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.

Answer 1

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 = – mgsinθ (from figure)

If θ is small

F= – mgθ 

(∵ sin θ ≈ θ)

Let P be any point on the path of pendulum and makes ∠OMP = θ which is small and arc OP be x (displacement) then

⇒ force ∝ displacement and opposite in direction hence an SHM Now this of form F = -kx ……(2)

⇒ k = mg/l (from (1) and (2)