Question

Two particles undergo SHM along parallel lines with the same time period (T) and equal amplitudes. At a particular instant, one particle is at its extreme position while the other is at its mean position. They move in the same direction. They will cross each other after a further time 

(a) T/8 

(b) 3T/8

(c) T/6 

(d) 4T/3

Answer 1

Correct Answer is: (b) 3T/8

For the particle starting from A,

x₁ = a cos ωt.

For the particle starting from O' and moving to the left,

x₂ = -a sin ωt.

The particles will cross when

x₁ = x₂ or -a sin ωt = a cos ωt

or tan ωt = -1 

or  ωt = 3π/4

or (2π/T) t = 3π/4

or t = 3T/8.