Two particles are in `SHM` in a straight line about same equilibrium position. Amplitude `A` and time period `T` of both the particles are equal. At time `t=0`, one particle is at displacement `y_(1)=+A` and the other at `y_(2)=-A//2`, and they are approaching towards each other. after what time they cross each other?

Options

A. `(T)/(3)`
B. `(T)/(4)`
C. `(4T)/(6)`
D. `(T)/(6)`

Answer

D

Explanation

From phasor diagram,
`omegat_0-(pi)/(6)+omegat_0=(pi)/(2)`
or `2omegat_0=(pi)/(6)+(pi)/(2)=(pi+3pi)/(6)=(4pi)/(6)=(2pi)/(3)`
`t_0=(2pi)/(6omega)=(2pi)/(6xx(2pi)/(T))=(T)/(6)`