Two particles `A` to `B` perform `SHM` along the same stright line with the same amplitude `'a'` same frequency `'f'` and same equilbrium position `'O'`. The greatest distance between them is found to be `3a//2`. At some instant of time they have the same displacement from mean position. what is the displacement?

Options

A. `a//2`
B. `asqrt(7)//4`
C. `sqrt(3)//a2`
D. `3a//4`

Answer

B

Explanation

`x_(1) = a sin omegat, x_(2) = a sin(omegat + phi)`
Greatest distance
`= |x_(2) - x_(1)|_(max) = 2a "sin" (phi)/(2) = (3a)/(2) rArr "sin" (phi)/(2) = (3)/(4)`
Now according to question
`x_(1) = x_(2)`
`rArr a sin omegat = a sin (omegat + phi)`
`rArr pi - omegat = omegat + phi rArr omegat = (pi - phi)/(2)`
`rArr x_(1) = a "sin" ((pi - phi)/(2)) =a "cos" (phi)/(2) = (asqrt(7))/(4)`.