hidden Thinking’ stages, as they are concerned with undertaking
the crucial behind-the-scenes preparatory work. You may have completed
them in terms of working through the book’s contents, but in visualisation
projects they will continue to command your attention, even if that is
reduced to a background concern.
You have now reached the second distinct part of the workflow which
involves developing your design solution. This stage follows a production
cycle, commencing with rationalising design ideas and moving through to
the development of a final solution.
The term cycle is appropriate to describe this stage as there are many loops
of iteration as you evolve rapidly between conceptual, practical and
technical thinking. The inevitability of this iterative cycle is, in large part,
again due to the nature of this pursuit being more about optimisation rather
than an expectation of achieving that elusive notion of perfection. Trade-
offs, compromises, and restrictions are omnipresent as you juggle ambition
and necessary pragmatism.
How you undertake this stage will differ considerably depending on the
nature of your task. The creation of a relatively simple, single chart to be
slotted into a report probably will not require the same rigour of a formal
production cycle that the development of a vast interactive visualisation to
be used by the public would demand. This is merely an outline of the most
you will need to do – you should edit, adapt and participate the steps to fit
with your context.
There are several discrete steps involved in this production cycle:
Conceiving ideas across the five layers of visualisation design.
Wireframing and storyboarding designs.
Developing prototypes or mock-up versions.
219
Testing.
Refining and completing.
Launching the solution.
Naturally, the specific approach for developing your design solution (from
prototyping through to launching) will vary hugely, depending particularly
on your skills and resources: it might be an Excel chart, or a Tableau
dashboard, an infographic created using Adobe Illustrator, or a web-based
interactive built with the D3.js library. As I have explained in the book’s
introduction, I’m not going to attempt to cover the myriad ways of
implementing a solution; that would be impossible to achieve as each task
and tool would require different instructions.
For the scope of this book, I am focusing on taking you through the first
two steps of this cycle – conceiving ideas and wireframing/storyboarding.
There are parallels here with the distinctions between architecture (design)
and engineering (execution) – I’m effectively chaperoning you through to
the conclusion of your design thinking.
To fulfil this, Part C presents a detailed breakdown of the many design
.
More Related Content
Similar to Lab 5 template Lab 5 - Your Name - MAT 275 Lab The M.docx
MATLAB DOCUMENTATION ON SOME OF THE MODULES
A.Generate videos in which a skeleton of a person doing the following Gestures.
1.Tilting his head to right and left
2.Tilting his hand to right and left
3.Walking
in matlab.
B. Write a MATLAB program that converts a decimal number to Roman number and vice versa.
C.Using EZ plot & anonymous functions plot the following:
· Y=Sqrt(X)
· Y= X^2
· Y=e^(-XY)
D.Take your picture and
· Show R, G, B channels along with RGB Image in same figure using sub figure.
· Convert into HSV( Hue, saturation and value) and show the H,S,V channels along with HSV image
E.Record your name pronounced by yourself. Try to display the signal(name) in a plot vs Time, using matlab.
F.Write a script to open a new figure and plot five circles, all centered at the origin and with increasing radii. Set the line width for each circle to something thick (at least 2 points), and use the colors from a 5-color jet colormap (jet).
G. NEWTON RAPHSON AND SECANT METHOD
H.Write any one of the program to do following things using file concept.
1.Create or Open a file
2. Read data from the file and write data to another file
3. Append some text to already existed file
4. Close the file
I.Write a function to perform following set operations
1.Union of A and B
2. Intersection of A and B
3. Complement of A and B
(Assume A= {1, 2, 3, 4, 5, 6}, B= {2, 4, 6})
LAB05ex1.m
function LAB05ex1
m = 1; % mass [kg]
k = 4; % spring constant [N/m]
omega0=sqrt(k/m);
y0=0.1; v0=0; % initial conditions
[t,Y]=ode45(@f,[0,10],[y0,v0],[],omega0); % solve for 0<t<10
y=Y(:,1); v=Y(:,2); % retrieve y, v from Y
figure(1); plot(t,y,'b+-',t,v,'ro-'); % time series for y and v
grid on;
%------------------------------------------------------
function dYdt= f(t,Y,omega0)
y = Y(1); v= Y(2);
dYdt = [v; -omega0^2*y];
__MACOSX/._LAB05ex1.m
LAB05ex1a.m
function LAB05ex1a
m = 1; % mass [kg]
k = 4; % spring constant [N/m]
c = 1; % friction coefficient [Ns/m]
omega0 = sqrt(k/m); p = c/(2*m);
y0 = 0.1; v0 = 0; % initial conditions
[t,Y]=ode45(@f,[0,10],[y0,v0],[],omega0,p); % solve for 0<t<10
y=Y(:,1); v=Y(:,2); % retrieve y, v from Y
figure(1); plot(t,y,'b+-',t,v,'ro-'); % time series for y and v
grid on
%------------------------------------------------------
function dYdt= f(t,Y,omega0,p)
y = Y(1); v= Y(2);
dYdt = [v; ?? ]; % fill-in dv/dt
__MACOSX/._LAB05ex1a.m
MAT275_LAB05.pdf
MATLAB sessions: Laboratory 5
MAT 275 Laboratory 5
The Mass-Spring System
In this laboratory we will examine harmonic oscillation. We will model the motion of a mass-spring
system with differential equations.
Our objectives are as follows:
1. Determine the effect of parameters on the solutions of differential equations.
2. Determine the behavior of the mass-spring system from the graph of the solution.
3. Determine the effect of the parameters on the behavior of the mass-spring.
The primary MATLAB command used is the ode45 function.
Mass-Spring System without Damping
The motion of a mass suspended to a vertical spring can be described as follows. When the spring is
not loaded it has length ℓ0 (situation (a)). When a mass m is attached to its lower end it has length ℓ
(situation (b)). From the first principle of mechanics we then obtain
mg︸︷︷︸
downward weight force
+ −k(ℓ − ℓ0)︸ ︷︷ ︸
upward tension force
= 0. (L5.1)
The term g measures the gravitational acceleration (g ≃ 9.8m/s2 ≃ 32ft/s2). The quantity k is a spring
constant measuring its stiffness. We now pull downwards on the mass by an amount y and let the mass
go (situation (c)). We expect the mass to oscillate around the position y = 0. The second principle of
mechanics yields
mg︸︷︷︸
weight
+ −k(ℓ + y − ℓ0)︸ ︷︷ ︸
upward tension force
= m
d2(ℓ + y)
dt2︸ ︷︷ ︸
acceleration of mass
, i.e., m
d2y
dt2
+ ky = 0 (L5.2)
using (L5.1). This ODE is second-order.
(a) (b) (c) (d)
y
ℓ
ℓ0
m
k
γ
Equation (L5.2) is rewritten
d2y
dt2
+ ω20y = 0 (L5.3)
c⃝2011 Stefania Tracogna, SoMSS, ASU
MATLAB sessions: Laboratory 5
where ω20 = k/m. Equation (L5.3) models simple harmonic motion. A numerica ...
MATLAB sessions: Laboratory 3
MAT 275 Laboratory 3
Numerical
Solution
s by Euler and Improved Euler Methods
(scalar equations)
In this session we look at basic numerical methods to help us understand the fundamentals of numerical
approximations. Our objective is as follows.
1. Implement Euler’s method as well as an improved version to numerically solve an IVP.
2. Compare the accuracy and efficiency of the methods with methods readily available in MATLAB.
3. Apply the methods to specific problems and investigate potential pitfalls of the methods.
Instructions: For your lab write-up follow the instructions of LAB 1.
Euler’s Method
To derive Euler’s method start from y(t0) = y0 and consider a Taylor expansion at t1 = t0 + h:
y(t1) = y(t0) + y
′(t0)(t1 − t0) + . . .
= y0 + hf(t0, y(t0)) + . . .
= y0 + hf(t0, y0) + . . .
For small enough h we get an approximation y1 for y(t1) by suppressing the . . ., namely
y1 = y0 + hf(t0, y0) (L3.1)
The iteration (L3.1) is repeated to obtain y2 ≃ y(t2), . . . such that
yn+1 = yn + hf(tn, yn)
tn+1 = tn + h
Geometrically, the approximation made is equivalent to replacing the
solution curve by the tangent line at (t0, y0). From the figure we have
f(t0, y0) = f(t0, y(t0)) = y
′(t0) = tan θ =
y1 − y0
h
,
from which (L3.1) follows.
.
...........
...........
...........
..........s
s
y0
y1
y(t1)
t0 t1
θ
h
�
�
�
�
�
�
As an example consider the IVP
y′ = 2y = f(t, y) with y(0) = 3.
Note that here f does not explicitly depend on t (the ODE is called autonomous), but does implicitly
through y = y(t). To apply Euler’s method we start with the initial condition and select a step size h.
Since we are constructing arrays t and y without dimensionalizing them first it is best to clear these
names in case they have been used already in the same MATLAB work session.
>> clear t y % no comma between t and y! type help clear for more info
>> y(1)=3; t(1)=0; h=0.1;
c⃝2011 Stefania Tracogna, SoMSS, ASU
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MATLAB sessions: Laboratory 3
Since f is simple enough we may use the inline syntax:
>> f=inline(’2*y’,’t’,’y’)
f =
Inline function:
f(t,y) = 2*y
Note that the initialization y(1)=3 should not be interpreted as “the value of y at 1 is 3”, but rather “the
first value in the array y is 3”. In other words the 1 in y(1) is an index, not a time value! Unfortunately,
MATLAB indices in arrays must be positive (a legacy from Fortran...). The ...
The name MATLAB stands for MATrix LABoratory.MATLAB is a high-performance language for technical computing.
It integrates computation, visualization, and programming environment. Furthermore, MATLAB is a modern programming language environment: it has sophisticated data structures, contains built-in editing and debugging tools, and supports object-oriented programming.
These factor make MATLAB an excellent tool for teaching and research.
MATLAB sessions: Laboratory 1
MAT 275 Laboratory 1
Introduction to MATLAB
MATLAB is a computer software commonly used in both education and industry to solve a wide range
of problems.
This Laboratory provides a brief introduction to MATLAB, and the tools and functions that help
you to work with MATLAB variables and files.
The MATLAB Environment
⋆ To start MATLAB double-click on the MATLAB shortcut icon. The MATLAB desktop will open.
On the left side you will generally find the Current Folder window and on the right the Workspace
and Command History windows. The Command Window is where the MATLAB commands are entered
and executed. Note that windows within the MATLAB desktop can be resized by dragging the separator
bar(s).
If you have never used MATLAB before, we suggest you type demo at the MATLAB prompt. Click
on Getting Started with MATLAB and run the file.
Basics And Help
Commands are entered in the Command Window.
⋆ Basic operations are +, -, *, and /. The sequence
>> a=2; b=3; a+b, a*b
ans =
5
ans =
6
defines variables a and b and assigns values 2 and 3, respectively, then computes the sum a+b and product
ab. Each command ends with , (output is visible) or ; (output is suppressed). The last command on a
line does not require a ,.
⋆ Standard functions can be invoked using their usual mathematical notations. For example
>> theta=pi/5;
>> cos(theta)^2+sin(theta)^2
ans =
1
verifies the trigonometric identity sin2 θ + cos2 θ = 1 for θ = π
5
. A list of elementary math functions can
be obtained by typing
>> help elfun
⋆ To obtain a description of the use of a particular function type help followed by the name of the
function. For example
>> help cosh
gives help on the hyperbolic cosine function.
⋆ To get a list of other groups of MATLAB programs already available enter help:
>> help
c⃝2011 Stefania Tracogna, SoMSS, ASU
MATLAB sessions: Laboratory 1
⋆ Another way to obtain help is through the desktop Help menu, Help > Product Help.
⋆ MATLAB is case-sensitive. For example
>> theta=1e-3, Theta=2e-5, ratio=theta/Theta
theta =
1.0000e-003
Theta =
2.0000e-005
ratio =
50
⋆ The quantities Inf (∞) and NaN (Not a Number) also appear frequently. Compare
>> c=1/0
c =
Inf
with
>> d=0/0
d =
NaN
Plotting with MATLAB
⋆ To plot a function you have to create two arrays (vectors): one containing the abscissae, the other the
corresponding function values. Both arrays should have the same length. For example, consider plotting
the function
y = f(x) =
x2 − sin(πx) + ex
x − 1
for 0 ≤ x ≤ 2. First choose a sample of x values in this interval:
>> x=[0,.1,.2,.3,.4,.5,.6,.7,.8,.9,1, ...
1.1,1.2,1.3,1.4,1.5,1.6,1.7,1.8,1.9,2]
x =
Columns 1 through 7
0 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000
Columns 8 through 14
0.7000 0.8000 0.9000 1.0000 1.1000 1.2000 1.3000
Columns 15 through 21
1.4000 1.5000 1.6000 1.7000 1.8000 1.9000 2.0000
Note that an ellipsis ... was used to continue a command too long to fit in a sing ...
EE380-4 Course project Experimental determination of a Ser.docxjack60216
EE380-4 Course project
Experimental determination of a Servo-Motor State Space Model
Dr. A. Masoud, Course Project, Posted Thursday, October 8, 2015, Due a week before the end of the semester 151.
Objective: To determine experimentally the state space model and the transfer function of the
control laboratory servo-trainer using physical measurements instead of mathematical
derivations. In addition, to be familiarized with the mathematical tools needed for doing this task
Background: The servo-process you will be examining in the EE380 laboratory is the DC
motor (figure-1). By now, you are familiar with how to model theoretically this process. To do
this, you need to know beforehand all the parameters of the system. These parameters are
usually not readily available. Computing them may be difficult or not possible. Therefore, the
only other alternative is to determine the model of the servo-process experimentally.
Figure-1: Equivalent circuit of a DC motor
The motor used in the laboratory servo-trainer is a permanent magnet DC motor. The field is
generated by the permanent magnet is a constant. This makes the armature voltage (Va) the
only means of control available, i.e the motor is in an armature control mode.
The state of the overall system (X) consists of the state of the electrical part which is the current
in the inductor (the armature current Ia), the angular position ( )θ and the velocity of the
mechanical part (θ ). As for the output, it can be selected as anyone of these variables. This
makes writing the output equation of the state space model of the motor a simple and a
straightforward task. The state vector of the overall system is: X=[ Ia θ θ ]T. However, we are
going to use a simplified model that neglects the electrical component and focus only on the
mechanical one. The state vector of the simplified model is: X=[θ θ ]T. The state equation of
the simplified model in (1)
Va,
dc
ba
⎥
⎦
⎤
⎢
⎣
⎡
+⎥
⎦
⎤
⎢
⎣
⎡
⎥
⎦
⎤
⎢
⎣
⎡
=⎥
⎦
⎤
⎢
⎣
⎡
f
e
θ
θ
θ
θ (1)
Determining the model means that the input (Va(t)), the states (θ (t), θ (t)) and their derivatives
can be directly measured or reliably computed. The parameters (a,b,c,d,e,f) are the unknowns
that need to be determined from the measurements.
To determine the parameters, we first need to change the form of the state space equations into
the form in (2)
,
f
e
d
c
b
a
Va0(t)(t)00
0Va00(t)(t)
(t)
(t)
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎣
⎡
⎥
⎦
⎤
⎢
⎣
⎡
=⎥
⎦
⎤
⎢
⎣
⎡
θθ
θθ
θ
θ
(2)
Now take “n” measurements of the states, their derivatives and the input and form the equations
in (3). Determining the time instants (t1, t2,..,tn) at which measurements are to be taken are left
up to the student. However, one should make sure that the measurements are distinct, i.e. do
not take the same measurement more than once. ...
Computers and Programming , Programming Languages Types, Problem solving, Introduction to the MATLAB environment, Using MATLAB Documentation
Introduction to the course, Operating methodology-Installation Procedure
1. Compare a sample code in C with MATLAB
2. Trajectory of a particle in projectile motion ( solving quadratic equations)
3. Ideal gas law problem to find volume
PART B Please response to these two original posts below. Wh.docxsmile790243
PART B
Please response to these two original posts below. When
responding to these posts, please either expand the
thought, add additional insights, or respectfully disagree
and explain why. Remember that we are after reasons
and arguments, and not simply the statement of
opinions.
Original Post 1
Are human lives intrinsically valuable? If so, in virtue of what? (Is
it our uniqueness, perhaps, or our autonomy, or something else?)
To begin, I would like to remind us that being intrinsically valuable
means having values for just being us and nothing else. I believe
that human lives are intrinsically valuable in virtue of our
uniqueness. As a bio nerd, I would like to state the fact that there
are a lot of crossover events during meiosis, which create trillions
of different DNA combinations. Hence, from a biological
standpoint, without considering other aspects, being you is
already valuable because you are that one sperm that won the
race and got fertilized. On a larger scale, there are hardly two
people whose look and behaviors are the same in the same
family, unless they are identical twins. However, identical twins
still act differently and have differences (such as fingerprints).
Since we are raised in different families, we are taught different
things and have different cultures. In general, we all have
different genetic information, appearances, personalities, senses
of humor, ambitions, talents, interests and life experiences. These
characteristics make up our “unique individual value” and make
us so unique and irreplaceable.
I would also love to discuss how our diversities enrich and
contribute to society, but that would be a talk about our extrinsic
values.
Original Post 2
Are human lives intrinsically valuable? If so, in virtue of what? (Is
it our uniqueness, perhaps, or our autonomy, or something else?)
I believe that human lives are intrinsically valuable due to a
number of reasons. Firstly, human lives aren’t replaceable. You
can’t replace a human being with another just like you can
replace a broken laptop with brand new one. Part of the reason
why we tend to think this way is that we were nurtured with the
notion that there is, indeed, a special value to human life. This
could be in virtue of our uniqueness-- the fact that we are
sentient and capable of complex thoughts and emotions
separates us from any other species on this planet. From a
scientific standpoint, this is also one of the reasons as to why
humans became the dominant species in today’s age.
Moreover, human lives aren’t disposable. I think this is largely due
to us humans having the ability to empathize with others. We
understand that it’s morally inappropriate to take the life of
another individual even if they’re complete strangers because
they’re another human being like us who has their own thoughts,
values, memories, and stories. In a way, we have a strong
emotional connection to our own species. As .
Part C Developing Your Design SolutionThe Production Cycle.docxsmile790243
Part C Developing Your Design
Solution
The Production Cycle
Within the four stages of the design workflow there are two distinct parts.
The first three stages, as presented in Part B of this book, were described
as ‘The Hidden Thinking’ stages, as they are concerned with undertaking
the crucial behind-the-scenes preparatory work. You may have completed
them in terms of working through the book’s contents, but in visualisation
projects they will continue to command your attention, even if that is
reduced to a background concern.
You have now reached the second distinct part of the workflow which
involves developing your design solution. This stage follows a production
cycle, commencing with rationalising design ideas and moving through to
the development of a final solution.
The term cycle is appropriate to describe this stage as there are many loops
of iteration as you evolve rapidly between conceptual, practical and
technical thinking. The inevitability of this iterative cycle is, in large part,
again due to the nature of this pursuit being more about optimisation rather
than an expectation of achieving that elusive notion of perfection. Trade-
offs, compromises, and restrictions are omnipresent as you juggle ambition
and necessary pragmatism.
How you undertake this stage will differ considerably depending on the
nature of your task. The creation of a relatively simple, single chart to be
slotted into a report probably will not require the same rigour of a formal
production cycle that the development of a vast interactive visualisation to
be used by the public would demand. This is merely an outline of the most
you will need to do – you should edit, adapt and participate the steps to fit
with your context.
There are several discrete steps involved in this production cycle:
Conceiving ideas across the five layers of visualisation design.
Wireframing and storyboarding designs.
Developing prototypes or mock-up versions.
219
Testing.
Refining and completing.
Launching the solution.
Naturally, the specific approach for developing your design solution (from
prototyping through to launching) will vary hugely, depending particularly
on your skills and resources: it might be an Excel chart, or a Tableau
dashboard, an infographic created using Adobe Illustrator, or a web-based
interactive built with the D3.js library. As I have explained in the book’s
introduction, I’m not going to attempt to cover the myriad ways of
implementing a solution; that would be impossible to achieve as each task
and tool would require different instructions.
For the scope of this book, I am focusing on taking you through the first
two steps of this cycle – conceiving ideas and wireframing/storyboarding.
There are parallels here with the distinctions between architecture (design)
and engineering (execution) – I’m effectively chaperoning you through to
the conclusion of your design thinking.
To fulfil this, Part C presents a detailed breakdown of the many design
.
PART A You will create a media piece based around the theme of a.docxsmile790243
PART A:
You will create a media piece based around the theme of “alternative facts.
Fake News:
Create a
series of 3
short, “fake news” articles or news videos. They should follow a specific theme. Make sure to have a clear understanding of WHY your fake news is being created (fake news is used by people, groups, companies, etc to convince an unsuspecting audience of something. It’s supposed to seem real, but the motivation behind it is to deceive. As part of this option, consider what your motivations are for your deception).
Part A: should be around 750 words for written tasks (or 250 for each 3 part task)
PART B:
The focus for this assignment is to demonstrate a
clear understanding of media conventions
, as well as
purpose
and
audience
. Therefore, along with your media product, you’ll also be required to submit a short
reflection
detailing why you created your product and for whom it was intended. You must discuss and analyze the elements within your media product (including why & how you used the persuasive techniques of ethos, logos and pathos) as well as the other elements of media you used and why.
.
Part 4. Implications to Nursing Practice & Implication to Patien.docxsmile790243
Part 4. Implications to Nursing Practice & Implication to Patient Outcomes
Provide a paragraph summary addressing the topics implications to nursing practice and patient outcomes. This section is NOT another review of the literature or introduction of new topics related to the PICOT question.
You may find if helpful to begin each topic with -
Nurses need to know …
Important patient outcomes include …
Example
– please note this is an older previous students work and so some references are older than 5 years.
Be sure to provide the PICOT question to begin this post.
PICOT Question:
P=Patient Population
I=Intervention
C=Comparison
O=Outcome
T=Time (duration):
In patients in the hospital, (P)
how does frequently provided patient hand washing (I)
compared with patient initiated hand washing (C)
affect hospital acquired infection (O)
within the hospital stay (T)
Implications to Nursing Practice & Patient Outcomes
Nurses need to know that they play a significant role in the reduction of hospital acquired infection by ensuring by health care workers and patients wash hands since nurses have the most interactions with patients. Implementing hand hygiene protocol with patients can enhance awareness and decrease healthcare associated infection (HAI). Both nurses and patients need to know that HAI is associated with increased morbidity and mortality as well cost of treatment and length of hospital stay. Nurses and patients also need to know that most HAI is preventable. Gujral (2015) notes that proper hand hygiene is the single most important, simplest, and least expensive means of reducing prevalence of HAI and the spread of antimicrobial resistance. Nurse and patient hand washing plays a vital role in decreasing healthcare costs and infections in all settings.
References
Gujral, H. (2015.) Survey shows importance of hand washing for infection prevention. American Nurse Today, 10 (10), 20. Retrieved from hEp://www.nursingworld.org/AmericanNurseToday
.
PART AHepatitis C is a chronic liver infection that can be e.docxsmile790243
PART A
Hepatitis C is a chronic liver infection that can be either silent (with no noticeable symptoms) or debilitating. Either way, 80% of infected persons experience continuing liver destruction. Chronic hepatitis C infection is the leading cause of liver transplants in the United States. The virus that causes it is blood borne, and therefore patients who undergo frequent procedures involving transfer of blood are particularly susceptible to infection. Kidney dialysis patients belong to this group. In 2008, a for-profit hemodialysis facility in New York was shut down after nine of its patients were confirmed as having become infected with hepatitis C while undergoing hemodialysis treatments there between 2001 and 2008.
When the investigation was conducted in 2008, investigators found that 20 of the facility’s 162 patients had been documented with hepatitis C infection at the time they began their association with the clinic. All the current patients were then offered hepatitis C testing, to determine how many had acquired hepatitis C during the time they were receiving treatment at the clinic. They were considered positive if enzyme-linked immunosorbent assay (ELISA) tests showed the presence of antibodies to the hepatitis C virus.
Health officials did not test the workers at the hemodialysis facility for hepatitis C because they did not view them as likely sources of the nine new infections. Why not?
Why do you think patients were tested for antibody to the virus instead of for the presence of the virus itself?
Ref.: Cowan, M. K. (2014) (4th Ed.). Microbiology: A Systems Approach, McGraw Hill
PART B
Summary:
Directions for the students: There are 4 essay questions. Please be sure to complete all of them with thorough substantive responses. Current APA Citations are required for all responses.
1. Precisely what is microbial death?
2. Why does a population of microbes not die instantaneously when exposed to an antimicrobial agent?
3. Explain what is wrong with this statement: “Prior to vaccination, the patient’s skin was sterilized with alcohol.” What would be a more correct wording?
4. Conduct additional research on the use of triclosan and other chemical agents in antimicrobial products today. Develop an opinion on whether this process should continue, providing evidence and citations to support your stance.
.
Part A post your answer to the following question1. How m.docxsmile790243
Part A post
your answer to the following question:
1. How might potential reactions to an adolescent’s questioning of their sexual identity, or gender role, impact their social environment, behavior and self-esteem?
2. As social workers, what role can we play in assuring the best outcomes for these adolescents?
Please use the Learning Resources to support your answer.
Part B
post
your answer to the following question:
1. How can social workers work toward assuring the best outcomes for adolescents questioning their sexual orientation or gender identity.
Please use the Learning Resources to support your answer.
.
PART BPlease response to these two original posts below..docxsmile790243
PART B
Please response to these two original posts below. When responding to
these posts, please either expand the thought, add additional insights, or
respectfully disagree and explain why. Remember that we are after reasons
and arguments, and not simply the statement of opinions.
Original Post 1
"What is moral relativism? Why might people be attracted to it? Is
it plausible?"
First of all, moral relativism is the view that moral truths are
subjective and depend on each individual's standpoints. Based
on this, everyone's moral view is legitimate. This can be attracted
because it sounds liberating and there is no need to argue for a
particular position. Moral relativism seems convincing in some
cases. For example, some people are okay with giving money to
homeless people, thinking that it's good to provide for the people
in need. Some people, on the other hand, claim that they can
work to satisfy their own needs. Moral relativism works well in
these cases because they all seem legitimate. However, there are
cases that moral relativism does not seem reasonable. For
example, child sacrifice in some cultures seems cruel and
uncivilized to most people. Hence, moral relativism is not
absolutely true.
Original Post 2
“Is your death bad for you, specifically, or only (at most) for others? Why
might someone claim that it isn’t bad for you?”
I'd start off by acknowledging what the two ancient philosophers,
Lucretius and Epicurus, outlined about death. They made the
point that death isn't necessarily bad for you since no suffering
takes place and that you yourself don't realize your own death. In
this way, one could make the claim that death isn't intrinsically
bad for you.
Another perspective I wanted to add was the influence of death
(both on you and others around you). Specifically, the event of
death itself may not be bad for you, but the idea of impending
death could impact one's life. Some may live freely, totally care-
free, accepting of death and enjoy life in the moment. Others may
be frightened by the idea of death that they live in constant fear
and hence death causing their mental health to take its toll. In
this way, I'd argue that death could, in fact, be bad for you. One
common reason for being afraid of death is the fear of being
forgotten. Not to mention the death of an individual certainly
affects others; death doesn't affect one's life but also all that is
connected to it. Focusing back to the point, it's clear that the
very idea of death directly affects the concerned individual. The
fact that those who live in fear of death are looking for legacies
and footprints to leave after they leave this world is telling of how
death could be arguably bad for you before it even happens.
PART A
Pick one or more questions below and write a substantive post
with >100 words. Please try to provide evidence(s) to support
your idea(s).
Questions:
• Do we have a duty to work out whe.
Part A (50 Points)Various men and women throughout history .docxsmile790243
Part A (50 Points):
Various men and women throughout history have made important contributions to the development of statistical science. Select any one (1) individual from the list below and write a 2 page summary of their influence on statistics. Be specific in detail to explain the concepts they developed and how this advanced our understanding and application of statistics.
Florence Nightingale
Francis Galton
Thomas Bayes
Part B (50 Points):
Select any one statistical concept you learned in this course and explain how it can be applied to our understanding of the Covid-19 pandemic (2 pages). You should use a specific example and include at least one diagram to illustrate your answer.
Please note: Your work must be original and not copied directly from other sources. No citations are needed. Be sure to submit this assignment in Blackboard on the due date specified.
.
Part A:
1. K
2. D
3. N
4. C
5. A
6. O
7. F
8. Q
9. H
10. M
11. S
12. Y
13. I
14. U
15. X
Part B:
1.
A. UTI is short form for Urinary tract infection. Means infection which affects organs of urinary tract. Such as urethra, urinary bladder and kidney. This are main organ for formation of urine and helps to expel it out of body.
B. Kidneys, urethra and urinary bladder gets affected during Urinary tract infection. Generally infection begins with urethra then travels to kidney.
When only lower part gets affected which is called lower UTI also cystitis because involves bladder
And when infection spread to upper side involving kidneys known as pyelonephritis.
2.
A. Microorganism in UTI
Escherichia coli
Klebsiella pneumoniae
B. Coli bacteria lives in intestine. So they also seen near anal canal. From which gets transferred to urethra.
C. Bacteria enters urinary tract from urethra. In very less cases kidney gets infected by blood stream.
3.
Signs and symptoms:
A) Pain with urination:
The infection cause inflammation of urinary tract, the urine from the inflammed urinary tract cause pain in urination.
B) orange or red colour urine:
The inflammation of urinary tract may cause a orange or red colour urine. It is common sign in UTI due to inflammation of urinary tract.
4.
UTI:
Urinary tract infection (UTI) any infection on the urinary tract causing difficult in urination. It most commonly affects the woman because thet are more prone to it.
Diagnosis And treatment:
A) The diagnostic test for UTI:
The two major diagnostic test for UTI are:
Urinalysis:
Urine is collected from the patient who came for test. This test shows the bacterial or any infectious organism in the urine.
The collected urine sample is added to the substance which promotes the growth of the organism in the urine.
If the growth is organism doesn't takes place then the test is negative.
If the organism growth in the urine takes place then the test is positive.
Ultra sound:
The sound waves from the transducer of ultra produce a imaging of the internal organs.
Patient lower abdomen is scanned by ultra sound to detect any abnormality in the organs and structures of urinary tract.
B) The medications for UTI are antibiotics or antimicrobial.
The two drugs are amoxicillin, sulfasulfamethaxazole.
Both of these drugs act on UTI by fighting against the microorganisms in the UTI. By assisting the immune system, it fight against the microorganisms and that relieves the symptoms of UTI.
5.
answer. a) In women at the time of pregnancy the drainage system from the kidney towards bladder become wide, hence, urine does not pass out as quickly. This makes it easier to get an infection. Similarly women has shorter urethra than a man have, the shorter distance make the way easy to bacteria to travel into the bladder.
b) There are no of ways by which women can reduce the risk of getting UTI. Like women should drink plenty of water this will help of getting rid from UTI, a women should protect their urethra .
Part A Develop an original age-appropriate activity for your .docxsmile790243
Part A:
Develop an original age-appropriate activity for your preschool class using
one
of the following.
Froebel’s cube gift
Froebel’s parquetry gift
Lincoln Logs
Describe the activity that you have developed.
Identify at least two (2) skills that the activity would help develop.
Part B:
Develop an original age-appropriate activity for your preschool class promoting the same skill(s) as the activity above, but develop the activity based on the Montessori method.
Describe the activity that you have developed.
What are at least two key differences between the two activities you developed?
.
Part 3 Social Situations2. Identify multicultural challenges th.docxsmile790243
Part 3: Social Situations
2. Identify multicultural challenges that your chosen individual may face as a recent
refugee.
• What are some of the issues that can arise for someone who has recently
immigrated to a new country?
• Explain how these multicultural challenges could impact your chosen individual’s
four areas of development?
3. Suggest plans of action or resources that you feel should be provided to this family to
assist them in proper develop
Part 3: Social Situations
• Proposal paper which identifies multicultural challenges that your chosen individual may face as a recent refugee.
• Suggested plan of action and/or resources which should be implemented to address the multicultural challenges.
• 2-3 Pages in length
• APA Formatting
• Submission will be checked for plagiaris
.
Part A (1000 words) Annotated Bibliography - Create an annota.docxsmile790243
Part A
(1000 words): Annotated Bibliography - Create an annotated bibliography that focuses on ONE particular aspect of current Software Engineering that face a world with different cultural standards. At least seven (7) peer-reviewed articles must be used for this exercise.
Part B
(3000 words):
Research Report
- Write a report of the analysis and synthesis using the
(Part A
) foundational
Annotated Bibliography
.
Part C (500 words): Why is it important to try to minimize complexity in a software system.
Part D (500 words): What are the advantages and disadvantages to companies that are developing software products that use cloud servers to support their development process?
Part E (500 words): Explain why each microservice should maintain its own data. Explain how data in service replicas can be kept consistent?
.
Part 6 Disseminating Results Create a 5-minute, 5- to 6-sli.docxsmile790243
Part 6: Disseminating Results
Create a 5-minute, 5- to 6-slide narrated PowerPoint presentation of your Evidence-Based Project:
· Be sure to incorporate any feedback or changes from your presentation submission in Module 5.
· Explain how you would disseminate the results of your project to an audience. Provide a rationale for why you selected this dissemination strategy.
Points Range: 81 (81%) - 90 (90%)
The narrated presentation accurately and completely summarizes the evidence-based project. The narrated presentation is professional in nature and thoroughly addresses all components of the evidence-based project.
The narrated presentation accurately and clearly explains in detail how to disseminate the results of the project to an audience, citing specific and relevant examples.
The narrated presentation accurately and clearly provides a justification that details the selection of this dissemination strategy that is fully supported by specific and relevant examples.
The narrated presentation provides a complete, detailed, and specific synthesis of two outside resources related to the dissemination strategy explained. The narrated presentation fully integrates at least two outside resources and two or three course-specific resources that fully support the presentation.
Written Expression and Formatting—Paragraph Development and Organization:
Paragraphs make clear points that support well-developed ideas, flow logically, and demonstrate continuity of ideas. Sentences are carefully focused—neither long and rambling nor short and lacking substance. A clear and comprehensive purpose statement and introduction is provided which delineates all required criteria.
Points Range: 5 (5%) - 5 (5%)
Paragraphs and sentences follow writing standards for flow, continuity, and clarity.
A clear and comprehensive purpose statement, introduction, and conclusion is provided which delineates all required criteria.
Written Expression and Formatting—English Writing Standards:
Correct grammar, mechanics, and proper punctuation.
Points Range: 5 (5%) - 5 (5%)
Uses correct grammar, spelling, and punctuation with no errors.
Evidenced Based Change
Leslie Hill
Walden University
Introduction/PurposeChange is inevitable.Health care organizations need change to improve.There are challenges that need to be addressed(Baraka-Johnson et al. 2019).Challenges should be addressed using evidence-based research.These changes enhance professionalism therefore improving quality of care and quality of life.The purpose of this paper is to identify an existing problem in health care and suggest a change idea that would be effective in addressing the problem. The paper also articulates risks associated with the change process, how to distribute the change information and how to implement change successfully.
Organizational CultureThe Organization is a hospice facilityOffers end of life care for pain and symptom managementThe health care providers cu.
Part 3 Social Situations • Proposal paper which identifies multicul.docxsmile790243
Part 3: Social Situations • Proposal paper which identifies multicultural challenges that your chosen individual may face as a recent refugee. • Suggested plan of action and/or resources which should be implemented to address the multicultural challenges. • 2-3 Pages in length • APA Formatting • Submission will be checked for plagiarism
Part 3: Social Situations 2. Identify multicultural challenges that your chosen individual may face as a recent refugee. • What are some of the issues that can arise for someone who has recently immigrated to a new country? • Explain how these multicultural challenges could impact your chosen individual’s four areas of development? 3. Suggest plans of action or resources that you feel should be provided to this family to assist them in proper development.
.
Part 3 Social Situations 2. Identify multicultural challenges that .docxsmile790243
Part 3: Social Situations 2. Identify multicultural challenges that your chosen individual may face as a recent refugee. • What are some of the issues that can arise for someone who has recently immigrated to a new country? • Explain how these multicultural challenges could impact your chosen individual’s four areas of development? 3. Suggest plans of action or resources that you feel should be provided to this family to assist them in proper development.
Part 3: Social Situations • Proposal paper which identifies multicultural challenges that your chosen individual may face as a recent refugee. • Suggested plan of action and/or resources which should be implemented to address the multicultural challenges. • 2-3 Pages in length • APA Formatting • Submission will be checked for plagiarism
.
Part 2The client is a 32-year-old Hispanic American male who c.docxsmile790243
Part 2
The client is a 32-year-old Hispanic American male who came to the United States when he was in high school with his father. His mother died back in Mexico when he was in school. He presents today to the PMHNPs office for an initial appointment for complaints of depression. The client was referred by his PCP after “routine” medical work-up to rule out an organic basis for his depression. He has no other health issues except for some occasional back pain and “stiff” shoulders which he attributes to his current work as a laborer in a warehouse. the “Montgomery- Asberg Depression Rating Scale (MADRS)” and obtained a score of 51 (indicating severe depression). reports that he always felt like an outsider as he was “teased” a lot for being “black” in high school. States that he had few friends, and basically kept to himself. He also reports a remarkably diminished interest in engaging in usual activities, states that he has gained 15 pounds in the last 2 months. He is also troubled with insomnia which began about 6 months ago, but have been progressively getting worse. He does report poor concentration which he reports is getting in “trouble” at work.
· Decision #1: start Zoloft 25mg orally daily
· Which decision did you select?
· Why did you select this decision? Support your response with evidence and references to the Learning Resources.
· What were you hoping to achieve by making this decision? Support your response with evidence and references to the Learning Resources.
· Explain any difference between what you expected to achieve with Decision #1 and the results of the decision. Why were they different?
· Decision #2: Client returns to clinic in four weeks, reports a 25% decrease in symptoms but concerned over the new onset of erectile dysfunction
*add Augmentin Wellbutrin IR 150mg in the morning
· Why did you select this decision? Support y our response with evidence and references to the Learning Resources.
· What were you hoping to achieve by making this decision? Support your response with evidence and references to the Learning Resources.
· Explain any difference between what you expected to achieve with Decision #2 and the results of the decision. Why were they different?
· Decision #3: Client returns to clinic in four weeks, Client stated that depressive symptoms have decreased even more and his erectile dysfunction has abated
· Client reports that he has been feeling “jittery” and sometimes “nervous”
*change to Wellbutrin XL 150mg daily
· Why did you select this decision? Support your response with evidence and references to the Learning Resources.
· What were you hoping to achieve by making this decision? Support your response with evidence and references to the Learning Resources.
· Explain any difference between what you expected to achieve with Decision #3 and the results of the decision. Why were they different?
Explain how ethical considerations might impact your treatment plan and communication with clients.
Conclusion.
Part 2For this section of the template, focus on gathering deta.docxsmile790243
Part 2:
For this section of the template, focus on gathering details about common, specific learning disabilities. These disabilities fall under the IDEA disability categories you researched for the chart above. Review the textbook and the topic study materials and use them to complete the chart.
Learning Disability Definition Characteristics Common Assessments for Diagnosis Potential Effect on Learning and Other Areas of Life Basic Strategies for Addressing the Disability
Attention Deficit Hyperactivity Disorder (ADHD)
Auditory Processing Disorder (APD)
Dyscalculia
Dysgraphia
Dyslexia
Dysphasia/Aphasia
Dyspraxia
Language Processing Disorder (LPD)
Non-Verbal Learning Disabilities
Visual Perceptual/Visual Motor Deficit
.
Part 2 Observation Summary and Analysis • Summary paper of observat.docxsmile790243
Part 2: Observation Summary and Analysis • Summary paper of observation findings for each area of development and connection to the observed participant. • Comprehensive description of the observed participant. • Analyzed observation experience with course material to determine whetherthe participant is developmentally on track for each area of development. • 4 Pages in length • APA Formatting • Submission will be checked for plagiarism
Part 2: Observation Summary and Analysis 1. Review and implement any comments from your instructor for Part 1: Observation. 2. Describe the participant that you observed. • Share your participant’s first name (can be fictional name if participant wants to remain anonymous), age, physical attributes, and you initial impressions. 3. Analyze your observation findings for each area of development (physical, cognitive, social/emotional, and spiritual/moral). • Explain how your observations support the 3-5 bullets for each area of development that you identified in your Development Observation Guidefrom Part 1: Observation. • Explain whether or not your participant is developmentally on track for each area of development. 4. What stood out the most to you about the observation? 5. Include at least 2 credible sources
.
Part 2 Observation Summary and Analysis 1. Review and implement any.docxsmile790243
Part 2: Observation Summary and Analysis 1. Review and implement any comments from your instructor for Part 1: Observation. 2. Describe the participant that you observed. • Share your participant’s first name (can be fictional name if participant wants to remain anonymous), age, physical attributes, and you initial impressions. 3. Analyze your observation findings for each area of development (physical, cognitive, social/emotional, and spiritual/moral). • Explain how your observations support the 3-5 bullets for each area of development that you identified in your Development Observation Guidefrom Part 1: Observation. • Explain whether or not your participant is developmentally on track for each area of development. 4. What stood out the most to you about the observation? 5. Include at least 2 credible sources
Part 2: Observation Summary and Analysis • Summary paper of observation findings for each area of development and connection to the observed participant. • Comprehensive description of the observed participant. • Analyzed observation experience with course material to determine whetherthe participant is developmentally on track for each area of development. • 4-6 Pages in length • APA Formatting • Submission will be checked for plagiarism
.
Part 2Data collectionfrom your change study initiative,.docxsmile790243
Part 2:
Data collection
from your change study initiative, sample, method, display of the results of the data itself, process, and method of analysis (graphs, charts, frequency counts, descriptive statistics of the data, narrative)
Part 3: Interpretation of the results of the Data
Collection and
Analysis, address likely resistance, and provide recommendations for continuing
the study
or evaluating your change study/initiative.
.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
Embracing GenAI - A Strategic ImperativePeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
Introduction to AI for Nonprofits with Tapp NetworkTechSoup
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
A Strategic Approach: GenAI in EducationPeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Thesis Statement for students diagnonsed withADHD.ppt
Lab 5 template Lab 5 - Your Name - MAT 275 Lab The M.docx
1. Lab 5 template
%% Lab 5 - Your Name - MAT 275 Lab
% The Mass-Spring System
%% EX 1 10 pts
%A) 1 pts | short comment
%
%B) 2 pts | short comment
%
%C) 1 pts | short comment
%
%D) 1 pts
%E) 2 pts | List the first 3-4 t values either in decimal format or
as
%fractions involving pi
%F) 3 pts | comments. | (1 pts for including two distinct graphs,
each with y(t) and v(t) plotted)
%% EX 2 10 pts
%A) 5 pts
% add commands to LAB05ex1 to compute and plot E(t). Then
use ylim([~,~]) to change the yaxis limits.
% You don't need to include this code but at least one plot of
E(t) and a comment must be
% included!
%B) 2 pts | write out main steps here
% first differentiate E(t) with respect to t using the chain rule.
Then
% make substitutions using the expression for omega0 and using
the
2. % differential equation
%C) 3 pts | show plot and comment
%% EX 3 10 pts
%A) 3 pts | modify the system of equations in LAB05ex1a
% write the t value and either a) show correponding graph or b)
explain given matlab
% commands
%B) 2 pts | write t value and max |V| value; include figure
%note: velocity magnitude is like absolute value!
%C) 3 pts | include 3 figures here + comments.
% use title('text') to attach a title to the figure
%D) 2 pts | What needs to happen (in terms of the characteristic
equation)
%in order for there to be no oscillations? Impose a condition on
the
%characteristic equation to find the critical c value. Write out
main steps
%% EX4 10 pts
% A) 5 pts | include 1 figure and comment
%B) 2 pts
% again find dE/dt using the chain rule and make substitutions
based on the
% differential equation. You should reach an expression for
dE/dt which is
% in terms of y'
%C) 3 pts | include one figure and comment
Exercise (1):
function LAB05ex1
3. m = 1; % mass [kg]
k = 9; % spring constant [N/m]
omega0=sqrt(k/m);
y0=0.4; v0=0; % initial conditions
[t,Y]=ode45(@f,[0,10],[y0,v0],[],omega0); % solve for 0<t<10
y=Y(:,1); v=Y(:,2); % retrieve y, v from Y
figure(1); plot(t,y,'b+-',t,v,'ro-'); % time series for y and v
grid on;
%------------------------------------------------------
function dYdt= f(t,Y,omega0)
y = Y(1); v= Y(2);
dYdt = [v; -omega0^2*y];
Exercise (1a):
function LAB05ex1a
m = 1; % mass [kg]
k = 9; % spring constant [N/m]
c = 1; % friction coefficient [Ns/m]
omega0 = sqrt(k/m); p = c/(2*m);
y0 = 0.4; v0 = 0; % initial conditions
[t,Y]=ode45(@f,[0,10],[y0,v0],[],omega0,p); % solve for
0<t<10
y=Y(:,1); v=Y(:,2); % retrieve y, v from Y
figure(1); plot(t,y,'b+-',t,v,'ro-'); % time series for y and v
grid on
%------------------------------------------------------
function dYdt= f(t,Y,omega0,p)
4. y = Y(1); v= Y(2);
dYdt = [v; ?? ]; % fill-in dv/dt
More instructions for the lab write-up:
1) You are not obligated to use the 'diary' function. It was
presented only for you convenience. You
should be copying and pasting your code, plots, and results
into some sort of "Word" type editor that
will allow you to import graphs and such. Make sure you
always include the commands to generate
what is been asked and include the outputs (from command
window and plots), unless the problem
says to suppress it.
2) Edit this document: there should be no code or MATLAB
commands that do not pertain to the
exercises you are presenting in your final submission. For
each exercise, only the relevant code that
performs the task should be included. Do not include error
messages. So once you have determined
either the command line instructions or the appropriate script
file that will perform the task you are
given for the exercise, you should only include that and the
associated output. Copy/paste these into
your final submission document followed by the output
(including plots) that these MATLAB
instructions generate.
3) All code, output and plots for an exercise are to be grouped
together. Do not put them in appendix, at
the end of the writeup, etc. In particular, put any mfiles you
write BEFORE you first call them.
Each exercise, as well as the part of the exercises, is to be
5. clearly demarked. Do not blend them all
together into some sort of composition style paper,
complimentary to this: do NOT double space.
You can have spacing that makes your lab report look nice,
but do not double space sections of text
as you would in a literature paper.
4) You can suppress much of the MATLAB output. If you need
to create a vector, "x = 0:0.1:10" for
example, for use, there is no need to include this as output in
your writeup. Just make sure you
include whatever result you are asked to show. Plots also do
not have to be a full, or even half page.
They just have to be large enough that the relevant structure
can be seen.
5) Before you put down any code, plots, etc. answer whatever
questions that the exercise asks first.
You will follow this with the results of your work that
support your answer.
SAMPLE QUESTION:
Exercise 1: Consider the function
f (x,C)=
sin(C x)
Cx
(a) Create a vector x with 100 elements from -3*pi to 3*pi.
Write f as an inline or anonymous function
and generate the vectors y1 = f(x,C1), y2 = f(x,C2) and y3 =
f(x,C3), where C1 = 1, C2 = 2 and
6. C3 = 3. Make sure you suppress the output of x and y's
vectors. Plot the function f (for the three
C's above), name the axis, give a title to the plot and include
a legend to identify the plots. Add a
grid to the plot.
(b) Without using inline or anonymous functions write a
function+function structure m-file that does
the same job as in part (a)
SAMPLE LAB WRITEUP:
MAT 275 MATLAB LAB 1
NAME: __________________________
LAB DAY and TIME:______________
Instructor: _______________________
Exercise 1
(a)
x = linspace(-3*pi,3*pi); % generating x vector - default value
for number
% of pts linspace is 100
f= @(x,C) sin(C*x)./(C*x) % C will be just a constant, no need
for ".*"
C1 = 1, C2 = 2, C3 = 3 % Using commans to separate commands
y1 = f(x,C1); y2 = f(x,C2); y3 = f(x,C3); % supressing the y's
plot(x,y1,'b.-', x,y2,'ro-', x,y3,'ks-') % using different markers
for
% black and white plots
xlabel('x'), ylabel('y') % labeling the axis
7. title('f(x,C) = sin(Cx)/(Cx)') % adding a title
legend('C = 1','C = 2','C = 3') % adding a legend
grid on
Command window output:
f =
@(x,C)sin(C*x)./(C*x)
C1 =
1
C2 =
2
C3 =
3
(b)
M-file of structure function+function
function ex1
x = linspace(-3*pi,3*pi); % generating x vector - default value
for number
% of pts linspace is 100
C1 = 1, C2 = 2, C3 = 3 % Using commans to separate commands
y1 = f(x,C1); y2 = f(x,C2); y3 = f(x,C3); % function f is defined
below
plot(x,y1,'b.-', x,y2,'ro-', x,y3,'ks-') % using different markers
8. for
% black and white plots
xlabel('x'), ylabel('y') % labeling the axis
title('f(x,C) = sin(Cx)/(Cx)') % adding a title
legend('C = 1','C = 2','C = 3') % adding a legend
grid on
end
function y = f(x,C)
y = sin(C*x)./(C*x);
end
Command window output:
C1 =
1
C2 =
2
C3 =
3
MATLAB sessions: Laboratory 5
MAT 275 Laboratory 5
The Mass-Spring System
In this laboratory we will examine harmonic oscillation. We
will model the motion of a mass-spring
9. system with differential equations.
Our objectives are as follows:
1. Determine the effect of parameters on the solutions of
differential equations.
2. Determine the behavior of the mass-spring system from the
graph of the solution.
3. Determine the effect of the parameters on the behavior of the
mass-spring.
The primary MATLAB command used is the ode45 function.
Mass-Spring System without Damping
The motion of a mass suspended to a vertical spring can be
described as follows. When the spring is
not loaded it has length `0 (situation (a)). When a mass m is
attached to its lower end it has length `
(situation (b)). From the first principle of mechanics we then
obtain
mg︸︷︷︸
downward weight force
+ −k(` − `0)︸ ︷︷ ︸
upward tension force
= 0. (L5.1)
The term g measures the gravitational acceleration (g ' 9.8m/s2 '
32ft/s2). The quantity k is a spring
constant measuring its stiffness. We now pull downwards on the
mass by an amount y and let the mass
10. go (situation (c)). We expect the mass to oscillate around the
position y = 0. The second principle of
mechanics yields
mg︸︷︷︸
weight
+ −k(` + y − `0)︸ ︷︷ ︸
upward tension force
= m
d2(` + y)
dt2︸ ︷︷ ︸
acceleration of mass
, i.e., m
d2y
dt2
+ ky = 0 (L5.2)
using (L5.1). This ODE is second-order.
(a) (b) (c) (d)
y
`
`0
m
k
12. [t,Y] = ode45(@f,[0,10],[y0,v0],[],omega0); % solve for 0<t<10
y = Y(:,1); v = Y(:,2); % retrieve y, v from Y
figure(1); plot(t,y,’b+-’,t,v,’ro-’); % time series for y and v
grid on;
%-----------------------------------------
function dYdt = f(t,Y,omega0)
y = Y(1); v = Y(2);
dYdt = [ v ; -omega0^2*y ];
Note that the parameter ω0 was passed as an argument to ode45
rather than set to its value ω0 = 3
directly in the function f. The advantage is that its value can
easily be changed in the driver part of the
program rather than in the function, for example when multiple
plots with different values of ω0 need
to be compared in a single MATLAB figure window.
0 1 2 3 4 5 6 7 8 9 10
-1.5
-1
-0.5
0
0.5
14. the magnify button , and by using the periodicity of the velocity
function.
(f) How does the size of the mass m and the stiffness k of the
spring affect the motion?
Support your answer first with a theoretical analysis on how ω0
– and therefore the period
of the oscillation – is related to m and k, and then graphically
by running LAB05ex1.m first
with m = 5 and k = 9 and then with m = 1 and k = 18. Include
the corresponding graphs.
2. The energy of the mass-spring system is given by the sum of
the potential energy and kinetic
energy. In absence of damping, the energy is conserved.
(a) Plot the quantity E = 1
2
mv2 + 1
2
ky2 as a function of time. What do you observe? (pay close
attention to the y-axis scale and, if necessary, use ylim to get a
better graph). Does the graph
confirm the fact that the energy is conserved?
(b) Show analytically that dE
dt
= 0.(Note that this proves that the energy is constant).
(c) Plot v vs y (phase plot). Does the curve ever get close to the
origin? Why or why not? What
does that mean for the mass-spring system?
15. Mass-Spring System with Damping
When the movement of the mass is damped due to viscous
effects (e.g., the mass moves in a cylinder
containing oil, situation (d)), an additional term proportional to
the velocity must be added. The
resulting equation becomes
m
d2y
dt2
+ c
dy
dt
+ ky = 0 or
d2y
dt2
+ 2p
dy
dt
+ ω20y = 0 (L5.4)
by setting p = c
2m
. The program LAB05ex1 is updated by modifying the function
f:
function LAB05ex1a
16. m = 1; % mass [kg]
k = 9; % spring constant [N/m]
c = 1; % friction coefficient [Ns/m]
omega0 = sqrt(k/m); p = c/(2*m);
y0 = 0.4; v0 = 0; % initial conditions
[t,Y] = ode45(@f,[0,10],[y0,v0],[],omega0,p); % solve for
0<t<10
y = Y(:,1); v = Y(:,2); % retrieve y, v from Y
figure(1); plot(t,y,’b+-’,t,v,’ro-’); % time series for y and v
grid on;
%-------------------------------------------
function dYdt = f(t,Y,omega0,p)
y = Y(1); v = Y(2);
dYdt = [ v ; ?? ]; % fill-in dv/dt
3. Fill in LAB05ex1a.m to reproduce Fig. L5b and then answer
the following questions.
(a) For what minimal time t1 will the mass-spring system
satisfy |y(t)| < 0.02 for all t > t1? You
can answer the question either by magnifying the MATLAB
figure using the magnify button
18. m(i)=max(abs(y(i:end)));
end
i = find(m<0.02); i = i(1);
disp([’|y|<0.02 for t>t1 with ’ num2str(t(i-1)) ’<t1<’
num2str(t(i))])
(b) What is the maximum (in magnitude) velocity attained by
the mass, and when is it attained?
Answer by using the magnify button and include the
corresponding picture.
(c) How does the size of c affect the motion? To support your
answer, run the file LAB05ex1.m
for c = 2, c = 6 and c = 10. Include the corresponding graphs
with a title indicating the
value of c used.
(d) Determine analytically the smallest (critical) value of c such
that no oscillation appears in
the solution.
4. (a) Plot the quantity E = 1
2
mv2 + 1
2
ky2 as a function of time. What do you observe? Is the
energy conserved in this case?
(b) Show analytically that dE
dt