Question

A particle executes SHM with a time period of 4 s. Find the time taken by the particle to go directly from its mean position to half of its amplitude.

Answer 1

The time taken by the particle to go directly from its mean position to half of its amplitude.

Explanation:

The displacement equation x=A sin (wt) where A is the amplitude of oscillation

The particle is at mean position initially i.e at t=0, x=0

At the instant t, the particle is at a position of half amplitude i.e x =  A/2

​A / 2 = A sinωt

0.5 = sin ωt

ωt = π / 6

2 π / T  x t = π / 6

t = T / 12

Thus the time taken by the particle to go directly from its mean position to half of its amplitude.