The driven pendulum is a simple pendulum whose pivot oscillates with amplitude A and frequency v. A diagram of the vertically driven pendulum is shown below:

As with the Double Pendulum and the Spherical Pendulum, we use Lagrange's equations to equation of motion for this pendulum. Below are the equations of motion for both the vertically driven pendulum () and the horizontally driven pendulum ():
(Click Here to see the proof)

You can see this pendulum in motion in the applet below:

If you can read this writing then either you do not have Java installed, or your Java is not new enough to view the applets on this site. You need Java 1.4 to view these applets.

You can adjust the initial values of and , as well as A, l and v. Also, you can alternate between either the vertically driven or horizontally driven pendulums, and turn the oscillations on/off.

© Michael Hart 2004