Exploration 16.5: Driven Motion and Resonance

 

show velocity     driving force, Fdriving = cos(2π* *t)

restoring force, Fy(y) = −  *y 

Please wait for the animation to completely load.

Enter a value for the magnitude of the driving force and its frequency, the spring constant of the restoring force, or check the "show velocity" box, then press the "set parameters, then drag the ball" button.  When you have done this, drag the ball into position and press "play" to run the animation (position is given in meters and time is given in seconds).   Restart.   When you get a good-looking graph, right-click on it to clone the graph and resize it for a better view.

  1. Find the mass of the ball by using your knowledge of simple harmonic motion.
  2. Enable the velocity graph.  Does the velocity lead or lag the position graph during simple harmonic motion?

Set the restoring force to -2*y and the initial displacement from equilibrium to 0 m.  Also set the magnitude of the driving force to -1 N.  Vary the driving frequency between 0.10 Hz and 0.20 Hz in 0.01-Hz steps.  You may want each animation to run a while before determining the maximum amplitude.

  1. Draw a graph of the maximum amplitude of motion as a function of the frequency. 
  2. What frequency gives the maximum amplitude?

Note that the mass is not allowed to oscillate past about 22 m.

 

 

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