Swinging Pendulum

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This Demonstration shows an animated model of a pendulum suspended from a swinging arm.


The pendulum, a spherical bob attached to a rigid rod, is suspended from an arm that can freely swing around a pole hanging from the ceiling.

Lagrangian mechanics are used to model the system, taking into account its kinetic energy, including the rotational energy of the arm and pendulum rod. Friction is assumed negligible.


Contributed by: Erik Mahieu (August 2011)
Open content licensed under CC BY-NC-SA



If is the density of the material, is the length of the arm, and is the length of the pendulum rod, the moment of inertia of the arm is , and the moment of inertia of the rod is .

The Lagrangian of the system is:

and the equations of motion are:



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