Question

prove that the phase difference between displacement and velocity of an object in shm is pi/2.

Answer 1

Displacement in SHM is given by x = A sin( wt) where A is amplitude, w is angular velocity, t is instantaneous time.

Velocity is rate of change of displacement with time. Differentiating displacement with respect to time, we have,

V = Aw cos(wt)

Phase difference between sin and cos function is 90 degrees or pi/2 radians . Hence phase difference between displacement and velocity is 90 degrees or pi/2 radians.

Similarly, acceleration can be obtained by differentiating equation of velocity.

Acceleration a = - Aw^2 sin (wt)

Hence phase difference between velocity and acceleration is also pi/2.

Phase difference between displacement and acceleration is pi radians or 180 degrees.