The function of time representing a simple harmonic motion with a period of  $\frac{\pi }{\omega }$  is :

$y=3\cos (\frac{\pi }{4}-2\omega t)$        $\Rightarrow y=3\cos (2\omega t-\pi /4)$     It is in SHM
$T=\frac{2\pi }{2\omega }=\frac{\pi }{\omega }$ 
Or
$y={\sin }^{2}x$               $=\frac{1}{2}-\frac{1}{2}\cos 2\left(wt\right)$