Which of the following functions of time represent (a) simple harmonic, (b) periodic but not simple harmonic, and (c) non-periodic motion? Give period for each case of periodic motion (`omega` is any positive constant):
(a) `sinomegat-cosomegat`
(b) `sin^(3)omegat`
(c) `3cos(pi//4-2omegat)`
(d) `cosomegat+cos3omegat+cos5omegat`
(e) `exp(-omega^(2)t^(2))`
(f) `1+omegat+omega^(2)t^(2)`

Explanation

(a) Simple harmonic, `T = (2pi//omega)`, (b) periodic, `T =(2pi//omega)` but not simple harmonic,
(c) simple harmonic, `T = (pi//omega)`, (d) periodic, `T = (2pi//omega)` but not simple harmonic,
(e) non-periodic, (f) non-periodic (physically not acceptable as the function `to oo` as `t to oo`