Question

# 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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Solution
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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 ........(1) force displacement and opposite in direction hence an SHMNow this of form F = -kx...............(2) k = mg/I (from (1) and (2)

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