The motion of a particle represented by y = s | vedclass

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(B) Given equation: $y = \sin \omega t - \cos \omega t$Multiply and divide by $\sqrt{2}$:$y = \sqrt{2} \left( \frac{1}{\sqrt{2}} \sin \omega t - \frac

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$S.H.M.$ with period $\frac{2\pi}{\omega}$,amplitude $\sqrt{2}$

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(B) Given equation: $y = \sin \omega t - \cos \omega t$Multiply and divide by $\sqrt{2}$:$y = \sqrt{2} \left( \frac{1}{\sqrt{2}} \sin \omega t - \frac{1}{\sqrt{2}} \cos \omega t \right)$Using trigonometric identities $\sin \frac{\pi}{4} = \cos \frac{\pi}{4} = \frac{1}{\sqrt{2}}$:$y = \sqrt{2} \left( \sin \omega t \cos \frac{\pi}{4} - \cos \omega t \sin \frac{\pi}{4} \right)$Using the identity $\sin(A - B) = \sin A \cos B - \cos A \sin B$:$y = \sqrt{2} \sin \left( \omega t - \frac{\pi}{4} \right)$This is the standard equation of $S.H.M.$ of the form $y = A \sin(\omega t + \phi)$,where amplitude $A = \sqrt{2}$ and angular frequency is $\omega$.The time period $T$ is given by $T = \frac{2\pi}{\omega}$.

The motion of a particle represented by $y = \sin \omega t - \cos \omega t$ is

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