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Restoring Force

The force which is always directed towards the mean position during an oscillatory motion is called restoring force. SHM occurs whenever restoring force on a particle is proportional to the displacement.

Let us now briefly study the motion of a simple pendulum, an example for periodic motion.

Simple Pendulum

A small heavy metallic bob suspended from a rigid support using a light inextensible string is called a simple pendulum.

The end tied to a rigid support is called the point of suspension ‘S’ [Figure 7.1(a)].

It can be shown that period (T) of the pendulum is given by the expression
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where T is the period of simple pendulum, L the length and g the acceleration due to gravity at a given place. Thus, T depends on length and acceleration due to gravity at the place.


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  • T does not depend on the
    1. mass of the bob,
    2. nature of the material of the bob and
    3. amplitude of the oscillation.
  • The graph of T vs. L is a parabola.
  • The graph of T 2 vs. L is a straight line.
  • A second’s pendulum has a time period of 2 s.

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