The function (sin omega t - cos omega t) repr | vedclass

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(B) Given function: $x = \sin \omega t - \cos \omega t$We can rewrite this as: $x = \sqrt{2} \left( \frac{1}{\sqrt{2}} \sin \omega t - \frac{1}{\sqrt{

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a simple harmonic motion with a period $\frac{2\pi}{\omega}$

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(B) Given function: $x = \sin \omega t - \cos \omega t$We can rewrite this as: $x = \sqrt{2} \left( \frac{1}{\sqrt{2}} \sin \omega t - \frac{1}{\sqrt{2}} \cos \omega t \right)$Using the trigonometric identity $\sin(A - B) = \sin A \cos B - \cos A \sin B$,where $B = \frac{\pi}{4}$:$x = \sqrt{2} \sin \left( \omega t - \frac{\pi}{4} \right)$Comparing this with the standard equation of Simple Harmonic Motion $(SHM)$: $x = A \sin(\omega t + \phi)$:Here,amplitude $A = \sqrt{2}$ and angular frequency is $\omega$.The time period $T$ is given by $T = \frac{2\pi}{\omega}$.Since the function can be expressed in the form $A \sin(\omega t + \phi)$,it represents a simple harmonic motion with a period of $\frac{2\pi}{\omega}$.

The function $(\sin \omega t - \cos \omega t)$ represents

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