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The document analyzes the motion of an inverted pendulum with an oscillating support. It uses Lagrangian mechanics to derive an equation of motion for the pendulum's angle θ. For small oscillations of θ, the equation is approximated as θ̈ + θaω2cos(ωt) - ω02 = 0, where a and ω are constants related to the support oscillation. If the support oscillation frequency ω is high enough, θ undergoes small oscillations correlated with cos(ωt), preventing the pendulum from falling over on average. The full motion of θ consists of these small oscillations modulated by an overall oscillation with frequency Ω related to ω and a.

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Jawaban soal-latihan1mekanika

1. The document provides solutions to 7 miscellaneous physics problems involving kinematics, dynamics, and rotational motion. The problems involve calculating quantities like angular speeds, forces, and times using principles like conservation of energy, angular momentum, and equations of motion. Complex algebraic and calculus solutions are shown.
2. Key steps involve setting up and solving equations derived from applying relevant physics principles to diagrams of the systems. Calculus techniques like differentiation and numerical integration are used.
3. Emphasis is placed on being able to instantly solve equations of the form f(x)=0 that arise, with references provided to resources on techniques like Newton-Raphson iteration.

Soal latihan1mekanika

The document contains 14 problems related to classical mechanics. Problem 1 describes two ladders leaning against two walls, with their intersection point 3 m above the ground, and asks for the distance between the walls. Problem 3 involves a pendulum whose length below a board can be varied, and asks the reader to show various relationships involving the semi-vertical angle, angular speed, and pendulum length are constant. Problem 4 describes a rod initially vertical on a table that is given an angular displacement and falls over, and asks for expressions involving the rod's angular speed, center speed, lower end speed, and the table's normal reaction.

Cycloidal pendulum

The shape of the limiting curve that eliminates the amplitude dependence of a pendulum's period is a cycloid. By deriving the equations of motion for a particle moving under gravity along a curved path, the document shows that the trajectory is a cycloid. Specifically, (1) the equation of motion along the curved path is the same as that of a simple pendulum if the path is a cycloid, (2) integrating the equations of motion yields parametric equations defining a cycloid, and (3) therefore, the limiting curve that gives a period independent of amplitude is the evolute of a cycloid.

Workshop presentations l_bworkshop_reis

The document discusses issues with pinning and facetting in lattice Boltzmann simulations of multiphase flows. It presents a lattice Boltzmann model for propagating sharp interfaces using a phase field approach. Sharpening the phase field interface causes it to become pinned to the lattice or develop facets. Introducing randomness via a random projection method or random threshold prevents pinning and delays facetting, allowing the interface to propagate at the correct speed even for very sharp boundaries.

The lattice Boltzmann equation: background, boundary conditions, and Burnett-...

An overview of the lattice Boltzmann equation and a discussion of moment-based boundary conditions. Includes applications to the slip flow regime and the Burnett stress. Some analysis sheds insight into the physical and numerical behaviour of the algorithm.

Pinning and facetting in multiphase LBMs

This document presents a stochastic sharpening approach for improving the pinning and facetting of sharp phase boundaries in lattice Boltzmann simulations. It summarizes that multiphase lattice Boltzmann models are prone to unphysical pinning and facetting of interfaces. By replacing the deterministic sharpening threshold with a random variable, the approach delays the onset of these issues and better predicts propagation speeds, even with very sharp boundaries. The random projection method preserves the shape of a propagating circular patch, unlike the standard LeVeque model which results in facetting and non-circular shapes at high sharpness ratios.

Understanding lattice Boltzmann boundary conditions through moments

This document provides an overview of the key points that will be covered in a lecture about understanding lattice Boltzmann boundary conditions through moments. The lecture will focus on connecting LB boundary conditions to LB distribution function moments. It will discuss interpreting other boundary condition methods in terms of moments and analyzing boundary condition accuracy, including for slip and no-slip flow conditions. The goal is to provide a clear perspective on LB boundary conditions and how to determine the appropriate conditions for different applications.

The lattice Boltzmann equation: background and boundary conditions

The document summarizes the lattice Boltzmann equation (LBE) method for computational fluid dynamics. It begins by discussing how the LBE is derived from kinetic theory and discrete kinetic theory, rather than directly from fluid equations. Taking moments of the discrete Boltzmann equation recovers the compressible Navier-Stokes equations through Chapman-Enskog expansion. The document then derives an analytic solution for the LBE governing Poiseuille flow between stationary walls under the influence of gravity.

Jawaban soal-latihan1mekanika

1. The document provides solutions to 7 miscellaneous physics problems involving kinematics, dynamics, and rotational motion. The problems involve calculating quantities like angular speeds, forces, and times using principles like conservation of energy, angular momentum, and equations of motion. Complex algebraic and calculus solutions are shown.
2. Key steps involve setting up and solving equations derived from applying relevant physics principles to diagrams of the systems. Calculus techniques like differentiation and numerical integration are used.
3. Emphasis is placed on being able to instantly solve equations of the form f(x)=0 that arise, with references provided to resources on techniques like Newton-Raphson iteration.

Soal latihan1mekanika

The document contains 14 problems related to classical mechanics. Problem 1 describes two ladders leaning against two walls, with their intersection point 3 m above the ground, and asks for the distance between the walls. Problem 3 involves a pendulum whose length below a board can be varied, and asks the reader to show various relationships involving the semi-vertical angle, angular speed, and pendulum length are constant. Problem 4 describes a rod initially vertical on a table that is given an angular displacement and falls over, and asks for expressions involving the rod's angular speed, center speed, lower end speed, and the table's normal reaction.

Cycloidal pendulum

The shape of the limiting curve that eliminates the amplitude dependence of a pendulum's period is a cycloid. By deriving the equations of motion for a particle moving under gravity along a curved path, the document shows that the trajectory is a cycloid. Specifically, (1) the equation of motion along the curved path is the same as that of a simple pendulum if the path is a cycloid, (2) integrating the equations of motion yields parametric equations defining a cycloid, and (3) therefore, the limiting curve that gives a period independent of amplitude is the evolute of a cycloid.

Workshop presentations l_bworkshop_reis

The document discusses issues with pinning and facetting in lattice Boltzmann simulations of multiphase flows. It presents a lattice Boltzmann model for propagating sharp interfaces using a phase field approach. Sharpening the phase field interface causes it to become pinned to the lattice or develop facets. Introducing randomness via a random projection method or random threshold prevents pinning and delays facetting, allowing the interface to propagate at the correct speed even for very sharp boundaries.

The lattice Boltzmann equation: background, boundary conditions, and Burnett-...

An overview of the lattice Boltzmann equation and a discussion of moment-based boundary conditions. Includes applications to the slip flow regime and the Burnett stress. Some analysis sheds insight into the physical and numerical behaviour of the algorithm.

Pinning and facetting in multiphase LBMs

This document presents a stochastic sharpening approach for improving the pinning and facetting of sharp phase boundaries in lattice Boltzmann simulations. It summarizes that multiphase lattice Boltzmann models are prone to unphysical pinning and facetting of interfaces. By replacing the deterministic sharpening threshold with a random variable, the approach delays the onset of these issues and better predicts propagation speeds, even with very sharp boundaries. The random projection method preserves the shape of a propagating circular patch, unlike the standard LeVeque model which results in facetting and non-circular shapes at high sharpness ratios.

Understanding lattice Boltzmann boundary conditions through moments

This document provides an overview of the key points that will be covered in a lecture about understanding lattice Boltzmann boundary conditions through moments. The lecture will focus on connecting LB boundary conditions to LB distribution function moments. It will discuss interpreting other boundary condition methods in terms of moments and analyzing boundary condition accuracy, including for slip and no-slip flow conditions. The goal is to provide a clear perspective on LB boundary conditions and how to determine the appropriate conditions for different applications.

The lattice Boltzmann equation: background and boundary conditions

The document summarizes the lattice Boltzmann equation (LBE) method for computational fluid dynamics. It begins by discussing how the LBE is derived from kinetic theory and discrete kinetic theory, rather than directly from fluid equations. Taking moments of the discrete Boltzmann equation recovers the compressible Navier-Stokes equations through Chapman-Enskog expansion. The document then derives an analytic solution for the LBE governing Poiseuille flow between stationary walls under the influence of gravity.

1 d wave equation

The one-dimensional wave equation governs vibrations of an elastic string. It is solved by separating variables, yielding solutions of the form F(x)G(t) where F and G satisfy ordinary differential equations. Boundary conditions require F(x) to be sinusoidal, with wavelengths that are integer multiples of the string length. The general solution is a superposition of these sinusoidal modes, with coefficients determined by the initial conditions. Motions of strings with different initial displacements are expressed as solutions to the one-dimensional wave equation.

Laplace equation

This document discusses techniques for calculating electric potential, including:
1. Laplace's equation and its solutions in 1D, 2D, and 3D, including boundary conditions.
2. The method of images, which uses fictitious "image" charges to solve problems involving conductors. The classical image problem and induced surface charge on a conductor are examined.
3. Other techniques like multipole expansion, separation of variables, and numerical methods like relaxation are mentioned but not explained in detail.

Plank sol

This document provides a solution to calculating the frequency of an oscillating plank on a log. It presents the Lagrangian of the system using polar coordinates and derives an expression for the time period of oscillation. For small angles, it shows the Euler-Lagrange equation can be expanded to the first order, resulting in a simple expression for the frequency as a function of the mass, length, and moment of inertia.

Introduction to Diffusion Monte Carlo

This document provides an introduction and overview of quantum Monte Carlo methods. It begins by reviewing the Metropolis algorithm and how it can be used to evaluate integrals and quantum mechanical operators. It then outlines the key topics which will be covered, including the path integral formulation of quantum mechanics, diffusion Monte Carlo, and calculating the one-body density matrix and excitation energies. The document proceeds to explain how the path integral formulation leads to the Schrodinger equation in the limit of small time steps, and how imaginary time evolution can be used to project out the ground state wavefunction. It concludes by providing examples of applying these methods to calculate properties of hydrogen, molecular hydrogen, and the one-body density matrix of silicon.

Mit2 092 f09_lec16

All of material inside is un-licence, kindly use it for educational only but please do not to commercialize it.
Based on 'ilman nafi'an, hopefully this file beneficially for you.
Thank you.

Applications of Differential Equations of First order and First Degree

The document describes how to calculate the time it takes for a population growing at 5% annually to double in size using a differential equation model. It is also solved to be 20loge2 years, or approximately 14 years. A second problem involves calculating the final temperature of liquid in an insulated cylindrical tank over 5 days using a heat transfer model. A third problem uses kinematics equations to find how far a drag racer will travel in 8 seconds if its speed increases by 40 feet per second each second.

Mit2 092 f09_lec05

All of material inside is un-licence, kindly use it for educational only but please do not to commercialize it.
Based on 'ilman nafi'an, hopefully this file beneficially for you.
Thank you.

Mit2 092 f09_lec15

All of material inside is un-licence, kindly use it for educational only but please do not to commercialize it.
Based on 'ilman nafi'an, hopefully this file beneficially for you.
Thank you.

Solucionario serway cap 3

Aqui esta lo que buscabamos Y ahora a trabajar!

Geodesic bh sqrd

This document discusses the derivation of geodesic equations in general relativity. It begins by defining the action for a particle as the integral of its proper time along its worldline. Taking variations of the action with respect to the particle's coordinates and proper time parameter results in the geodesic equation, which describes the particle's path through spacetime. The document shows that two different forms of the action lead to the same geodesic equation. This equation describes particles moving along the straightest possible paths in a curved spacetime.

Using blurred images to assess damage in bridge structures?

Faster trains and augmented traffic have significantly increased the number and amplitude of loading cycles experienced on a daily basis by composite steel-concrete bridges. This higher demand accelerates the occurrence of damage in the shear connectors between the two materials, which in turn can severely affect performance and reliability of these structures. The aim of this talk is to present the preliminary results of theoretical and experimental investigations undertaken to assess the feasibility of using the envelope of deflections and rotations induced by moving loads as a practical and cost-effective alternative to traditional methods of health monitoring for composite bridges. Both analytical and numerical formulations for this dynamic problem are presented and the results of a parametric study are discussed. A novel photogrammetric approach is also introduced, which allows identifying vibration patterns in civil engineering structures by analysing blurred targets in long-exposure digital images. The initial experimental validation of this approach is presented and further challenges are highlighted.

Trigo cheat sheet_reduced

1) This document provides a trigonometry cheat sheet with formulas and identities for tangent, cotangent, sine, cosine, and other trig functions.
2) It includes definitions, properties, and formulas related to right triangles, the unit circle, inverse trig functions, and laws of sines, cosines, and tangents.
3) Examples are provided to demonstrate how to use formulas like half-angle, double-angle, sum and difference, and cofunction identities as well as inverse trig functions and trigonometric equations.

Simple harmonic motion1

The document describes simple harmonic motion (SHM). Some key points:
1) SHM is motion where the acceleration is proportional to and directed towards the displacement from a fixed point.
2) Common examples include a vibrating tuning fork, weight on a spring, boy on a swing.
3) The motion can be defined by the force equation F = -kx, where k is the spring constant.
4) Kinematics equations for SHM include the position equation x = x0sin(ωt + φ) and related equations for velocity and acceleration.

I. Antoniadis - "Introduction to Supersymmetry" 2/2

1) The Supersymmetric Standard Model (SSM) extends the particle content of the Standard Model by introducing supersymmetric partners for each particle, called sparticles. This includes gluinos, winos, binos, squarks, sleptons, and higgsinos as sparticle counterparts to gluons, W/Z bosons, photons, quarks, leptons, and Higgs bosons.
2) The SSM Lagrangian contains additional terms beyond the Standard Model including gauge interactions between fermions and gauginos, quartic scalar interactions, and a superpotential with Yukawa-like couplings.
3) Spontaneous supersymmetry breaking is required to make sparticles heavy enough to have evaded detection

Linear integral equations

The document describes the method of successive approximations to solve linear integral equations of the second kind. It presents the iterative scheme which begins with an initial approximation go(s) and calculates successive approximations gn(s). If gn(s) converges uniformly to a limit g(s) as n approaches infinity, then g(s) is the solution.
The iterative scheme leads to the Neumann series representation of the solution. For the series to converge, the condition |A|B < 1 must be satisfied. The resolvent kernel f(s,t;A) is defined as the limit of the iterated kernels Km(s,t). Examples are provided to demonstrate solving integral equations using this method.

Ch06 4

The document discusses solving differential equations with discontinuous forcing functions through examples. It summarizes the solution process for two initial value problems (IVPs). The solutions are composed of three separate IVPs corresponding to different time intervals defined by the forcing function. Jump discontinuities in the forcing function result in corresponding jump discontinuities in the highest derivative of the solution.

I. Antoniadis - "Introduction to Supersymmetry" 1/2

Supersymmetry (SUSY) is a symmetry that relates bosonic and fermionic degrees of freedom. It extends the Poincaré algebra by including spinorial generators (supercharges) that transform bosonic fields into fermionic fields and vice versa. SUSY provides motivations like natural elementary scalars, gauge coupling unification, and a dark matter candidate. SUSY is formulated using superspace, which extends spacetime by Grassmann coordinates. Chiral and vector superfields contain the bosonic and fermionic components of supermultiplets and allow constructing SUSY invariant actions.

Ch10

1) The document discusses dynamics of rotational motion, including Newton's second law for rotation which states that torque equals the product of moment of inertia and angular acceleration.
2) It defines important rotational concepts like torque, angular momentum, moment of inertia, and establishes relationships between them using principles like conservation of energy and angular momentum.
3) Examples are provided to demonstrate applications of rotational dynamics like rolling motion without slipping, combined translation and rotation, gyroscopes and precession. Analogies between rotational and translational motions are also highlighted.

Fourier series

The document discusses Fourier series and two of its applications. It provides an overview of Fourier series, including its definition as an infinite series representation of periodic functions in terms of sine and cosine terms. It also discusses two key applications of Fourier series: (1) modeling forced oscillations, where a Fourier series is used to represent periodic forcing functions; and (2) solving the heat equation, where Fourier series are used to represent temperature distributions over time.

Sol56

1) The document proves Stirling's formula for N! through a series of steps including using integration by parts and Taylor series expansions. It shows that N! is approximately equal to NN e−N√2πN.
2) Higher order corrections of 1/N and 1/N^2 are then derived by keeping additional terms in the Taylor series expansions. This leads to the final form of Stirling's formula as N! ≈ NN e−N+1/12N√2πN, accurate to order 1/N^3.
3) The derivation makes use of known integrals of the form ∫−∞∞x^2ne^-ax^2dx to

Sol45

The document summarizes the physics of an object sliding down an inclined plane. It explains that the normal and friction forces acting on the object are equal in magnitude to the gravitational force down the plane. This causes the object's speed along the plane to decrease at the same rate as its speed down the plane increases. The document derives an equation showing the object's total velocity remains constant, and uses this to find the object's final speed down the plane is half its initial speed along the plane.

Sol47

This document summarizes the solution to a problem involving a sliding ladder losing contact with a wall. It finds that:
1) By assuming the ladder's center of mass moves in a circular path, the ladder loses contact when the horizontal speed of the center of mass starts decreasing, where the normal force would become negative.
2) Using conservation of energy equations, it is determined that this occurs when the angle between the ladder and wall reaches 48.2 degrees, independent of the ladder's distribution of mass.
3) The final horizontal speed of the center of mass as it loses contact is the square root of g/3.

1 d wave equation

The one-dimensional wave equation governs vibrations of an elastic string. It is solved by separating variables, yielding solutions of the form F(x)G(t) where F and G satisfy ordinary differential equations. Boundary conditions require F(x) to be sinusoidal, with wavelengths that are integer multiples of the string length. The general solution is a superposition of these sinusoidal modes, with coefficients determined by the initial conditions. Motions of strings with different initial displacements are expressed as solutions to the one-dimensional wave equation.

Laplace equation

This document discusses techniques for calculating electric potential, including:
1. Laplace's equation and its solutions in 1D, 2D, and 3D, including boundary conditions.
2. The method of images, which uses fictitious "image" charges to solve problems involving conductors. The classical image problem and induced surface charge on a conductor are examined.
3. Other techniques like multipole expansion, separation of variables, and numerical methods like relaxation are mentioned but not explained in detail.

Plank sol

This document provides a solution to calculating the frequency of an oscillating plank on a log. It presents the Lagrangian of the system using polar coordinates and derives an expression for the time period of oscillation. For small angles, it shows the Euler-Lagrange equation can be expanded to the first order, resulting in a simple expression for the frequency as a function of the mass, length, and moment of inertia.

Introduction to Diffusion Monte Carlo

This document provides an introduction and overview of quantum Monte Carlo methods. It begins by reviewing the Metropolis algorithm and how it can be used to evaluate integrals and quantum mechanical operators. It then outlines the key topics which will be covered, including the path integral formulation of quantum mechanics, diffusion Monte Carlo, and calculating the one-body density matrix and excitation energies. The document proceeds to explain how the path integral formulation leads to the Schrodinger equation in the limit of small time steps, and how imaginary time evolution can be used to project out the ground state wavefunction. It concludes by providing examples of applying these methods to calculate properties of hydrogen, molecular hydrogen, and the one-body density matrix of silicon.

Mit2 092 f09_lec16All of material inside is un-licence, kindly use it for educational only but please do not to commercialize it.
Based on 'ilman nafi'an, hopefully this file beneficially for you.
Thank you.

Applications of Differential Equations of First order and First Degree

The document describes how to calculate the time it takes for a population growing at 5% annually to double in size using a differential equation model. It is also solved to be 20loge2 years, or approximately 14 years. A second problem involves calculating the final temperature of liquid in an insulated cylindrical tank over 5 days using a heat transfer model. A third problem uses kinematics equations to find how far a drag racer will travel in 8 seconds if its speed increases by 40 feet per second each second.

Mit2 092 f09_lec05All of material inside is un-licence, kindly use it for educational only but please do not to commercialize it.
Based on 'ilman nafi'an, hopefully this file beneficially for you.
Thank you.

Mit2 092 f09_lec15All of material inside is un-licence, kindly use it for educational only but please do not to commercialize it.
Based on 'ilman nafi'an, hopefully this file beneficially for you.
Thank you.

Solucionario serway cap 3

Aqui esta lo que buscabamos Y ahora a trabajar!

Geodesic bh sqrd

This document discusses the derivation of geodesic equations in general relativity. It begins by defining the action for a particle as the integral of its proper time along its worldline. Taking variations of the action with respect to the particle's coordinates and proper time parameter results in the geodesic equation, which describes the particle's path through spacetime. The document shows that two different forms of the action lead to the same geodesic equation. This equation describes particles moving along the straightest possible paths in a curved spacetime.

Using blurred images to assess damage in bridge structures?

Faster trains and augmented traffic have significantly increased the number and amplitude of loading cycles experienced on a daily basis by composite steel-concrete bridges. This higher demand accelerates the occurrence of damage in the shear connectors between the two materials, which in turn can severely affect performance and reliability of these structures. The aim of this talk is to present the preliminary results of theoretical and experimental investigations undertaken to assess the feasibility of using the envelope of deflections and rotations induced by moving loads as a practical and cost-effective alternative to traditional methods of health monitoring for composite bridges. Both analytical and numerical formulations for this dynamic problem are presented and the results of a parametric study are discussed. A novel photogrammetric approach is also introduced, which allows identifying vibration patterns in civil engineering structures by analysing blurred targets in long-exposure digital images. The initial experimental validation of this approach is presented and further challenges are highlighted.

Trigo cheat sheet_reduced

1) This document provides a trigonometry cheat sheet with formulas and identities for tangent, cotangent, sine, cosine, and other trig functions.
2) It includes definitions, properties, and formulas related to right triangles, the unit circle, inverse trig functions, and laws of sines, cosines, and tangents.
3) Examples are provided to demonstrate how to use formulas like half-angle, double-angle, sum and difference, and cofunction identities as well as inverse trig functions and trigonometric equations.

Simple harmonic motion1

The document describes simple harmonic motion (SHM). Some key points:
1) SHM is motion where the acceleration is proportional to and directed towards the displacement from a fixed point.
2) Common examples include a vibrating tuning fork, weight on a spring, boy on a swing.
3) The motion can be defined by the force equation F = -kx, where k is the spring constant.
4) Kinematics equations for SHM include the position equation x = x0sin(ωt + φ) and related equations for velocity and acceleration.

I. Antoniadis - "Introduction to Supersymmetry" 2/2

1) The Supersymmetric Standard Model (SSM) extends the particle content of the Standard Model by introducing supersymmetric partners for each particle, called sparticles. This includes gluinos, winos, binos, squarks, sleptons, and higgsinos as sparticle counterparts to gluons, W/Z bosons, photons, quarks, leptons, and Higgs bosons.
2) The SSM Lagrangian contains additional terms beyond the Standard Model including gauge interactions between fermions and gauginos, quartic scalar interactions, and a superpotential with Yukawa-like couplings.
3) Spontaneous supersymmetry breaking is required to make sparticles heavy enough to have evaded detection

Linear integral equations

The document describes the method of successive approximations to solve linear integral equations of the second kind. It presents the iterative scheme which begins with an initial approximation go(s) and calculates successive approximations gn(s). If gn(s) converges uniformly to a limit g(s) as n approaches infinity, then g(s) is the solution.
The iterative scheme leads to the Neumann series representation of the solution. For the series to converge, the condition |A|B < 1 must be satisfied. The resolvent kernel f(s,t;A) is defined as the limit of the iterated kernels Km(s,t). Examples are provided to demonstrate solving integral equations using this method.

Ch06 4

The document discusses solving differential equations with discontinuous forcing functions through examples. It summarizes the solution process for two initial value problems (IVPs). The solutions are composed of three separate IVPs corresponding to different time intervals defined by the forcing function. Jump discontinuities in the forcing function result in corresponding jump discontinuities in the highest derivative of the solution.

I. Antoniadis - "Introduction to Supersymmetry" 1/2

Supersymmetry (SUSY) is a symmetry that relates bosonic and fermionic degrees of freedom. It extends the Poincaré algebra by including spinorial generators (supercharges) that transform bosonic fields into fermionic fields and vice versa. SUSY provides motivations like natural elementary scalars, gauge coupling unification, and a dark matter candidate. SUSY is formulated using superspace, which extends spacetime by Grassmann coordinates. Chiral and vector superfields contain the bosonic and fermionic components of supermultiplets and allow constructing SUSY invariant actions.

Ch10

1) The document discusses dynamics of rotational motion, including Newton's second law for rotation which states that torque equals the product of moment of inertia and angular acceleration.
2) It defines important rotational concepts like torque, angular momentum, moment of inertia, and establishes relationships between them using principles like conservation of energy and angular momentum.
3) Examples are provided to demonstrate applications of rotational dynamics like rolling motion without slipping, combined translation and rotation, gyroscopes and precession. Analogies between rotational and translational motions are also highlighted.

Fourier series

The document discusses Fourier series and two of its applications. It provides an overview of Fourier series, including its definition as an infinite series representation of periodic functions in terms of sine and cosine terms. It also discusses two key applications of Fourier series: (1) modeling forced oscillations, where a Fourier series is used to represent periodic forcing functions; and (2) solving the heat equation, where Fourier series are used to represent temperature distributions over time.

1 d wave equation

1 d wave equation

Laplace equation

Laplace equation

Plank sol

Plank sol

Introduction to Diffusion Monte Carlo

Introduction to Diffusion Monte Carlo

Mit2 092 f09_lec16

Mit2 092 f09_lec16

Applications of Differential Equations of First order and First Degree

Applications of Differential Equations of First order and First Degree

Mit2 092 f09_lec05

Mit2 092 f09_lec05

Mit2 092 f09_lec15

Mit2 092 f09_lec15

Solucionario serway cap 3

Solucionario serway cap 3

Geodesic bh sqrd

Geodesic bh sqrd

Using blurred images to assess damage in bridge structures?

Using blurred images to assess damage in bridge structures?

Trigo cheat sheet_reduced

Trigo cheat sheet_reduced

Simple harmonic motion1

Simple harmonic motion1

I. Antoniadis - "Introduction to Supersymmetry" 2/2

I. Antoniadis - "Introduction to Supersymmetry" 2/2

Linear integral equations

Linear integral equations

Ch06 4

Ch06 4

I. Antoniadis - "Introduction to Supersymmetry" 1/2

I. Antoniadis - "Introduction to Supersymmetry" 1/2

Ch10

Ch10

Fourier series

Fourier series

Sol56

1) The document proves Stirling's formula for N! through a series of steps including using integration by parts and Taylor series expansions. It shows that N! is approximately equal to NN e−N√2πN.
2) Higher order corrections of 1/N and 1/N^2 are then derived by keeping additional terms in the Taylor series expansions. This leads to the final form of Stirling's formula as N! ≈ NN e−N+1/12N√2πN, accurate to order 1/N^3.
3) The derivation makes use of known integrals of the form ∫−∞∞x^2ne^-ax^2dx to

Sol45

The document summarizes the physics of an object sliding down an inclined plane. It explains that the normal and friction forces acting on the object are equal in magnitude to the gravitational force down the plane. This causes the object's speed along the plane to decrease at the same rate as its speed down the plane increases. The document derives an equation showing the object's total velocity remains constant, and uses this to find the object's final speed down the plane is half its initial speed along the plane.

Sol47

This document summarizes the solution to a problem involving a sliding ladder losing contact with a wall. It finds that:
1) By assuming the ladder's center of mass moves in a circular path, the ladder loses contact when the horizontal speed of the center of mass starts decreasing, where the normal force would become negative.
2) Using conservation of energy equations, it is determined that this occurs when the angle between the ladder and wall reaches 48.2 degrees, independent of the ladder's distribution of mass.
3) The final horizontal speed of the center of mass as it loses contact is the square root of g/3.

Sol58

1) There is a goal to find an approximate expression for the probability of obtaining N + x heads in 2N coin flips when N is large.
2) Using Stirling's formula and Taylor expansions, the probability is shown to approximate a Gaussian distribution: P(x) ≈ e^-x^2/N/√πN.
3) This Gaussian approximation is only valid when x is on the order of √N or less; for larger x ∼ N^3/4, higher-order terms become important.

Sol66

After pulling one end of a noodle from a bowl of spaghetti, there is a 1/(2N-1) chance of forming a loop by selecting the other end of the same noodle. This process is repeated, resulting in an average total number of loops that grows very slowly with the number of noodles N. The average number of loops is approximately equal to 1/2 times the sum of the integer reciprocals up to 1/N, or (ln N)/2. A better approximation relates N to n, the number of loops expected, as N ≈ e2n-γ/4.

Sol60

1) The document presents two solutions for calculating the average number of cereal boxes that must be opened to collect all N different prizes.
2) The first solution derives an expression for the average number of boxes needed to obtain each subsequent prize, and sums these values to obtain an expression for the total average boxes of N(lnN + γ) for large N.
3) The second solution calculates the probability P(n) that the final prize is obtained on the nth box, and uses this to express the average total boxes as a sum involving P(n). Both solutions yield the same result.

Sol43

1) This document provides two solutions to finding the acceleration of masses in an infinite Atwood's machine system.
2) The first solution shows that the acceleration of each subsequent mass is half the acceleration of the mass above it, with the top mass experiencing an acceleration of g/2.
3) The second solution models the system as an iterative function that approaches a fixed point of 3m, equivalent to two masses of m and 3m over the top pulley, also yielding a top acceleration of g/2.

Sol54

The document summarizes the solution to a probability problem about two players rolling a die repeatedly until one player wins by rolling a higher number. It proves that the probability the first player loses, PL, is 1 - (1/N)^N, where N is the number of sides on the die. It shows this formula approaches 1 - 1/e ≈ 63.2% as N increases. For a standard 6-sided die, the probability the first player wins is approximately 66.5%. The solution breaks down the probability the first player wins into the individual probabilities of winning based on the first roll.

Criminalistica

El documento habla sobre la relación entre los avances científicos y técnicos y su utilización por la criminalística en la investigación de delitos. Explica que aunque la criminalística surgió a mediados del siglo XIX, no fue hasta el siglo XX que se conformó como una ciencia. Además, señala que disciplinas como la biología, química, física, medicina y matemática han enriquecido las opciones de estudio propias de la investigación criminalística.

Sol55

This document solves for the precessional motion of a symmetric top where the top part moves in a fixed circle around the z-axis. It derives an expression for the angular momentum L of the top and shows that precessional motion is only possible if the moment of inertia I3 about the z-axis is greater than the moment of inertia I about the x and y axes. Applying this condition to the specific top geometry derives an expression for the precession frequency Ω in terms of the physical parameters of the top.

Learn and Share event 25th February 2015 NCVO volunteering in care homes proj...

Learn and Share event 25th February 2015 NCVO volunteering in care homes proj...NCVO - National Council for Voluntary Organisations

The document summarizes findings from an evaluation of a volunteering in care homes project. Key findings include:
1) Volunteers provide benefits like more one-on-one interaction for residents, combating loneliness, and potential emotional and social impacts. However, the biggest impacts seem to come from regular, substantial long-term volunteer commitments.
2) While recruitment, selection and training of volunteers is generally satisfactory, ongoing volunteer management needs further development to maintain volunteers and maximize benefits.
3) There is significant variability across care homes and volunteers in terms of hours contributed. Developing the volunteers who contribute the most hours could help increase impacts.Sol57

This document summarizes the analysis of a beach ball being thrown upward and falling back down under the influence of both gravity and drag forces. It presents two methods for calculating the total time of flight. The first method derives expressions for the upward and downward times separately and adds them. The second method directly integrates the acceleration equation with respect to time over the full trajectory. Both methods show that the total time is shorter than if no drag were present, due to the ball reaching a lower maximum height and slower terminal velocity during descent.

resume_A Busel 3_23_15

Alex Busel seeks a full-time position in a fast-paced business environment utilizing strong customer service, communication, and team-building skills. He has 5 years of customer service experience and is proficient in Microsoft Office, Smartworks, iPro, SalesForce.com, and Forefield. He has held various roles including sales associate, brand ambassador, receiving/shipping associate, and grocery associate developing skills in customer relations, supply chain management, and team leadership.

Jurnal ilmiah hapalan shalat delisa

Dokumen tersebut merangkum penelitian tentang nilai-nilai yang tercermin dalam novel Hafalan Shalat Delisa karya Tere Liye. Penelitian ini menganalisis nilai-nilai yang terkait hubungan manusia dengan Tuhan, sesama manusia, dan alam sesuai metode sosiologi sastra. Hasilnya menunjukkan nilai-nilai seperti iman, ibadah, tolong menolong, dan kelestarian lingkungan.

Sol46

The document discusses the birthday problem and provides multiple solutions to calculate the probability that two people in a group have the same birthday.
The key points are:
1) Using an exact calculation, the probability of a match is 50% with a group of 23 people from among 365 days.
2) An approximate formula shows the number of people needed for a 50% probability scales as the square root of the number of days, matching the exact results.
3) The formula can be extended to calculate the number of people needed for probabilities other than 50% and for matches of more than two people.

Sol62

The document summarizes the solution to calculating the average leftover length of dental floss after cutting segments from two rolls until one runs out. It uses a binomial distribution to calculate the probability that the process ends with a given leftover length on one roll. Approximating the binomial coefficient using a Gaussian function allows simplifying the expression for the average leftover length to (2/√π)√Ld, where L is the initial total floss length and d is the segment length. So the average leftover amount is proportional to the geometric mean of the total length and segment length.

Sol40

1) The document describes a method for calculating the probability that candidate A's vote total is always greater than or equal to candidate B's vote total as votes are counted. It models the vote counting as paths on a lattice from the origin to the point (a,b) representing the final vote totals.
2) It proves that the number of "bad" paths that pass through the region where B's total is greater than A's is equal to a+b/b-1.
3) It then uses this to calculate the probability that A's total is always greater as 1 - the number of bad paths divided by the total number of paths, which equals 1 - b/(a+1).

Sol48

The document summarizes the solution to the hotel problem of maximizing the probability of choosing the cheapest hotel by selecting a random fraction x of the total hotels initially. It shows that:
1) The probability P(x) of selecting the cheapest hotel is equal to the sum of the probabilities of the highest ranked hotel in the first x being each hotel, weighted by the probability the better hotels are in the remaining 1-x fraction.
2) This can be expressed as P(x) = -x ln x, with the maximum probability of 1/e occurring when x = 1/e.
3) Therefore, the optimal strategy is to initially pass up 1/e ≈ 37%

Sol41

GMm/R^3 describes simple harmonic motion for an object in a gravity tunnel between the Earth's surfaces, with a period of 2π(R^3/GM). For a tunnel through the Earth, this gives a round trip time of approximately 84 minutes, with a one-way time of 42 minutes. Notably, this result is independent of the tunnel's location and could describe motion in a room-sized gravity tunnel.

Sol61

The document presents two solutions to the problem of a rope falling through a hole.
(1) Using conservation of energy, the final speed of the rope is calculated to be √gL.
(2) Applying Newton's second law F=ma to the length of rope hanging down, the acceleration is calculated to be g/3 and the final speed 2√(gL/3), which is smaller than the first solution.
Accounting for the added momentum from new sections of rope joining the moving part leads to a more accurate solution than using conservation of energy alone.

Sol56

Sol56

Sol45

Sol45

Sol47

Sol47

Sol58

Sol58

Sol66

Sol66

Sol60

Sol60

Sol43

Sol43

Sol54

Sol54

Criminalistica

Criminalistica

Sol55

Sol55

Learn and Share event 25th February 2015 NCVO volunteering in care homes proj...

Learn and Share event 25th February 2015 NCVO volunteering in care homes proj...

Sol57

Sol57

resume_A Busel 3_23_15

resume_A Busel 3_23_15

Jurnal ilmiah hapalan shalat delisa

Jurnal ilmiah hapalan shalat delisa

Sol46

Sol46

Sol62

Sol62

Sol40

Sol40

Sol48

Sol48

Sol41

Sol41

Sol61

Sol61

Ch03 9

1. Forced vibrations with damping are modeled by an equation of the form mü + γu̇ + ku = F0cos(ωt), where m is mass, γ is damping coefficient, k is spring constant, F0 and ω are the force amplitude and frequency.
2. The general solution has the form u(t) = uC(t) + U(t), where uC(t) is the transient solution and U(t) is the steady-state or forced response.
3. The amplitude R of the steady-state forced response depends on the driving frequency ω, with a maximum value of Rmax occurring at the resonant frequency ωmax, which is

Quantum pensil seimbang

The document calculates the maximum time a pencil can remain in apparent equilibrium when accounting for quantum and thermal effects.
For quantum effects, the calculation uses the Heisenberg uncertainty principle to determine the minimum possible initial conditions for the pencil's angle and angular velocity. This yields a maximum equilibrium time of about 3.47 seconds.
For thermal effects, the calculation uses the classical equipartition theorem to determine initial conditions based on temperature. This yields a maximum equilibrium time of about 1.95 seconds.
A general formula is presented that relates the maximum time to fundamental constants like plank's constant, Boltzmann's constant, and the system's energy corresponding to each degree of freedom.

MATLAB sessions Laboratory 6MAT 275 Laboratory 6Forced .docx

MATLAB sessions: Laboratory 6
MAT 275 Laboratory 6
Forced Equations and Resonance
In this laboratory we take a deeper look at second-order nonhomogeneous equations. We will concentrate
on equations with a periodic harmonic forcing term. This will lead to a study of the phenomenon known
as resonance. The equation we consider has the form
d2y
dt2
+ c
dy
dt
+ ω20y = cosωt. (L6.1)
This equation models the movement of a mass-spring system similar to the one described in Laboratory
5. The forcing term on the right-hand side of (L6.1) models a vibration, with amplitude 1 and frequency
ω (in radians per second = 12π rotation per second =
60
2π rotations per minute, or RPM) of the plate
holding the mass-spring system. All physical constants are assumed to be positive.
Let ω1 =
√
ω20 − c2/4. When c < 2ω0 the general solution of (L6.1) is
y(t) = e−
1
2 ct(c1 cos(ω1t) + c2 sin(ω1t)) + C cos (ωt− α) (L6.2)
with
C =
1√
(ω20 − ω2)
2
+ c2ω2
, (L6.3)
α =
⎧
⎨
⎩
arctan
(
cω
ω20−ω2
)
if ω0 > ω
π + arctan
(
cω
ω20−ω2
)
if ω0 < ω
(L6.4)
and c1 and c2 determined by the initial conditions. The first term in (L6.2) represents the complementary
solution, that is, the general solution to the homogeneous equation (independent of ω), while the second
term represents a particular solution of the full ODE.
Note that when c > 0 the first term vanishes for large t due to the decreasing exponential factor.
The solution then settles into a (forced) oscillation with amplitude C given by (L6.3). The objectives of
this laboratory are then to understand
1. the effect of the forcing term on the behavior of the solution for different values of ω, in particular
on the amplitude of the solution.
2. the phenomena of resonance and beats in the absence of friction.
The Amplitude of Forced Oscillations
We assume here that ω0 = 2 and c = 1 are fixed. Initial conditions are set to 0. For each value of ω, the
amplitude C can be obtained numerically by taking half the difference between the highs and the lows
of the solution computed with a MATLAB ODE solver after a sufficiently large time, as follows: (note
that in the M-file below we set ω = 1.4).
1 function LAB06ex1
2 omega0 = 2; c = 1; omega = 1.4;
3 param = [omega0,c,omega];
4 t0 = 0; y0 = 0; v0 = 0; Y0 = [y0;v0]; tf = 50;
5 options = odeset(’AbsTol’,1e-10,’RelTol’,1e-10);
6 [t,Y] = ode45(@f,[t0,tf],Y0,options,param);
7 y = Y(:,1); v = Y(:,2);
8 figure(1)
9 plot(t,y,’b-’); ylabel(’y’); grid on;
c⃝2011 Stefania Tracogna, SoMSS, ASU 1
MATLAB sessions: Laboratory 6
10 t1 = 25; i = find(t>t1);
11 C = (max(Y(i,1))-min(Y(i,1)))/2;
12 disp([’computed amplitude of forced oscillation = ’ num2str(C)]);
13 Ctheory = 1/sqrt((omega0^2-omega^2)^2+(c*omega)^2);
14 disp([’theoretical amplitude = ’ num2str(Ctheory)]);
15 %----------------------------------------------------------------
16 function dYdt = f(t,Y,param)
17 y = Y(1); v = Y(2);
18 omega0 = param(1); c = param(2); omega = param(3);
19 dYdt = [ v ; cos(omega ...

Solution a ph o 3

This document provides the solution to a physics problem involving a rail gun.
(1) The equations of motion for the rod on the rail are derived, showing that the acceleration depends on parameters like the current, magnetic field, and mass.
(2) Expressions are obtained for the velocity and time spent on the rail, as well as the time of flight over water.
(3) The total time is calculated involving integrals and shown to depend on the angle and width of the strait.
(4) Graphs are plotted of the total time and distance traveled on the rail as a function of angle to determine the allowed range of angles that satisfy the constraints.

Mit2 092 f09_lec20All of material inside is un-licence, kindly use it for educational only but please do not to commercialize it.
Based on 'ilman nafi'an, hopefully this file beneficially for you.
Thank you.

Ps02 cmth03 unit 1

This document defines and provides examples of curves and parametrized curves. It discusses regular and unit-speed curves. The key points are:
i) A parametrized curve is a continuous function from an interval to Rn. Examples of parametrized curves include ellipses, parabolas, and helices.
ii) A regular curve is one where the derivative of the parametrization is never zero. A unit-speed curve has a derivative of constant length 1.
iii) The arc-length of a curve is defined as the integral of the derivative of the parametrization. Any reparametrization of a regular curve is also regular. A curve has a unit-

Sect5 4

This document discusses various types of mechanical vibrations including undamped, underdamped, critically damped, and overdamped motion. It provides examples of solving differential equations describing simple harmonic motion under different damping conditions and applying the solutions to problems involving springs, pendulums, and other oscillating systems. Specific cases are worked through to determine characteristics like frequency, period, and damping behavior.

physics-of-vibration-and-waves-solutions-pain

1. This document contains solutions to problems from Chapter 1 of the textbook "The Physics of Vibrations and Waves".
2. It provides detailed calculations and explanations for problems related to simple harmonic motion, including determining restoring forces, stiffness, frequencies, and solving differential equations of motion.
3. Examples include a simple pendulum, a mass on a spring, and vibrations of strings, membranes, and gas columns.

Computer Controlled Systems (solutions manual). Astrom. 3rd edition 1997

This document contains solutions to problems in a textbook on computer-controlled systems. It provides solutions to problems from Chapter 2, which deals with modeling continuous systems as discrete-time systems using sampling. The document includes analytical solutions to several problems involving sampling continuous systems and determining the corresponding discrete-time models. It also contains the solutions presented in matrix form.

Anomalous Diffusion Through Homopolar Membrane: One-Dimensional Model_ Crimso...

Anomalous Diffusion Through Homopolar Membrane: One-Dimensional Model_ Crimso...Crimsonpublishers-Mechanicalengineering

Anomalous Diffusion Through Homopolar Membrane: One-Dimensional Model by Guilherme Garcia Gimenez and Adélcio C Oliveira* in Evolutions in Mechanical Engineering
Signals and Systems Assignment Help

I am Martina J. I am a Signals and Systems Assignment Expert at matlabassignmentexperts.com. I hold a Master's in Matlab, from the University of Maryland. I have been helping students with their assignments for the past 9 years. I solve assignments related to Signals and Systems.
Visit matlabassignmentexperts.com or email info@matlabassignmentexperts.com.
You can also call on +1 678 648 4277 for any assistance with Signals and Systems assignments.

Notes mech v

1) A mass attached to a spring can move up and down from its equilibrium position. Its movement is modeled by a differential equation that depends on factors like the mass, spring constant, damping, and any external forcing.
2) There are three types of behavior for damped systems without external forcing: underdamped systems oscillate with a decaying amplitude, critically damped systems do not oscillate and cross the equilibrium at most once, and overdamped systems do not oscillate and may or may not cross the equilibrium.
3) For an undamped system with external periodic forcing, the behavior depends on whether the forcing frequency matches the natural frequency. If they are different, the displacement takes the form of a

Automatic Calibration 3 D

The document describes an automatic calibration algorithm for a three-axis magnetic compass module. The algorithm has two stages:
1) The first stage characterizes the magnetic environment and corrects for distortions using an upper triangular soft iron matrix and hard iron offset vector. This makes the magnetometer measurements orthogonal and gain matched.
2) The second stage refines the soft iron matrix estimation by determining a rotation matrix to align the magnetometer coordinate system with the accelerometer coordinate system, improving heading accuracy. Given successful calibration, heading accuracies of 2 degrees or better can be achieved.

Get bebas redaman_2014

The document describes a problem involving a damped spring-mass system. It is determined that the system is underdamped with a damping ratio of 0.625. The damped natural frequency is calculated to be 1.561 rad/s. The displacement of the mass at time t=2s is calculated to be -0.01616m.

Sol71

This document provides the calculation of the maximum trajectory length of a ball thrown at an angle θ.
The trajectory length is derived as an integral function of θ involving the ball's initial velocity v, gravitational acceleration g, and trigonometric functions of θ.
Numerically solving the derivative of this function shows that the maximum trajectory length occurs at an angle of approximately 56.5 degrees.

Mit2 092 f09_lec18All of material inside is un-licence, kindly use it for educational only but please do not to commercialize it.
Based on 'ilman nafi'an, hopefully this file beneficially for you.
Thank you.

Kittel c. introduction to solid state physics 8 th edition - solution manual

1. The document discusses crystallographic planes and directions in a cube, the Miller indices of planes with respect to primitive axes, and the spacing between dots projected onto different planes of a crystal structure.
2. Key concepts from crystallography such as Miller indices, primitive lattice vectors, reciprocal lattice vectors, and the first Brillouin zone are defined. Calculations of interplanar spacing and lattice parameters are shown for simple cubic and face-centered cubic lattices.
3. Binding energies, cohesive energies, and equilibrium properties are calculated and compared for body-centered cubic and face-centered cubic crystal structures. Approximations made in describing crystal binding using Madelung energies and pair potentials are

Solucionario Mecácnica Clásica Goldstein

This document contains Homer Reid's solutions to problems from Goldstein's Classical Mechanics textbook. The first problem solved involves a radioactive nucleus decaying and emitting an electron and neutrino. The solution finds the direction and momentum of the recoiling nucleus. The next problems solved include deriving the escape velocity of Earth, the equation of motion for a rocket, relating kinetic energy to momentum for varying mass systems, and several other kinematic and constraint problems.

Gold1

This document contains Homer Reid's solutions to problems from Goldstein's Classical Mechanics textbook. The solutions covered include:
1) Finding the momentum and kinetic energy of a nucleus that decays by emitting an electron and neutrino.
2) Deriving the escape velocity of Earth from the conservation of energy.
3) Deriving an equation of motion for a vertically launched rocket where mass decreases over time.
4) Deriving equations relating kinetic energy to force and momentum for particles with constant and varying mass.
5) Deriving an expression for the distance of a center of mass from an origin.
6) Deriving constraint equations for a system of two wheels on an axle rolling without slipping

Gold1

- A disk of radius a rolls without slipping on a horizontal plane. The disk has a point mass m located at a distance l from its center along the radius.
- There are two non-holonomic constraint equations relating the angular velocity of the disk φ ̇ to the velocities of the center of mass and the point mass.
- There is also one holonomic constraint equation expressing the angle θ between the radius vector to the point mass and a fixed line in terms of φ and constants.

Ch03 9

Ch03 9

Quantum pensil seimbang

Quantum pensil seimbang

MATLAB sessions Laboratory 6MAT 275 Laboratory 6Forced .docx

MATLAB sessions Laboratory 6MAT 275 Laboratory 6Forced .docx

Solution a ph o 3

Solution a ph o 3

Mit2 092 f09_lec20

Mit2 092 f09_lec20

Ps02 cmth03 unit 1

Ps02 cmth03 unit 1

Sect5 4

Sect5 4

physics-of-vibration-and-waves-solutions-pain

physics-of-vibration-and-waves-solutions-pain

Computer Controlled Systems (solutions manual). Astrom. 3rd edition 1997

Computer Controlled Systems (solutions manual). Astrom. 3rd edition 1997

Anomalous Diffusion Through Homopolar Membrane: One-Dimensional Model_ Crimso...

Anomalous Diffusion Through Homopolar Membrane: One-Dimensional Model_ Crimso...

Signals and Systems Assignment Help

Signals and Systems Assignment Help

Notes mech v

Notes mech v

Automatic Calibration 3 D

Automatic Calibration 3 D

Get bebas redaman_2014

Get bebas redaman_2014

Sol71

Sol71

Mit2 092 f09_lec18

Mit2 092 f09_lec18

Kittel c. introduction to solid state physics 8 th edition - solution manual

Kittel c. introduction to solid state physics 8 th edition - solution manual

Solucionario Mecácnica Clásica Goldstein

Solucionario Mecácnica Clásica Goldstein

Gold1

Gold1

Gold1

Gold1

Up ppg daljab latihan soal-pgsd-set-2

Paragraf pertama membahas tentang Anisa, siswa terpandai di kelasnya yang humoris dan gemar membaca. Paragraf berikutnya membahas tentang kriteria bahan pembelajaran sastra untuk kelas rendah yaitu keterbacaan dan kesesuaian. Paragraf terakhir menjelaskan tentang struktur bahasa Indonesia baku yang ditunjukkan pada suatu kalimat contoh.

Soal utn plus kunci gurusd.net

Dokumen tersebut berisi soal-soal ujian untuk mengetahui tingkat pemahaman siswa tentang berbagai konsep pendidikan seperti teori belajar, strategi pembelajaran, penilaian hasil belajar, dan penerapan kurikulum 2013. Soal-soal tersebut mencakup 32 pertanyaan pilihan ganda.

Soal up sosial kepribadian pendidik 5

Teks tersebut berisi 17 pertanyaan mengenai situasi dan tanggapan yang tepat bagi seorang guru dalam berbagai kondisi. Ringkasannya adalah: Teks tersebut memberikan opsi-opsi tanggapan yang tepat bagi seorang guru dalam menghadapi berbagai situasi sehari-hari di sekolah seperti menangani konflik antar siswa, menilai prestasi belajar siswa, serta menjalankan tugas sebagai guru dan petugas tata tertib

Soal up sosial kepribadian pendidik 4

koleksi soal soal ppg 2019

Soal up sosial kepribadian pendidik 3

koleksi soal soal ppg 2019

Soal up sosial kepribadian pendidik 2

Teks tersebut membahas tentang kompetensi pedagogik, sosial, dan kepribadian yang harus dimiliki seorang guru. Beberapa poin penting yang diangkat antara lain terlibat aktif dalam perencanaan program sekolah, membantu peserta didik yang kurang mampu, serta mengutamakan keselamatan diri dan orang lain dalam menjalankan tugas.

Soal up sosial kepribadian pendidik 1

koleksi soal soal ppg 2019

Soal up akmal

Teks tersebut membahas berbagai soal tentang sosial dan kepribadian, model pembelajaran, penanganan masalah siswa, dan tugas seorang guru. Secara garis besar, teks tersebut memberikan saran agar guru dapat menangani berbagai situasi dengan bijak, adil, dan melibatkan semua pihak terkait.

Soal tkp serta kunci jawabannya

Teks tersebut berisi soal-soal untuk mengetahui sikap dan tanggapan seseorang dalam berbagai situasi. Soal-soal tersebut meliputi berbagai topik seperti tanggung jawab sebagai PNS, tanggapan terhadap kesalahan, kerjasama tim, dan kerahasiaan informasi.

Soal tes wawasan kebangsaan

Teks tersebut membahas mengenai kecenderungan wisatawan Indonesia untuk berlibur ke luar negeri daripada mengunjungi objek wisata di dalam negeri. Hal ini disebabkan oleh beberapa faktor seperti daya tarik objek wisata luar negeri, keterbatasan sarana transportasi dan fasilitas pariwisata di dalam negeri, serta mahalnya biaya. Teks ini juga menyebutkan peningkatan jumlah wisatawan Indonesia yang berkunjung ke luar neger

Soal sospri ukm ulang i 2017 1 (1)

1. Menggali informasi dari guru dan peserta didik secara terpisah. Kemudian, dengan kesepakatan bersama mengajak dialog keduanya agar keduanya dapat saling memahami.
2. Semua peserta didik dengan prestasi tinggi maupun rendah sama-sama memiliki kebutuhan untuk memelihara motivasi belajar mereka, tetapi bentuk dan strateginya yang berbeda.
3. Sudah menjadi kewajiban guru untuk mengatasi masalah belajar

Soal perkembangan kognitif peserta didik

Dokumen tersebut membahas mengenai perkembangan kognitif peserta didik, perkembangan sosial-emosional, perkembangan moral, kesulitan belajar siswa, teori belajar, dan perencanaan pelaksanaan pembelajaran. Dokumen ini memberikan penjelasan mengenai berbagai aspek perkembangan peserta didik dan prinsip-prinsip dasar dalam merencanakan dan melaksanakan pembelajaran.

Soal latihan utn pedagogik plpg 2017

Dokumen tersebut berisi soal latihan mengenai perkembangan kognitif, sosial-emosional, dan moral peserta didik. Juga membahas teori belajar, perencanaan pembelajaran, dan kesulitan belajar siswa. Terdiri dari 31 pertanyaan pilihan ganda.

Rekap soal kompetensi pedagogi

Dokumen tersebut berisi kumpulan soal tes formatif dan sumatif untuk mata pelajaran kompetensi pedagogi. Soal-soal tersebut mencakup pengertian pengukuran, penilaian, tes, dan evaluasi serta mata pelajaran lainnya seperti perencanaan pembelajaran, strategi pembelajaran, dan pengelolaan kelas.

Bank soal pedagogik terbaru 175 soal-v2

koleksi soal soal ppg 2019

Bank soal ppg

Buku ini berisi ringkasan singkat mengenai kisi-kisi soal Ujian Kompetensi Mahasiswa Pendidikan Profesi Guru (UKMPPG) Program Studi Pendidikan Guru Sekolah Dasar (PGSD) tahun 2017. Terdiri dari kisi-kisi soal untuk kompetensi pedagogik dan profesional mata ujian Bahasa Indonesia, Matematika, IPA, IPS, dan PPKn beserta indikator esensialnya.

Soal cpns-paket-17

latihan soal-soal cpns 2018

Soal cpns-paket-14

Dokumen tersebut berisi paket soal untuk tes kemampuan verbal, kuantitatif, dan logika yang terdiri dari 75 soal pilihan ganda. Soal meliputi materi seperti analogi, hitungan matematika, deret bilangan, persentase, dan logika.

Soal cpns-paket-13

latihan soal-soal cpns 2018

Soal cpns-paket-12

Teks tersebut merupakan soal tes yang terdiri dari 5 subtes yaitu: 1) Padanan kata, 2) Lawan kata, 3) Pemahaman wacana, 4) Deret angka, dan 5) Aritmetika dan konsep aljabar. Subtes tersebut berisi soal-soal pilihan ganda untuk mengetahui kemampuan verbal, kuantitatif, dan logika peserta ujian.

Up ppg daljab latihan soal-pgsd-set-2

Up ppg daljab latihan soal-pgsd-set-2

Soal utn plus kunci gurusd.net

Soal utn plus kunci gurusd.net

Soal up sosial kepribadian pendidik 5

Soal up sosial kepribadian pendidik 5

Soal up sosial kepribadian pendidik 4

Soal up sosial kepribadian pendidik 4

Soal up sosial kepribadian pendidik 3

Soal up sosial kepribadian pendidik 3

Soal up sosial kepribadian pendidik 2

Soal up sosial kepribadian pendidik 2

Soal up sosial kepribadian pendidik 1

Soal up sosial kepribadian pendidik 1

Soal up akmal

Soal up akmal

Soal tkp serta kunci jawabannya

Soal tkp serta kunci jawabannya

Soal tes wawasan kebangsaan

Soal tes wawasan kebangsaan

Soal sospri ukm ulang i 2017 1 (1)

Soal sospri ukm ulang i 2017 1 (1)

Soal perkembangan kognitif peserta didik

Soal perkembangan kognitif peserta didik

Soal latihan utn pedagogik plpg 2017

Soal latihan utn pedagogik plpg 2017

Rekap soal kompetensi pedagogi

Rekap soal kompetensi pedagogi

Bank soal pedagogik terbaru 175 soal-v2

Bank soal pedagogik terbaru 175 soal-v2

Bank soal ppg

Bank soal ppg

Soal cpns-paket-17

Soal cpns-paket-17

Soal cpns-paket-14

Soal cpns-paket-14

Soal cpns-paket-13

Soal cpns-paket-13

Soal cpns-paket-12

Soal cpns-paket-12

I Know Dino Trivia: Part 3. Test your dino knowledge

How much do you know about dinosaurs?

_7 OTT App Builders to Support the Development of Your Video Applications_.pdf

Due to their ability to produce engaging content more quickly, over-the-top (OTT) app builders have made the process of creating video applications more accessible. The invitation to explore these platforms emphasizes how over-the-top (OTT) applications hold the potential to transform digital entertainment.

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The way we consume television has evolved dramatically over the past decade. Internet Protocol Television (IPTV) has emerged as a popular alternative to traditional cable and satellite TV, offering a wide range of channels and on-demand content via the internet. In Ireland, IPTV is rapidly gaining traction, with Xtreame HDTV being one of the prominent providers in the market. This comprehensive guide will delve into everything you need to know about IPTV Ireland, focusing on Xtreame HDTV, its features, benefits, and how it is revolutionizing TV viewing for Irish audiences.

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Christian Louboutin is celebrated for his innovative approach to footwear design, marked by his trademark red soles. This in-depth look at his life and career explores the origins of his creativity, the milestones in his journey, and the impact of his work on the fashion industry. Learn how Louboutin's bold vision and dedication to excellence have made his brand synonymous with luxury and style.

Meet Dinah Mattingly – Larry Bird’s Partner in Life and Love

Get an intimate look at Dinah Mattingly’s life alongside NBA icon Larry Bird. From their humble beginnings to their life today, discover the love and partnership that have defined their relationship.

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Barbie Movie Review has gotten brilliant surveys for its fun and creative story. Coordinated by Greta Gerwig, it stars Margot Robbie as Barbie and Ryan Gosling as Insight. Critics adore its perky humor, dynamic visuals, and intelligent take on the notorious doll's world. It's lauded for being engaging for both kids and grown-ups. The Astras profoundly prescribes observing the Barbie Review for a delightful and colorful cinematic involvement.https://theastras.com/hca-member-gradebooks/hca-gradebook-barbie/

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Emcee Subbu_ My emcee profile till 2024 June

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The teleprotection market size has grown
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The Evolution of the Leonardo DiCaprio Haircut: A Journey Through Style and C...

Leonardo DiCaprio, a name synonymous with Hollywood stardom and acting excellence. has captivated audiences for decades with his talent and charisma. But, the Leonardo DiCaprio haircut is one aspect of his public persona that has garnered attention. From his early days as a teenage heartthrob to his current status as a seasoned actor and environmental activist. DiCaprio's hairstyles have evolved. reflecting both his personal growth and the changing trends in fashion. This article delves into the many phases of the Leonardo DiCaprio haircut. exploring its significance and impact on pop culture.

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At Digidev, we are working to be the leader in interactive streaming platforms of choice by smart device users worldwide.
Our goal is to become the ultimate distribution service of entertainment content. The Digidev application will offer the next generation television highway for users to discover and engage in a variety of content. While also providing a fresh and
innovative approach towards advertainment with vast revenue opportunities. Designed and developed by Joe Q. Bretz

Orpah Winfrey Dwayne Johnson: Titans of Influence and Inspiration

Introduction
In the realm of entertainment, few names resonate as Orpah Winfrey Dwayne Johnson. Both figures have carved unique paths in the industry. achieving unparalleled success and becoming iconic symbols of perseverance, resilience, and inspiration. This article delves into the lives, careers. and enduring legacies of Orpah Winfrey Dwayne Johnson. exploring how their journeys intersect and what we can learn from their remarkable stories.
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Early Life and Backgrounds
Orpah Winfrey: From Humble Beginnings to Media Mogul
Orpah Winfrey, often known as Oprah due to a misspelling on her birth certificate. was born on January 29, 1954, in Kosciusko, Mississippi. Raised in poverty by her grandmother, Winfrey's early life was marked by hardship and adversity. Despite these challenges. she demonstrated a keen intellect and an early talent for public speaking.
Winfrey's journey to success began with a scholarship to Tennessee State University. where she studied communication. Her first job in media was as a co-anchor for the local evening news in Nashville. This role paved the way for her eventual transition to talk show hosting. where she found her true calling.
Dwayne Johnson: From Wrestling Royalty to Hollywood Superstar
Dwayne Johnson, also known by his ring name "The Rock," was born on May 2, 1972, in Hayward, California. He comes from a family of professional wrestlers, with both his father, Rocky Johnson. and his grandfather, Peter Maivia, being notable figures in the wrestling world. Johnson's early life was spent moving between New Zealand and the United States. experiencing a variety of cultural influences.
Before entering the world of professional wrestling. Johnson had aspirations of becoming a professional football player. He played college football at the University of Miami. where he was part of a national championship team. But, injuries curtailed his football career, leading him to follow in his family's footsteps and enter the wrestling ring.
Career Milestones
Orpah Winfrey: The Queen of All Media
Winfrey's career breakthrough came in 1986 when she launched "The Oprah Winfrey Show." The show became a cultural phenomenon. drawing millions of viewers daily and earning many awards. Winfrey's empathetic and candid interviewing style resonated with audiences. helping her tackle diverse and often challenging topics.
Beyond her talk show, Winfrey expanded her empire to include the creation of Harpo Productions. a multimedia production company. She also launched "O, The Oprah Magazine" and OWN: Oprah Winfrey Network, further solidifying her status as a media mogul.
Dwayne Johnson: From The Ring to The Big Screen
Dwayne Johnson's wrestling career took off in the late 1990s. when he became one of the most charismatic and popular figures in WWE. His larger-than-life persona and catchphrases endeared him to fans. making him a household name. But, Johnson had ambitions beyond the wrestling ring.
In the early 20

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留信网认证的作用:
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4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
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Unveiling Paul Haggis Shaping Cinema Through Diversity. .pdf

Paul Haggis is undoubtedly a visionary filmmaker whose work has not only shaped cinema but has also pushed boundaries when it comes to diversity and representation within the industry. From his thought-provoking scripts to his engaging directorial style, Haggis has become a prominent figure in the world of film.

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Slide criativo e muito lindo, apenas editar, muito simples

Authenticity in Motion Pictures: How Steve Greisen Retains Real Stories

Learn about Steve Greisen's dedication to capture the spirit of his subjects in his documentaries with honesty and integrity.

From Swing Music to Big Band Fame_ 5 Iconic Artists.pptx

Know about the five famous artists who have transitioned to Big Band Music from Swing Music. Here is a glimpse of their work and contributions.

I Know Dino Trivia: Part 3. Test your dino knowledge

I Know Dino Trivia: Part 3. Test your dino knowledge

_7 OTT App Builders to Support the Development of Your Video Applications_.pdf

_7 OTT App Builders to Support the Development of Your Video Applications_.pdf

Everything You Need to Know About IPTV Ireland.pdf

Everything You Need to Know About IPTV Ireland.pdf

Modern Radio Frequency Access Control Systems: The Key to Efficiency and Safety

Modern Radio Frequency Access Control Systems: The Key to Efficiency and Safety

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定制(uow毕业证书)卧龙岗大学毕业证文凭学位证书原版一模一样

Christian Louboutin: Innovating with Red Soles

Christian Louboutin: Innovating with Red Soles

Meet Dinah Mattingly – Larry Bird’s Partner in Life and Love

Meet Dinah Mattingly – Larry Bird’s Partner in Life and Love

Barbie Movie Review - The Astras.pdfffff

Barbie Movie Review - The Astras.pdfffff

原版制作(Mercer毕业证书)摩斯大学毕业证在读证明一模一样

原版制作(Mercer毕业证书)摩斯大学毕业证在读证明一模一样

Emcee Profile_ Subbu from Bangalore .pdf

Emcee Profile_ Subbu from Bangalore .pdf

240529_Teleprotection Global Market Report 2024.pdf

240529_Teleprotection Global Market Report 2024.pdf

The Evolution of the Leonardo DiCaprio Haircut: A Journey Through Style and C...

The Evolution of the Leonardo DiCaprio Haircut: A Journey Through Style and C...

DIGIDEVTV A New area of OTT Distribution

DIGIDEVTV A New area of OTT Distribution

Orpah Winfrey Dwayne Johnson: Titans of Influence and Inspiration

Orpah Winfrey Dwayne Johnson: Titans of Influence and Inspiration

高仿(nyu毕业证书)美国纽约大学毕业证文凭毕业证原版一模一样

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Unveiling Paul Haggis Shaping Cinema Through Diversity. .pdf

Unveiling Paul Haggis Shaping Cinema Through Diversity. .pdf

Divertidamente SLIDE muito lindo e criativo, pptx

Divertidamente SLIDE muito lindo e criativo, pptx

Authenticity in Motion Pictures: How Steve Greisen Retains Real Stories

Authenticity in Motion Pictures: How Steve Greisen Retains Real Stories

From Swing Music to Big Band Fame_ 5 Iconic Artists.pptx

From Swing Music to Big Band Fame_ 5 Iconic Artists.pptx

- 1. Solution Week 67 (12/22/03) Inverted pendulum Let θ be deﬁned as shown below. We’ll use the Lagrangian method to determine the equation of motion for θ. θ l m y(t) With y(t) = A cos(ωt), the position of the mass m is given by (X, Y ) = ( sin θ, y + cos θ). (1) Taking the derivatives of these coordinates, we see that the square of the speed is V 2 = ˙X2 + ˙Y 2 = 2 ˙θ2 + ˙y2 − 2 ˙y ˙θ sin θ. (2) The Lagrangian is therefore L = K − U = 1 2 m( 2 ˙θ2 + ˙y2 − 2 ˙y ˙θ sin θ) − mg(y + cos θ). (3) The equation of motion for θ is d dt ∂L ∂ ˙θ = ∂L ∂θ =⇒ ¨θ − ¨y sin θ = g sin θ. (4) Plugging in the explicit form of y(t), we have ¨θ + sin θ Aω2 cos(ωt) − g = 0. (5) In retrospect, this makes sense. Someone in the reference frame of the support, which has acceleration ¨y = −Aω2 cos(ωt), may as well be living in a world where the acceleration from gravity is g − Aω2 cos(ωt) downward. Eq. (5) is simply the F = ma equation in the tangential direction in this accelerated frame. Assuming θ is small, we may set sin θ ≈ θ, which gives ¨θ + θ aω2 cos(ωt) − ω2 0 = 0, (6) where ω0 ≡ g/ , and a ≡ A/ . Eq. (6) cannot be solved exactly, but we can still get a good idea of how θ depends on time. We can do this both numerically and (approximately) analytically. The ﬁgures below show how θ depends on time for parameters with values = 1 m, A = 0.1 m, and g = 10 m/s2 (so a = 0.1, and ω2 0 = 10 s−2). In the ﬁrst plot, ω = 10 s−1. And in the second plot, ω = 100 s−1. The stick falls over in ﬁrst case, but undergoes oscillatory motion in the second case. Apparently, if ω is large enough the stick will not fall over. 1
- 2. 0.2 0.4 0.6 0.8 1 1.2 1.4 t 0.1 0.05 0.05 0.1 theta 0.2 0.4 0.6 0.8 1 1.2 1.4 t 0.25 0.5 0.75 1 1.25 1.5 1.75 theta Let’s now explain this phenomenon analytically. At ﬁrst glance, it’s rather sur- prising that the stick stays up. It seems like the average (over a few periods of the ω oscillations) of the tangential acceleration in eq. (6), namely −θ(aω2 cos(ωt) − ω2 0), equals the positive quantity θω2 0, because the cos(ωt) term averages to zero (or so it appears). So you might think that there is a net force making θ increase, causing the stick fall over. The fallacy in this reasoning is that the average of the −aω2θ cos(ωt) term is not zero, because θ undergoes tiny oscillations with frequency ω, as seen below. Both of these plots have a = 0.005, ω2 0 = 10 s−2, and ω = 1000 s−1 (we’ll work with small a and large ω from now on; more on this below). The second plot is a zoomed-in version of the ﬁrst one near t = 0. 2 4 6 8 t 0.1 0.05 0.05 0.1 theta 0.02 0.04 0.06 0.08 0.1 t 0.098 0.0985 0.099 0.0995 theta The important point here is that the tiny oscillations in θ shown in the second plot are correlated with cos(ωt). It turns out that the θ value at the t where cos(ωt) = 1 is larger than the θ value at the t where cos(ωt) = −1. So there is a net negative contribution to the −aω2θ cos(ωt) part of the acceleration. And it may indeed be large enough to keep the pendulum up, as we will now show. To get a handle on the −aω2θ cos(ωt) term, let’s work in the approximation where ω is large and a ≡ A/ is small. More precisely, we will assume a 1 and aω2 ω2 0, for reasons we will explain below. Look at one of the little oscillations in the second of the above plots. These oscillations have frequency ω, because they are due simply to the support moving up and down. When the support moves up, θ increases; and when the support moves down, θ decreases. Since the average position of the pendulum doesn’t change much over one of these small periods, we can look for an approximate solution to eq. (6) of the form θ(t) ≈ C + b cos(ωt), (7) 2
- 3. where b C. C will change over time, but on the scale of 1/ω it is essentially constant, if a ≡ A/ is small enough. Plugging this guess for θ into eq. (6), and using a 1 and aω2 ω2 0, we ﬁnd that −bω2 cos(ωt) + Caω2 cos(ωt) = 0, to leading order.1 So we must have b = aC. Our approximate solution for θ is therefore θ ≈ C 1 + a cos(ωt) . (8) Let’s now determine how C gradually changes with time. From eq. (6), the average acceleration of θ, over a period T = 2π/ω, is ¨θ = −θ aω2 cos(ωt) − ω2 0 ≈ −C 1 + a cos(ωt) aω2 cos(ωt) − ω2 0 = −C a2 ω2 cos2(ωt) − ω2 0 = −C a2ω2 2 − ω2 0 ≡ −CΩ2 , (9) where Ω = a2ω2 2 − g . (10) But if we take two derivatives of eq. (7), we see that ¨θ simply equals ¨C. Equating this value of ¨θ with the one in eq. (9) gives ¨C(t) + Ω2 C(t) ≈ 0. (11) This equation describes nice simple-harmonic motion. Therefore, C oscillates sinu- soidally with the frequency Ω given in eq. (10). This is the overall back and forth motion seen in the ﬁrst of the above plots. Note that we must have aω > √ 2ω0 if this frequency is to be real so that the pendulum stays up. Since we have assumed a 1, we see that a2ω2 > 2ω2 0 implies aω2 ω2 0, which is consistent with our initial assumption above. If aω ω0, then eq. (10) gives Ω ≈ aω/ √ 2. Such is the case if we change the setup and simply have the pendulum lie ﬂat on a horizontal table where the acceleration from gravity is zero. In this limit where g is irrelevant, dimensional analysis implies that the frequency of the C oscillations must be a multiple of ω, because ω is the only quantity in the problem with units of frequency. It just so happens that the multiple is a/ √ 2. 1 The reasons for the a 1 and aω2 ω2 0 qualiﬁcations are the following. If aω2 ω2 0, then the aω2 cos(ωt) term dominates the ω2 0 term in eq. (6). The one exception to this is when cos(ωt) ≈ 0, but this occurs for a negligibly small amount of time if aω2 ω2 0. If a 1, then we can legally ignore the ¨C term when eq. (7) is substituted into eq. (6). We will ﬁnd below, in eq. (9), that our assumptions lead to ¨C being roughly proportional to a2 ω2 . Since the other terms in eq. (6) are proportional to aω2 , we need a 1 in order for the ¨C term to be negligible. In short, a 1 is the condition under which C varies slowly on the time scale of 1/ω. 3