Write the phase difference between displacement and velocity,displacement and acceleration,and velocity and acceleration for a particle executing Simple Harmonic Motion $(SHM)$.

For a particle executing Simple Harmonic Motion $(SHM)$,the displacement is given by $x(t) = A \sin(\omega t + \phi)$.
$1$. Velocity $v(t) = \frac{dx}{dt} = A\omega \cos(\omega t + \phi) = A\omega \sin(\omega t + \phi + \frac{\pi}{2})$.
Comparing $x(t)$ and $v(t)$,the phase difference between displacement and velocity is $\frac{\pi}{2}$ radians.
$2$. Acceleration $a(t) = \frac{dv}{dt} = -A\omega^2 \sin(\omega t + \phi) = A\omega^2 \sin(\omega t + \phi + \pi)$.
Comparing $x(t)$ and $a(t)$,the phase difference between displacement and acceleration is $\pi$ radians.
$3$. Comparing $v(t) = A\omega \sin(\omega t + \phi + \frac{\pi}{2})$ and $a(t) = A\omega^2 \sin(\omega t + \phi + \pi)$,the phase difference between velocity and acceleration is $\pi - \frac{\pi}{2} = \frac{\pi}{2}$ radians.