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^(@)

Show that for a simple harmonic motion, the phase difference between.

1.	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^(@)
Answer» SOLUTION :(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`.