Show that for a simple harmonic motion, the phase difference between.
(a) displacement and velocity is `(pi)/(2)` radian or
(b) velocity and acceleration is `(pi)/(2)` radian or `90^(@)`.
(c) displacement and acceleration is `pi` radian or `180^(@)`

Explanation

(a)The displacement of the particle executing simple harmonic motion
`y=A sin omegat`
Velocity of the particle is
`v= A omega cos omega t`
`=A omega sin (omega t+(pi)/(2))`
The phase difference between displacement and velocity is `(pi)/(2)`
(b) The velociy of the particle is
`v=A omega cos omega t`
Acceleration of the particle is
`a=-A omega^(2) sin omega t`
The phase difference between velocity and acceleration is `(pi)/(2)`
(c) The displacement of the particle is
`y =A sin omega t`
Acceleration of the particle is
`a=-A omega^(2) sin omega t`
`=A omega^(2) sin (omega t+pi)`
The phase difference between displacement and acceleration is `pi`.