Which of the following functions of time represent (a) simple harmonic motion and (b) periodic but not simple harmonic? Give the period for each case.
(1) `sinomegat-cosomegat`
(2) `sin^(2)omegat`

Options

A. `sin omega t- cos omega t`
B. `sin^(2) omega t`
C. `sin omega t+ sin 2omega t`
D. `sin omega t- sin 2omega t`

Answer

A

Explanation

`y= sin omega t-cos omega t`
`= sqrt(2) [sin omega t*(1)/(sqrt(2))-cos omega t*(1)/(sqrt(2))]`
`= sqrt(2) [sin omega t*cos (pi)/(4)- cos omega t sin (pi)/(4)]`
`therefore y= sqrt(2) sin [omega t-(pi)/(4)]`
is similar to displacement in SHM
`y= A sin (omega t+ phi)`.