The function of time representing a simple harmonic motion with a...

Time period $T = \dfrac{2\pi}{\omega '}$

$\dfrac{\pi}{\omega} = \dfrac{2\pi}{\omega '}$

$\omega ' = 2\omega \to$ Angular frequency of SHM

Option $( 3 )$

$\sin^{2}\omegat = \dfrac{1}{2}\left(2\sin^{2}\omegat\right) = \dfrac{1}{2}\left(1 - \cos 2\omegat\right)$

Angular frequency of \left(\dfrac{1}{2} - \dfrac{1}{2}\cos 2\omegat\right)$is$2\omega$</p><p>Option$( 4 )$</p><p>Angular frequency of SHM</p><p>$3\cos \left(\dfrac{\pi}{4} - 2\omegat\right)$is$2\omega$.</p><p>So option$( 3 ) \text{ and } ( 4 )$both have angular frequency$2\omega$but option$( 4 ) is direct answer.