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

Explanation

(a) `sin omega t- cos omega t`
`= sin omega t - sin (pi//2 - omega t)`
`= 2 cos(pi//4) sin (omega t - pi//4)`
`= sqrt(2) sin (omega t-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) omega t`
`= 1//2 - 1//2 cos 2 omega t`
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.