What is a simple pendulum? Show that the motion of the pendulum is SHM and hence deduce an expression for the time period of pendulum. Also, define Second's pendulum.

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Simple pendulum is a point mass body suspended by a weightless thread or string from a rigid support about which it is free to oscillate.

Now restoring force acting on body can be given by
F = -mgsin (from figure)

If is small
F = -mg ( )

Let P be any point an the path of pendulum and makes which is small and arc OP be x (displacemebt) then


force displacement and opposite in direction hence an SHM

Now this of form F = -kx...............(2)
k = mg/I (from (1) and (2)

Solve any question of Oscillations with:-
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