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 `Xo. (Xo>A). If the maximum separation between them is (Xo+A), the phase difference between their motion is:

Options

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

Answer

B

Explanation

`x_(1) = Asin(omegat + phi_(1))`
`x_(2) = Asin(omegat + phi_(2))`
`x_(1) - x_(2) = A[2 sin[omegat + (phi_(1) + phi_(2))/(2)]sin[(phi_(1) - phi_(2))/(2)]]`
`A = 2A sin((phi_(1) - phi_(2))/(2))`
`(phi_(1) + phi_(2))/(2) = (pi)/(6)`
`phi_(1) = (pi)/(3)`