Question

Show that for small oscillations the motion of a simple pendulum is simple harmonic. Derive an expression for it's timeperiod. Does it depend on the mass of the bob?

Answer 1

when we consider mgsinθ as the restoring force and neglect the higher powers if sinθ,we get mgθ.
But θ=x÷l according to the formula angle=arc÷radius.
hence when we equate this to force,we arrive at a is proportional to -x,which shows the motion is SHM.
No.It does not depend on mass.

Regards,
Adithiya.