$\frac{\pi}{\omega}=\frac{2 \pi}{\omega^{\prime}}$
$\omega^{\prime}=2 \omega \rightarrow$ Angular frequency of $SHM$
Option $(3):$
$\sin ^{2} \omega t=\frac{1}{2}\left(2 \sin ^{2} \omega t\right)=\frac{1}{2}(1-\cos 2 \omega t)$
Angular frequency of $\left(\frac{1}{2}-\frac{1}{2} \cos 2 \omega t\right)$ is $2 \omega$
Option $(4):$
Angular frequency of $SHM$
$3 \cos \left(\frac{\pi}{4}-2 \omega t\right)$ is $2 \omega$
So option $(3)\, \& (4)$ both have angular frequency $2 \omega$ but option $(4)$ is direct answer.
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