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=Asinomegat`
Velocity of the particle is `v=Aomegacosomegat=Aomegasin(omegat+(pi)/(2))`
The phase difference between displacement and velocity is `(pi)/(2)`
(b) The velocity of the particle is`a=-Aomega^(2)sinomegat=Aomega^(2)cos(omegat=(pi)/(2))`
The phase difference between velocity and acceleration is `(pi)/(2)`
(c ) The displacement of the particle is `y=Asinomegat`
Acceleration of the particle is `a=-Aomega^(2)sinomegat=Aomega^(2)sin(omegat+pi)`
The phase difference between displacement and acceleration is `pi`.