A body is executing S.H.M. When its displacem | vedclass

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(C) The velocity $v$ of a body executing $S.H.M.$ at a displacement $y$ is given by the formula: $v = \omega \sqrt{a^2 - y^2}$,where $a$ is the amplit

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$\pi \, sec$

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(C) The velocity $v$ of a body executing $S.H.M.$ at a displacement $y$ is given by the formula: $v = \omega \sqrt{a^2 - y^2}$,where $a$ is the amplitude and $\omega$ is the angular frequency.For $y_1 = 4 \, cm$,$v_1 = 10 \, cm/sec$: $10 = \omega \sqrt{a^2 - 4^2} \implies 100 = \omega^2(a^2 - 16)$  --- $(1)$For $y_2 = 5 \, cm$,$v_2 = 8 \, cm/sec$: $8 = \omega \sqrt{a^2 - 5^2} \implies 64 = \omega^2(a^2 - 25)$  --- $(2)$Subtracting equation $(2)$ from equation $(1)$:$100 - 64 = \omega^2(a^2 - 16 - a^2 + 25)$$36 = \omega^2(9)$$\omega^2 = 4 \implies \omega = 2 \, rad/sec$.The time period $T$ is given by $T = \frac{2\pi}{\omega}$.$T = \frac{2\pi}{2} = \pi \, sec$.

$A$ body is executing $S.H.M.$ When its displacement from the mean position is $4 \, cm$ and $5 \, cm$,the corresponding velocity of the body is $10 \, cm/sec$ and $8 \, cm/sec$. Then the time period of the body is

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