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

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)

You can see the motion of this system demonstrated in the applet below:

You can change the initial values (at time *t*=0) for ,
, and ; as well as
, , , and
. 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.

© Michael Hart 2004