(i) sin ωt - cos ωt
= \(\sqrt 2[sin\,\omega tcos\frac{\pi}{4}-\,cos\,\omega t\,sin\,\frac{\pi}{4}]\)
= \(\sqrt 2\, sin\,(\omega t\,-\,\frac{\pi}{4})\)
This function represents S.H.M., having period
T = \(\frac{2\pi}{\omega}\) and initial phase = − \(\frac{\pi}{4}\)rad.
(ii) sin2ωt = (1 – cos2ωt)
The function is periodic, having a period
T = \(\frac{2\pi}{2\omega}=\frac{\pi}{\omega}\)
But does not represent S.H.M.