In the shown figure, mass m rests on smooth horizontal surface, connected with an ideal spring. If mass is displaced to the point A and released from rest, it reaches the point O in time `t_(0)`.
Now the block is displaced to the point B and released from rest. How much time it will take in travelling from point A to point O.

Explanation

Equation of motion is
`X = a cos (omega t + phi), t = 0, x = a`
`rArr a = a cos phi rArr phi = 0`
`:. x = a cos omega t`
at `x = 0, t = t_(0) rArr cos omega t_(0) = 0`
Second time, for motion of the mass also `x = 2a cos omega t and x =a, t= t, and x = 0` at `t= t_(2)`
`a = 2a cos omega t_(1)`,
`cos omega t_(1) = (1)/(2) rArr omega t_(1) = (pi)/(3) rArr t_(1) = (pi)/(3 omega)`
and `0 = 2a cos omega t_(2) rArr t_(2) = (pi)/(2 omega)`
`:. t_(2) - t_(1) = (pi)/(omega) ((1)/(2) - (1)/(3)) = (pi)/(6 omega) = (t_(0))/(3)`