Show that for a particle executing SHM, the velocity and displacement have a phase difference of π/2.

Hint: Use the equation of SHM.
Step 1: Find the equation of displacement.
Let us assume, the displacement function of SHM:
                     x= acosωt
where           a=amplitude of motion
Step 2: Find the equation of velocity.
             velocity, v =dxdt
or               dxdt=a(-sinωt)ω=-ω a sinωt
or             v=-ω asinωt
                  =ω acosπ2+ωt            sinωt=-cosπ2+ωt
Step 3: Find the phase difference.
Now, the phase of displacement =ωt
the phase of velocity =π2+ωt
 The difference in the phase of velocity to that of the phase of displacement=π2+ωt-ωt=π2