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

(a) `sinomegat-cosomegat`
`=sinomegat-sin(pi//2-omegat)`
`=2cos(pi//4)sin(omegat-pi//4)`
`=sqrt2sin(omegat-pi//4)`
This function represents a simple harmonic motion having a period `T=2pi//omega` and a phase angle `(-pi//4)` or `(7pi//4)`
(b) `sin^(2)omegat`
`=1//2-1//2cos2omegat`
The function is periodic having a period `T = pi//omega`. It also represents a harmonic motion with the point of equilibrium occurring at `1//2` instead of zero.