y = sin ωt − cos ωt
= \(\sqrt 2(cos\frac{1}{\sqrt2}sin\, \omega t\,-\,\frac{1}{\sqrt 2}cos\,\omega t)\)
= \(\sqrt 2(cos\frac{\pi}{4}sin\,\omega t\,-\,sin\frac{\pi}{4}cos\,\omega t)\)
∴ y = \(\sqrt 2sin(wt\,-\,\frac{\pi}{4})\)
∴ (sin ωt – cos ωt) represents SHM.
y = \(\sqrt 2sin(\omega t\,-\,\frac{\pi}{4})= \sqrt 2sin(\omega t\,-\,\frac{\pi}{4}\, +2\pi)\)
= \(\sqrt 2sin(\omega(t+\frac{2\pi}{\omega})\,-\frac{\pi}{4})\)
∴ Time period = \(\frac{2\pi}{\omega}\)
