What is phase ? Discuss the phase relations between displacement, velocity and acceleration in simple harmonic motion.

Explanation

Phase `(theta)` : Phase is defined as its state or condition as regards its position and direction of motion at that instant.
In S.H.M phase angle, `theta=omegat=2pi((t)/(T))`
a) Phase between velocity and displacement: in S.H.M., Displacement.
`y=Asin(omegat-phi)`
Velocity,`V=Aomegacos(omegat-phi)`
So phase difference between displacement and velocity is `90^(@)`.
b) Phase between displacement and acceleration : In S.H.M acceleration `'a'=-omega^(2)y` or `y=A sin omegat and a=-omega^(2)A sin omegat`
-ve sign indicates that acceleration and displacement are opposite.
So phase difference between displacement and acceleration is `180^(@)`.