Show that for a particle executing SHM, velocity and displacement have a phase difference of `(pi)/(2)`.

Explanation

The displacement of SHM particle
`x= A cos omega t`, where A= amplitude
Phase of displacement `theta_(1) = omega t`, initial phase taken as `phi = 0`
Differentiating this equation w.r.t. to .t.
`v= (dx)/(dt)= (d)/(dt) [A cos omega t]`
`therefore v= -A omega sin omega t`
`=A omega cos [(pi)/(2) + omega t]`
Phase of velocity `theta_(2) = (pi)/(2)+ omega t`
Difference of phase of velocity and displacement `=theta_(2)- theta_(1)`
`=(pi)/(2)+ omega t- omega t`
`=(pi)/(2)`.