Displacement vs. time curve for a particle executing S.H.M. is shown in figure. Choose the correct statements

Options

A. phase of the oscillator is same at `t = 0s` and `t =2s`
B. phase of the oscillator is same at `t = 2s` and `t = 6s`
C. phase of the oscillator is same at `t = 1s` and `t = 7s`
D. phase of the oscillator is same at `t = 1s` and `t = 5s`

Answer

B, D

Explanation

In option (a) at `t = 0s` and `t = 2s`, the displacements are in opposite directions, hence phase of the oscillator is not same which makes option incorrect. In option (b) it is clear from the curve that points corresponding to `t = 2s` and `t = 6s` and seperated by a distance belonging to one time period. Hence, these points must be in same phase. In option (c ) `t = 1s` and `t = 7s` though the displacement is zero but the particle moves in opposite directions, downwards at `t = 1s` and upwards at `t = 7s`. Hence phase of the oscillator is not same which makes option incorrect. In option (d) points belong to `t = 1s` and `t = 5s` are at separation of one time period, hence must be in phase.