The function $(sin\,\omega t -cos\,\omega t)$ represents
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$x=\sin \omega t-\cos \omega t$
$\Longrightarrow x=2 \cos \omega t=2 \sin \left(\omega t+\frac{\pi}{2}\right) \quad\left[\sin C-\sin D=2 \cos \left(\frac{C+D}{2}\right) \sin \left(\frac{C-D}{2}\right)\right]$
On comparing this with equation of $S H M: x=A \sin (\omega t+\phi)$
$\Longrightarrow A=2$ $\omega(\text { Angular frequency })$
$\Longrightarrow T=\frac{2 \pi}{\omega}$
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