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`

Explanation

`y= sin^(2) omega t = (1-cos^(2) omega t)/(2) = (1)/(2)-(1)/(2) cos 2omega t`
This function is periodic but not a simple harmonic, its period.
`T= (2pi)/(2omega)`
`therefore T= (pi)/(omega)`
It represents a harmonic motion with the point of equilibrium occurring at `(1)/(2)` insted of zero.