Explain the relation in phase between displacement velocity and acceleration in SHM, graphically as well as theoretically.

Explanation

The relation in phase between displacement, velocity and acceleration in SHM can be shown graphically.
Displacement `x=Asin(omegat+phi_(0))`.

Velocity, `v=omegaAcos(omegat+phi_(0))`

Acceleration `a=-omega^(2)Asin(omegat+phi_(0))`

Here, x and v differ in phase by `pi/2`, v and a differ in phase by `pi/2`.