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

Explanation

Let us assume the displacement function of SHM
`x=acosomegat`
where, a=amplitude of motion
velocity `v=(dx)/(dt)`
or `(dx)/(dt)=a(sinomegat)omega=-asinomegat`
or `v=-omegaasinomegat`
`=omegaacos((pi)/(2)+omegat)" "[:'sinomegat=-cos(pi/(2)+omegat)]`
Now, phase of displacement `=omegat`
Phase of velocity `=(pi)/(2)+omegat`
:. Difference in phase of velocity to that of phase of displacement
`=(pi)/(2)+omegat-omegat=(pi)/(2)`