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`

Options

A. a simple harmonic motion with a period `(pi)/(omega)`
B. a simple harmonic motion with a period `(2pi)/(omega)`
C. a periodic, but not simple harmonic motion with a period `(pi)/(omega)`
D. a periodic, but not simple harmonic motion with a period `(2pi)/(omega)`

Answer

C

Explanation

`sinomegat-cosomegat=sqrt(2)((1)/(sqrt(2))sinomegat-(1)/(sqrt(2))cosomegat)`
`=sqrt(2)(sinomegatcos.(pi)/(4)-cosomegatsin.(pi)/(4))=sqrt(2)sin(omegat-(pi)/(4))`
It represents SHM with a period `(2pi)/(omega)`.