Instructions:

This "Resource Window" opens in front of the applet window. You can move this window aside, resize it, or iconize it when you want it out of the way. To close it, use the Close option from the File menu, not the Quit or Back commands.

The applet displays solutions of the differential equation

m d2y(t)/dt2 + c dy(t)/dt +k y(t) = 0.
This equation describes a damped harmonic oscillator with mass m, damping constant c, and spring constant k. You choose m, c, and k by using the sliders or by typing directly in the right-hand control panels. You also choose the initial values y(0) and y'(0).

The applet updates its display every 1/2 second. The applet should render properly using any Java-enabled browser, such as Netscape 3.0. Macintosh users with Netscape 3.0 may experience difficulties. Sometimes the applet fails to correctly re-display after you have scrolled through the page. If so, simply click Reload.

If you receive a message informing you that your browser "does not understand the applet tag," examine the Security Preferences Menu of your browser. There should be a checkbox which you can use to enable Java; absence of such a box probably indicates you are using an older web-browser and you must upgrade it to a newer version in order to run the applet.

Please take a moment to send me an e-mail reporting any difficulties you may have experienced with the applet. The applet sometimes misbehaves when run under certain versions of Netscape.

Questions to Investigate:
• What do you expect should happen when the damping coefficient c is zero and the other coefficients are not?
• An interesting situation also occurs when k=0 and the other coefficients are not zero. How do such solutions behave in the limit as t goes to infinity? What happens if y'(0)=0 ? If y'(0) is non-zero, what role does it play in determining the limiting behaviour?
• There are values of m, c, k for which the differential equation has solutions of the straight line form y=at+b. Can you make the applet graph such a solution (both with and without setting y'=0)? Why are such solutions possible?
• Are there overdamped solutions which cross the t -axis?
• We did not give the applet the capability of considering the cases of c or k being less than zero, although there is no mathematical reason not to allow these cases. What do you think would happen? Physically, would it be sensible to let c be less than zero? Why did we not allow the applet to display the case m=0 ?