# Browsing Animations: Oscillations

### damped-1.iwp

The blue line plots position (vertical) as a function of time (horizontal) for damped SHM. The red line plots the decay of the amplitude.

### damped-SHM-template.iwp

This plots position (vertical) as a function of time (horizontal) for an object subject to a Hooke's Law restoring force. Suppose that the object is also subject to a force that always acts opposite the velocity, v, and is proportional to the magnitude of v. If the constant of proportionality is denoted R, then this damping force is -Rv. Modify the applet to display the motion of the object by doing the following: 1. Create a new input for R. Give R an initial value of 0. 2. Modify the equation for the object's y-acceleration to include a term that accounts for the damping. 3. Run the applet. Make sure it still runs correctly for the undamped case, R = 0. 4. Investigate the motion for different values of R (say 1, 5, 10, 20).

### lissajous-figures.iwp

An object is subject to independent restoring forces along the x- and y-axes. It's like being pulled on by springs along both axes simultaneously. Do the following. a. Change one input in order to make the object's path elliptical. In general, what must be true to produce an elliptical path? b. Restore the object to a circular path. Then change one input to make the object move in a straight, diagonal line with slope = 1 or -1. In general, what must be true to produce a diagonal line? c. Restore the object to a circular path. Then change one input to make the object move in a figure-8 path. Change the input to a different value in order to obtain a path with 4 closed loops. In general, what conditions are required to obtain a path with and integer number n of closed loops? The figures that you're generating are called Lissajous figures. They have value in electronics for precise comparison of frequencies.

### damped-SHM-template.iwp

This plots position (vertical) as a function of time (horizontal) for an object subject to a Hooke's Law restoring force. Suppose that the object is also subject to a force that always acts opposite the velocity, v, and is proportional to the magnitude of v. If the constant of proportionality is denoted R, then this damping force is -Rv. Modify the applet to display the motion of the object by doing the following: 1. Create a new input for R. Give R an initial value of 0. 2. Modify the equation for the object's y-acceleration to include a term that accounts for the damping. 3. Run the applet. Make sure it still runs correctly for the undamped case, R = 0. 4. Investigate the motion for different values of R (say 1, 5, 10, 20).

### lissajous-figures.iwp

An object is subject to independent restoring forces along the x- and y-axes. It's like being pulled on by springs along both axes simultaneously. Do the following. a. Change one input in order to make the object's path elliptical. In general, what must be true to produce an elliptical path? b. Restore the object to a circular path. Then change one input to make the object move in a straight, diagonal line with slope = 1 or -1. In general, what must be true to produce a diagonal line? c. Restore the object to a circular path. Then change one input to make the object move in a figure-8 path. Change the input to a different value in order to obtain a path with 4 closed loops. In general, what conditions are required to obtain a path with and integer number n of closed loops? The figures that you're generating are called Lissajous figures. They have value in electronics for precise comparison of frequencies.

### pendulum01.iwp

A pendulum is released from rest and oscillates in a vertical plane. The angle of release, mass of the bob, gravitational field, and length of the string can be adjusted. At large angles, the applet may show unphysical behavior.

### lissajous-figures.iwp

An object is subject to independent restoring forces along the x- and y-axes. It's like being pulled on by springs along both axes simultaneously. Do the following. a. Change one input in order to make the object's path elliptical. In general, what must be true to produce an elliptical path? b. Restore the object to a circular path. Then change one input to make the object move in a straight, diagonal line with slope = 1 or -1. In general, what must be true to produce a diagonal line? c. Restore the object to a circular path. Then change one input to make the object move in a figure-8 path. Change the input to a different value in order to obtain a path with 4 closed loops. In general, what conditions are required to obtain a path with and integer number n of closed loops? The figures that you're generating are called Lissajous figures. They have value in electronics for precise comparison of frequencies.

### pendulum01.iwp

A pendulum is released from rest and oscillates in a vertical plane. The angle of release, mass of the bob, gravitational field, and length of the string can be adjusted. At large angles, the applet may show unphysical behavior.

### shm-01.iwp

A ball is attached to a horizontal spring (not shown) which causes the ball to oscillate about the origin. Run the animation until it stops. Click on Show graph. Which graph represents position vs. time? How do you know? Which graph represents velocity vs. time? How do you know? Which graph represents acceleration vs. time? How do you know? What would a graph of net force on the ball vs. time look like? Why?

### pendulum01.iwp

A pendulum is released from rest and oscillates in a vertical plane. The angle of release, mass of the bob, gravitational field, and length of the string can be adjusted. At large angles, the applet may show unphysical behavior.

### shm-01.iwp

A ball is attached to a horizontal spring (not shown) which causes the ball to oscillate about the origin. Run the animation until it stops. Click on Show graph. Which graph represents position vs. time? How do you know? Which graph represents velocity vs. time? How do you know? Which graph represents acceleration vs. time? How do you know? What would a graph of net force on the ball vs. time look like? Why?

### shm-02.iwp

A ball is attached to a horizontal spring (not shown) which causes the ball to oscillate about the origin. Run the animation. Note that values of time, position, velocity, and acceleration appear above the play buttons. When the animation stops, click on Show graph to display graphs of position, velocity, and acceleration as a function of time.

### shm-01.iwp

A ball is attached to a horizontal spring (not shown) which causes the ball to oscillate about the origin. Run the animation until it stops. Click on Show graph. Which graph represents position vs. time? How do you know? Which graph represents velocity vs. time? How do you know? Which graph represents acceleration vs. time? How do you know? What would a graph of net force on the ball vs. time look like? Why?

### shm-02.iwp

A ball is attached to a horizontal spring (not shown) which causes the ball to oscillate about the origin. Run the animation. Note that values of time, position, velocity, and acceleration appear above the play buttons. When the animation stops, click on Show graph to display graphs of position, velocity, and acceleration as a function of time.

### shm-circle-analogy-01.iwp

Demonstration of the circular motion analogy for simple harmonic motion

### shm-02.iwp

A ball is attached to a horizontal spring (not shown) which causes the ball to oscillate about the origin. Run the animation. Note that values of time, position, velocity, and acceleration appear above the play buttons. When the animation stops, click on Show graph to display graphs of position, velocity, and acceleration as a function of time.

### shm-circle-analogy-01.iwp

Demonstration of the circular motion analogy for simple harmonic motion

### shm-compare-01.iwp

1. Two objects of equal mass oscillate independently in SHM about the origin. Find ratios of each of the following (blue/red): a. amplitude b. period c. spring constant d. total energy 2. The two objects are initially in phase. After how many cycles of the blue object will both objects be in phase again?

### shm-circle-analogy-01.iwp

Demonstration of the circular motion analogy for simple harmonic motion

### shm-compare-01.iwp

1. Two objects of equal mass oscillate independently in SHM about the origin. Find ratios of each of the following (blue/red): a. amplitude b. period c. spring constant d. total energy 2. The two objects are initially in phase. After how many cycles of the blue object will both objects be in phase again?

### shm-compare-template.iwp

The blue and red objects oscillate in SHM.

### shm-compare-01.iwp

1. Two objects of equal mass oscillate independently in SHM about the origin. Find ratios of each of the following (blue/red): a. amplitude b. period c. spring constant d. total energy 2. The two objects are initially in phase. After how many cycles of the blue object will both objects be in phase again?

### shm-compare-template.iwp

The blue and red objects oscillate in SHM.

### shm-graph-01.iwp

Run the applet to display a position vs. time graph of an object in simple harmonic motion. By entering a value of phase other than 0, a second graph will appear shifted in phase by the amount of the adjustment.

### shm-compare-template.iwp

The blue and red objects oscillate in SHM.

### shm-graph-01.iwp

Run the applet to display a position vs. time graph of an object in simple harmonic motion. By entering a value of phase other than 0, a second graph will appear shifted in phase by the amount of the adjustment.

### shm-graph-02.iwp

Run the applet to display a position vs. time graph of an object in simple harmonic motion.

### shm-graph-01.iwp

Run the applet to display a position vs. time graph of an object in simple harmonic motion. By entering a value of phase other than 0, a second graph will appear shifted in phase by the amount of the adjustment.

### shm-graph-02.iwp

Run the applet to display a position vs. time graph of an object in simple harmonic motion.

### shm-phase-01.iwp

The red and blue objects have the same mass and oscillate in SHM with the same period and amplitude. The only thing different is the phase. Change the phase of the blue object so that it starts at the same position and with the same velocity and acceleration as the red object.

### shm-graph-02.iwp

Run the applet to display a position vs. time graph of an object in simple harmonic motion.

### shm-phase-01.iwp

The red and blue objects have the same mass and oscillate in SHM with the same period and amplitude. The only thing different is the phase. Change the phase of the blue object so that it starts at the same position and with the same velocity and acceleration as the red object.

### shm-phase-02.iwp

The red and blue objects have the same mass and oscillate in SHM with the same period and amplitude. The only thing different is the phase. Determine what the phase of the blue object must be so that it starts at the same position and with the same velocity and acceleration as the red object.

### shm-phase-01.iwp

The red and blue objects have the same mass and oscillate in SHM with the same period and amplitude. The only thing different is the phase. Change the phase of the blue object so that it starts at the same position and with the same velocity and acceleration as the red object.

### shm-phase-02.iwp

The red and blue objects have the same mass and oscillate in SHM with the same period and amplitude. The only thing different is the phase. Determine what the phase of the blue object must be so that it starts at the same position and with the same velocity and acceleration as the red object.

### shm-phase-03.iwp

The red and blue objects have the same mass and oscillate in SHM with the same period and amplitude. The only thing different is the phase. Determine what the phase of the blue object must be so that it starts at the same position and with the same velocity and acceleration as the red object.

### shm-phase-02.iwp

The red and blue objects have the same mass and oscillate in SHM with the same period and amplitude. The only thing different is the phase. Determine what the phase of the blue object must be so that it starts at the same position and with the same velocity and acceleration as the red object.

### shm-phase-03.iwp

The red and blue objects have the same mass and oscillate in SHM with the same period and amplitude. The only thing different is the phase. Determine what the phase of the blue object must be so that it starts at the same position and with the same velocity and acceleration as the red object.

### shm-synchronize-02.iwp

Two objects of equal mass oscillate independently in SHM about the origin. The two objects are initially in phase. Let b = the minimum number of cycles the blue object object must execute for the objects to be in phase again. Let r = the minimum number of cycles the red object object must execute for the objects to be in phase again. a. Use the position vs. time graphs to find b and r. Change the time scale of the graph as needed. b. If Tr is the period of the red object and Tb is the period of the blue object, why should b/r = Tr/Tb? Verify your answer to #1 by finding the periods and forming their ratio.

### shm-phase-03.iwp

The red and blue objects have the same mass and oscillate in SHM with the same period and amplitude. The only thing different is the phase. Determine what the phase of the blue object must be so that it starts at the same position and with the same velocity and acceleration as the red object.

### shm-synchronize-02.iwp

Two objects of equal mass oscillate independently in SHM about the origin. The two objects are initially in phase. Let b = the minimum number of cycles the blue object object must execute for the objects to be in phase again. Let r = the minimum number of cycles the red object object must execute for the objects to be in phase again. a. Use the position vs. time graphs to find b and r. Change the time scale of the graph as needed. b. If Tr is the period of the red object and Tb is the period of the blue object, why should b/r = Tr/Tb? Verify your answer to #1 by finding the periods and forming their ratio.

### shm-synchronize.iwp

Two objects of equal mass oscillate independently in SHM about the origin. The two objects are initially in phase. Let b = the minimum number of cycles the blue object object must execute for the objects to be in phase again. Let r = the minimum number of cycles the red object object must execute for the objects to be in phase again. Use the position vs. time graphs to find b and r. Change the time scale of the graph as needed.

### shm-synchronize-02.iwp

Two objects of equal mass oscillate independently in SHM about the origin. The two objects are initially in phase. Let b = the minimum number of cycles the blue object object must execute for the objects to be in phase again. Let r = the minimum number of cycles the red object object must execute for the objects to be in phase again. a. Use the position vs. time graphs to find b and r. Change the time scale of the graph as needed. b. If Tr is the period of the red object and Tb is the period of the blue object, why should b/r = Tr/Tb? Verify your answer to #1 by finding the periods and forming their ratio.

### shm-synchronize.iwp

Two objects of equal mass oscillate independently in SHM about the origin. The two objects are initially in phase. Let b = the minimum number of cycles the blue object object must execute for the objects to be in phase again. Let r = the minimum number of cycles the red object object must execute for the objects to be in phase again. Use the position vs. time graphs to find b and r. Change the time scale of the graph as needed.

### shm-xva-plot.iwp

The black square shows an object in 1-dimensional simple harmonic motion along the x-axis. Each of the circular colored markers represents one of the following plots for the object's motion. a. x-axis: position y-axis: velocity b. x-axis: position y-axis: acceleration c x-axis: velocity y-axis: acceleration Which color marker goes with which lettered plot? (For a display of position, velocity, and acceleration vs. time graphs of the object's motion, click Show Graph.)

### shm-synchronize.iwp

Two objects of equal mass oscillate independently in SHM about the origin. The two objects are initially in phase. Let b = the minimum number of cycles the blue object object must execute for the objects to be in phase again. Let r = the minimum number of cycles the red object object must execute for the objects to be in phase again. Use the position vs. time graphs to find b and r. Change the time scale of the graph as needed.

### shm-xva-plot.iwp

The black square shows an object in 1-dimensional simple harmonic motion along the x-axis. Each of the circular colored markers represents one of the following plots for the object's motion. a. x-axis: position y-axis: velocity b. x-axis: position y-axis: acceleration c x-axis: velocity y-axis: acceleration Which color marker goes with which lettered plot? (For a display of position, velocity, and acceleration vs. time graphs of the object's motion, click Show Graph.)

### spring-motion.iwp

A red ball is connected to a spring which is fixed at the left side of the screen.

### shm-xva-plot.iwp

The black square shows an object in 1-dimensional simple harmonic motion along the x-axis. Each of the circular colored markers represents one of the following plots for the object's motion. a. x-axis: position y-axis: velocity b. x-axis: position y-axis: acceleration c x-axis: velocity y-axis: acceleration Which color marker goes with which lettered plot? (For a display of position, velocity, and acceleration vs. time graphs of the object's motion, click Show Graph.)

### spring-motion.iwp

A red ball is connected to a spring which is fixed at the left side of the screen.

### vertical-spring-01.iwp

A platform (black) of mass 0.0500 kg is suspended from a fixed support by a rubber band that obeys Hooke's Law. Standard masses can be added to the platform in increments of 0.0500 kg. When the red stick is pulled away, the platform with its weight will oscillate vertically about its equilibrium position.