Question

The phase difference between the instantaneous velocity and acceleration of a particle executing S.H.M is ____________.

Options

• zero

• 0.5 `pi`

• 0.707 `pi`

• `pi`

Answer 1

The phase difference between the instantaneous velocity and acceleration of a particle executing S.H.M is 0.5 `pi`.

Explanation:

For particle executing S.H.M,

`"x" = "A sin"  omega "t"`

`therefore "v" = "dx"/"dt" = "A"omega  "cos"  omega"t"`

`= "A"omega  "sin" (omega"t" + pi/2)` and `"a" = "dv"/"dt" = -"A"omega^2  "sin"  omega"t" = "A"omega^2  "sin"  (omega"t" + pi)`

Phase difference between acceleration and velocity is,

`pi - pi/2 = pi/2 = 0.5  pi.`