The simple pendulum is composed of a bob of mass m suspended by a massless rigid body of length l which experiences no friction.

This pendulum only exhibits one degree of freedom. This means that its position can be described in terms of a single variable - the angle between the pendulum and a reference line, usually taken as the vertical line straight down. The simple pendulum is shown in the diagram below:

The equation of motion used to calculate the position of the pendulum over time is derived using Newton's second law of motion:
(Click Here to see the proof)

Hence we can simulate the motion of the simple pendulum, as shown 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.

In the applet above, denotes the initial value (at time t=0) of , and represents the initial velocity of the pendulum.
l is the constant length of the pendulum rod.

© Michael Hart 2004