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What is Simple pendulum? Find an expression for the time period and frequency of a simple pendulum?

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A simple pendulum is the most common example of the body executing S.H.M, it consist of heavy point mass body suspended by a weightless inextensible and perfectly flexible string from a rigid support, which is free to oscillate. 

Let m = mass of bob 

l = length of pendulum 

Let O is the equilibrium position, OP = X 

Let θ = small angle through which the bob is displaced. 

The forces acting on the bob are:- 

1) The weight = M g acting vertically downwards. 

2) The tension = T in string acting along Ps. 

Resolving Mg into 2 components as Mg Cos θ and Mg Sin θ

Now, 

T = Mg Cos θ Restoring force F = - Mg Sin θ 

- ve sign shows force is directed towards mean position.

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