What is phase discuss the phase relation between displacement velocity and acceleration in simple harmonic motion?

Text Solution

Solution : Phase `(theta)` : Phase is defined as its state or condition as regards its position and direction of motion at that instant. <br> In S.H.M phase angle, `theta=omegat=2pi((t)/(T))` <br> a) Phase between velocity and displacement: in S.H.M., Displacement. <br> `y=Asin(omegat-phi)` <br> Velocity,`V=Aomegacos(omegat-phi)` <br> So phase difference between displacement and velocity is `90^(@)`. <br> 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` <br> -ve sign indicates that acceleration and displacement are opposite. <br> So phase difference between displacement and acceleration is `180^(@)`.