Question

The displacement of a particle in S.H.M. is x = A cos `(omegat+pi/6).` Its speed will be maximum at time ______.

Options

• `pi/(6omega)  "second"`

• `pi/(4omega)`

• `pi/(3omega)`

• `pi/(2omega)`

Answer 1

The displacement of a particle in S.H.M. is x = A cos `(omegat+pi/6).` Its speed will be maximum at time `underline(pi/(3omega))`.

Explanation:

`x=Acos(omegat+pi/6)`

`"v"=dx/dt=-Aomegasin(omegat+pi/6)`

v is maximum when `sin(omegat+pi/6)=1`

or

`omegat+pi/6=pi/2`

`thereforeomegat=pi/2-pi/6=pi/3`

`thereforet=pi/(3omega)`