The displacement of a particle along the x ax | vedclass

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(B) Given the displacement equation: $x = a \sin^2 \omega t$.Using the trigonometric identity $\sin^2 	heta = \frac{1 - \cos 2	heta}{2}$,we can rewr

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simple harmonic motion of frequency $\frac{\omega}{\pi}$

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(B) Given the displacement equation: $x = a \sin^2 \omega t$.Using the trigonometric identity $\sin^2 	heta = \frac{1 - \cos 2	heta}{2}$,we can rewrite the equation as:$x = \frac{a}{2}(1 - \cos 2\omega t) = \frac{a}{2} - \frac{a}{2} \cos 2\omega t$.This equation represents simple harmonic motion $(SHM)$ about the mean position $x = \frac{a}{2}$ with an amplitude of $\frac{a}{2}$ and an angular frequency $\omega' = 2\omega$.The frequency $f$ of the motion is given by $f = \frac{\omega'}{2\pi} = \frac{2\omega}{2\pi} = \frac{\omega}{\pi}$.Therefore,the motion is simple harmonic motion with a frequency of $\frac{\omega}{\pi}$.

The displacement of a particle along the $x$ axis is given by $x = a \sin^2 \omega t$. The motion of the particle corresponds to

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