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(D) The velocity $v$ of a particle in simple harmonic motion at a displacement $x$ is given by the formula: $v = \omega \sqrt{A^2 - x^2}$.Given that t

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$\frac{\sqrt{3} \pi A}{T}$

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(D) The velocity $v$ of a particle in simple harmonic motion at a displacement $x$ is given by the formula: $v = \omega \sqrt{A^2 - x^2}$.Given that the particle is halfway between the mean position $(x = 0)$ and the extreme position $(x = A)$,the displacement is $x = \frac{A}{2}$.The angular frequency $\omega$ is related to the period $T$ by $\omega = \frac{2 \pi}{T}$.Substituting these values into the velocity formula:$v = \frac{2 \pi}{T} \sqrt{A^2 - (\frac{A}{2})^2}$$v = \frac{2 \pi}{T} \sqrt{A^2 - \frac{A^2}{4}}$$v = \frac{2 \pi}{T} \sqrt{\frac{3 A^2}{4}}$$v = \frac{2 \pi}{T} 	imes \frac{\sqrt{3} A}{2}$$v = \frac{\sqrt{3} \pi A}{T}$

$A$ particle executes simple harmonic motion with amplitude $A$ and period $T$. If it is halfway between the mean position and the extreme position,then its speed at that point is:

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