Question

A simple pendulum performs S.H.M of period 4 seconds. How much time after crossing the mean position, will the displacement of the bob be one third of its amplitude.

Answer 1

Given : T = 4 s, x = A/3

The displacement of a particle starting into SHM from the mean position is

x =A sin ωt = A sin(2π/T)t

∴ A sin(2π/T)t = A/3

∴ (2π/T)t = sin^-1 0.3333 = 19.47° = 19.47 x π/180  rad

∴ t = 19.47/90 = 0.2163s

∴ The displacement of the bob will be one-third of its amplitude 0.2163s after crossing the mean position.