Simple Pendulum

"I wasted time, and now doth time waste me"
William Shakespeare (Richard II)

A simple pendulum consists of a (point) mass attached to the end of a string, the other end of which is fixed to a stationary object. In its equilibrium position the string hangs vertically with tension equal to mg. If the mass is displaced, such that the string remains taut and the angle between the string and the vertical (theta) is small, then released the pendulum will move in SHM.

The period of oscillation of the simple pendulum is given by

where L is the length of the pendulum and g is the acceleration due to gravity.
So long as the angular displacement is small (which means the motion is SHM) the period is independent of the displacement. This means that the simple pendulum can be used as a time keeping device , as in for example, the grandfather clock .

"Small" is of course a relative term when applied to displacment. As an example if the angle theta is less than about 20^o the SHM prediction of the period is good to about 2%.

"We'll continue our investigation into the political beliefs of nudists. We've already noticed a definite swing to the left."

Ronnie Barker

Dr. C. L. Davis
Physics Department
University of Louisville
email: c.l.davis@louisville.edu