The function of time representing a simple

Time period $\mathrm{T}=\frac{2 \pi}{\omega^{\prime}}$

$\frac{\pi}{\omega}=\frac{2 \pi}{\omega^{\prime}}$

$\omega^{\prime}=2 \omega \rightarrow$ Angular frequency of SHM

Option (3)

$\sin ^{2} \omega \mathrm{t}=\frac{1}{2}\left(2 \sin ^{2} \omega \mathrm{t}\right)=\frac{1}{2}(1-\cos 2 \omega \mathrm{t})$

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.