Please explain the working of a simple pendulum?

A Simple Pendulum

A simple pendulum is a pendulum with all the mass the same distance from the support point, like a ball on the end of a string. Gravity provides the restoring force (a component of the weight of the pendulum).

 
Summing torques, the restoring torque being the only one, gives:

 
For small angular displacements :

 
So, the torque equation becomes:

 
Whenever the acceleration is proportional to, and in the opposite direction as, the displacement, the motion is simple harmonic.
For a simple pendulum, with all the mass the same distance from the suspension point, the moment of inertia is:

 
The equation relating the angular acceleration to the angular displacement for a simple pendulum thus becomes:

 
This gives the angular frequency of the simple harmonic motion of the simple pendulum, because:

 
Note that the frequency is independent of the mass of the pendulum.