What is the phase difference the velocity and acceleration of a particle executing SHM?

Options

A. `pi`
B. `0.707pi`
C. zero
D. `0.5pi`

Answer

D

Explanation

Displacement of SHO `y= A sin omega t`
Instantaneous velocity `v= (dy)/(dt)= A omega cos omega t`
`=A omega sin (omega t +(pi)/(2))`
and instantaneous acceleration
`a= (dv)/(dt)= -omega^(2)y = -omega^(2) [A sin omega t]`
`therefore a= A omega^(2) sin (omega t+pi)`.
Hence, phase difference between instantaneous velocity and acceleration.
`=|(pi)/(2)-pi|=|-(pi)/(2)|=0.5pi`.