A simple pendulum consists of a heavy metallic bob suspended by an inextensible light thread. The distance from the point of support to the centre of the bob is the size L, of the pendulum. To set the pendulum into vibration or oscillation, the bob is pulled slightly to one side and then left. Suppose it vibrates from C to B and back to C and so on. 

The amplitude, 'a' of a vibration is the distance from the centre position to one of the extreme positions of the vibrating body. i.e.,     a = AB or AC

One vibration or oscillation is the complete to and fro motion of the vibrating body, i.e. from C to B and from B to C or from A to B, B to C and from C to A.

The time period, T of a vibrating body is the time taken for one complete vibration. It is also referred to as periodic time.

The frequency 'n' of a vibrating body is the number of vibrations it completes in one second. Its unit is Hertz (Hz) or vibrations/sec

            From definition:         

The time period T of a simple pendulum is given by,           

Where L is the size of the pendulum and g is acceleration due to gravity.

The time period T, therefore:

(i)         Does not depend on the mass of the bob if L and g are constant.

(ii)        Increases if the length of the pendulum increases i.e.          

(iii)       Decreases if the acceleration due to gravity increases:       

(iv)       Remains the same provided the amplitude is small.

A second's pendulum is one which swings from one end to other in 1 second i.e. its time period is 2 s. Thus using the expression:                       

But T=2s, T²=4s

  length of a second pendulum approximately.

Thus a pendulum about 1 m long will have a time period of 2 s.

Drawbacks of a simple pendulum: Although one of the simplest methods for determines the value of g at a place a simple pendulum suffers from a number of limitations, the more important of which are the following:

(i)         It is just an ideal conception, not realizable in actual practice, since it is not possible to have both a point-mass and a weightless string.

(ii)        The resistance and the buoyance of the appreciably affect the motion of the bob.

(iii)       The expression for the time-period    is true only for oscillations of infinitely small amplitude.

(iv)       The motion of the bob is not strictly simple. It has also a rotational motion about the axis of suspension.

(v)        The bob also has a rotational motion with respect to the string at the extremities of its amplitude on either side.

Experiment: In order to determine the periodic time of a pendulum, the time for at least twenty oscillations should be taken. The accuracy increases for more oscillations. Hence T, the time for one oscillation can be calculated. If the length is increased, T also increases.

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