y = sin$\omega$t – cos$\omega$t

$= \sqrt 2 \left[ {{1 \over {\sqrt 2 }}\sin \omega t - {1 \over {\sqrt 2 }}\cos \omega t} \right]$

$= \sqrt 2 \sin \left( {\omega t - {\pi \over 4}} \right)$

It represents a SHM with time period, $T = {{2\pi } \over \omega }$

$y = {\sin ^3}\omega t = {1 \over 4}\left[ {3\sin \omega t - \sin 3\omega t} \right]$

It represents a periodic motion with time period

$T = {{2\pi } \over \omega }$ but now SHM.

$y = 5\cos \left( {{{3\pi } \over 4} - 3\omega t} \right)$

$= 5\cos \left( {3\omega t - {{3\pi } \over 4}} \right)$   $\left[ \because {\cos \left( { - \theta } \right) = \cos \theta } \right]$

It represents a SHM with time period, $T = {{2\pi } \over {3\omega }}$

$y = 1 + \omega t + {\omega ^2}{t^2}$

It represents a non-periodic motion. Also it is not physically acceptable as y $\to$ $\infty$ as t $\to$ $\infty$.