The phase difference between the instantaneous velocity and acceleration of a particle executing simple harmonic motion is

Options

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

Answer

A

Explanation

Displacement
`y=Asinomegat`
velocity `(v)=(dy)/(dt)=Aomegacosomegat=Aomegasin(omegat+(pi)/(2))`
Acceleration `(a)=(dv)/(dt)=-Aomega^(2)sinomegat=Aomega^(2)sin(omegat+pi)`
Phase difference between velocity and acceleration
`Deltaphi=omegat+pi-omegat-pi//2=pi//2=0.5pi`.