\(=\sqrt{2}\left[\frac{1}{\sqrt{2}} \sin \omega t-\frac{1}{\sqrt{2}} \cos \omega t\right]=\sqrt{2} \sin \left(\omega t-\frac{\pi}{4}\right)\)

It represents a \(SHM\) with time period, \(T=\frac{2 \pi}{\omega}\)

\(y=\sin ^{3} \omega t=\frac{1}{4}[3 \sin \omega t-\sin 3 \omega t]\)

It represents a periodic motion with time period

\(T=\frac{2 \pi}{\omega}\) but not \(SHM\)

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

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

It represents a \(SHM\) with time period, \(T=\frac{2 \pi}{3 \omega}\)

\(y=1+\omega t+\omega^{2} t^{2}\)

It represents a non-periodic motion. Also it is not physically acceptable as \(y \rightarrow \infty\) as \(t \rightarrow \infty\)