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:

Time period (T)=4sec

To find:

The time required for the particle to displace (1/3)rd  of the amplitude

The displacement equired of the particle is given by x=Asinωt Initially the particle is at the mean position so t=0 and x=0 Let after time t is crosses (31)rd of its amplitude x=Asinωt

(3A)=Asinωt

sinωt=31

By applying the value of sin−1(31)ωt=0.3398

(T2π)t=0.3398

t=0.3398×2π4

t=0.216sec

The time required for the particle to displace (1/3)rd of the amplitude is 0.216s