Oscillating Pendulum

The Oscillating Pendulum (Click on the picture to see a larger version)

Diagram by Roger Breum

Click here to see a diagram by Mike Falls.

This development relates to what is called the simple pendulum. This consists of a pendulum with a rod of length l (L) to which a mass m is attached at one end. The simplifying assumptions are made that the mass of the rod is negligible, no external forces act on the system, and there is no damping. The displacement angle is measured from the vertical as shown in the diagram on the left and is considered positive when measured to the right of OP and negative when measured to the left of OP.

The acceleration in the direction of motion (tangent to the circular path) of the mass at the end of the rod of the pendulum will be

The force in the direction of motion will be

In the diagram we see that the magnitude of the tangential component of the force due to the weight W is

The differential equation governing the position of the mass at the end of the rod in terms of theta is found by equating the two representations of the tangential component of force.

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Lane Vosbury, Mathematics, Seminole State College email: vosburyl@seminolestate.edu