Exploring the Damped Driven Harmonic Oscillator

Your assignment is to play with this applet (web animation) and discuss a set of exploratory questions with your partner. Please thoroughly discuss the questions and the applet, especially taking time to explore and discuss the ideas and concepts that interest you. You should write down your answers to these questions, as Walter is treating this as a homework assignment, but be sure to have fun as well. This assignment is meant to be both fun and educational!

Questions:

1. To use this animation, select a quality factor (Q) of 15 with the slider and then select a drive frequency by clicking on either of the two graphs. Try some different values of Q and drive frequency. At what drive frequency do we get the greatest amplitude?
2. The phase graph shows the phase relationship between the motion of the drive and the motion of the oscillator. What is the phase relationship between the motion of the drive and the motion of the oscillator at the point that you just found of greatest amplitude? How about at the two extremes of very low drive frequency and very high drive frequency?
3. This point is called resonance. Now, click the check box labeled "Show Velocity" and observe the small velocity indicator to the right of the oscillator. This represents the velocity of the oscillator. What is its phase relationship to the drive motion at resonance? Why does this make sense?
4. Generally speaking, how does varying Q affect the amplitude and phase diagrams? Given the look of the amplitude variation, why do you think that Q is called the 'quality factor'?
5. This animation ignores 'transients.' Because of this, what state of a damped-driven harmonic oscillator system are we seeing? Explain.

If you are having problems displaying this applet, find out what version of Java you are running. You probably need at least version 1.3. To get the newest version of Java, visit this site. You can contact me here with suggetions/bug reports/etc. Thank you!