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1. Dynamics & Control
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2. Problem 1 : Matrix creation with loop
i) Create a 5×5 matrix in which each element has a value equal to the sum of its row and column
numbers.
ii) Create a 5×5 matrix in which each element has a value equal to the square of the sum of the element’s
row and column numbers.
Solution:
(i) With nested for loops, control variables i and j indicates row number and column number respectively.
ai, j = i + j where i, j = 1, 2,L, 5

3. (ii) Similar to i), ai, j = (i + j )2 where i, j = 1, 2,L, 5

4. Problem 2 : Matrix creation with conditional
Make a one dimensional array that contains all integers in the range of 1 to 100 that are not divisible by 2, 3, and
7.
Solution:
Mod() function calculates reminder of division. (See mod() in help menu) Unless at least one of a number
modulo 2, 3, or 7 is zero, array contains this number.

5. Problem 3 : Velocity and acceleration profile calculation from the ball
trajectory
Use the same trajectory file, ‘ball.mat’ from the last homework. Time(t) and trajectory(x) are from the first
and the second columns, respectively. Write an m-file to calculate the ball’s velocity and acceleration in two
different ways. You should follow the below guidelines to make m-file.
Solution:

6. This neighboring point approach is the best to estimate instantaneous velocity and acceleration of ball if
trajectory was measured in the noise free environment. However, in the presence of noise, this approach is
bad since it is quite sensitive to noise or disturbance when you estimate instantaneous velocity and even more
sensitive in the estimate of instantaneous acceleration due to more noise propagation. To minimize noise
sensitivity, averaging data over several data points is recommended such as