PERIOD OF A PENDULUM

PERIODIC MOTION

The motion which repeats itself after fixed time intervals is called periodic motion

The best example of periodic motion are the pendulum clocks.

A SIMPLE PENDULUM

A string with a mass at the end which is free to swing is called a pendulum.

LENGTH OF THE PENDULUM

The length of the string from the point of suspension to the center of mass of the pendulum bob is called the length of the pendulum.

It is denoted by L.

The unit is meter.

AMPLITUDE OF THE PENDULUM

θ

The angle θ is called amplitude.

It is measured from the maximum swing position to the vertical line.

The unit is degree.

MASS OF THE PENDULUM

The mass of a pendulum bob is m.

The unit is kg.

m

OSCILLATION

The motion of the mass from its extreme position A to C and back to A is called an oscillation.

PERIOD FOR ONE OSCILLATION

The time taken for one oscillation is very short and therefore, difficult to measure accurately.

To find the time taken, we find the time taken for large number say 10/20 oscillations. This time divided by 10/20 will give us time taken for one oscillation.

The period is denoted as T.

The unit of T is second.

LENGTH vs. PERIOD OF THE PENDULUM

The graph of the relationship between length and time period of the pendulum is a parabola.

Thus the relationship can be expressed as

L=constant X T2

Pendulum Equation

The Period of the pendulum T is related to the length L by the relation.

This equation is only an approximation when amplitude θ is small.