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Pendulum

A simple pendulum consists of an object suspended by a string of length l. The bob swings back and force. The gravitational force, the weight (W), is resolved into two components. The parallel component is along the direction of the spring. The perpendicular component is at right angles to the direction of the spring. When the bob is pulled to the right, the perpendicular component is to the left, and vice versa. That is, the component of the weight (perpendicular), is a restoring force. Further, for small angles (less than 15°) the magnitude of perpendicular component is proportional to the displacement of the bob. Thus, small-displacement pendulum motion is an example of simple harmonic motion.

The period of simple pendulum of length l is given by an equation:

T = 2p Ö l / |g|.

Note that for small-angle displacements, the period depends only on the length of the pendulum, not its mass or amplitude. By measuring the length and a period of a pendulum, we can find the magnitude of the local value of gravitational acceleration, |g|. The frequency of a pendulum is the number of complete cycles of motion in one second. It can be found from the period using the equation: f = 1 / T.

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August 1999 © 1999, Physics by Demonstrations