Question

A particle undergoes SHM with a time period of 2 seconds. In how much time will it travel from its mean position to a displacement equal to half of its amplitude?

(a) 1/2 s 

(b) 1/3 s 

(c) 1/4 s 

(d) 1/6 s

Answer 1

Correct Answer is: (d) 1/6 s

T = 2π/ω = 2 or ω = π.

For a particle undergoing SHM, starting from the origin,

x = asin ωt.

For x = a / 2,

a / 2 = asin ωt

or ωt = π/6

or t = π/6ω = π/6π = 1/6 s.