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

The function will represent a periodic motion, if it is identically repeated after a fixed interval of time and will represent SHM if it can be written uniquely in the form of `cos ((2pi)/(T)+phi)" or a "sin((2pi)/(T)+phi)`, where T is the time period.
`sin^(3) omega t`
`sin^(3) omega t = (1)/(4) (3sin omega t- sin 3 omega t)" "[therefore sin3A = 3sinA - 4sin^(3)A]`
Here each term `sin 3omega t` of right side individually represents SHM, but the outcome of the superposition of two SHMs will only be periodic but not SHMs. Its time period is `(2pi)/(omega)`.