Simple Pendulum Double Pendulum Spherical Pendulum Driven Pendulum Coupled Pendulum Spinning Tops

The coupled pendulum is composed of 2 simple pendulums whose bobs are connected by a spring, as shown in the diagram below:

The Coupled Pendulum



It is possible to derive the equations of motion for this system without the use of Lagrangian's equations; but by using Hooke's Law, Newton's second law of motion and standard trigonometry. The equations we use to model the motion of the coupled pendulum are:
(Click Here to see the proof)

The Coupled Pendulum Equations of Motion



You can see the motion of this system demonstrated 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 change the initial values (at time t=0) for theta1, theta2, theta1dot and theta2dot; as well as l1, l2, m1, and m2. You can also adjust the value of k, the spring constant. This represents the strength of the spring.

Also note that this applet only accurately models the motion of the pendulum for small oscillations. The equations of motion used in the applet would need to be altered in order to take different configurations of the system into account.

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© Michael Hart 2004