Two particles are executing simple harmonic of the same amplitude (A) and frequency `omega` along the x-axis . Their mean position is separated by distance `X_(0)(X_(0)gtA). If the maximum separation between them is (X_(0)+A), the phase difference between their motion is:

Options

A. `(pi)/(4)`
B. `(pi)/(6)`
C. `(pi)/(2)`
D. `(pi)/(3)`

Answer

D

Explanation

`X_(1) = Asinomegat`
`X_(2) = X_(0) + A sin (omegat + phi)`
`X_(2) - X_(1) = X_(0) + A sin (omegat + phi) - A sin omegat`
Become `|X_(2) - X_(1)|_("max") = X_(0) + A`
`|A sin (omegat + phi) - A sin omegat|_(max) = A`
`rArr phi = (pi)/(3)`