The velocity of a particle executing SHM varies with displacement $( x )$ as $4 v ^2=50- x ^2$. The time period of oscillations is $\frac{x}{7} s$. The value of $x$ is $............$ $\left(\right.$ Take $\left.\pi=\frac{22}{7}\right)$
JEE MAIN 2023, Medium
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$4 v ^2=50- x ^2$
$\Rightarrow \quad v =\frac{1}{2} \sqrt{50- x ^2}$
$\omega=\frac{1}{2}$
$T =\frac{2 \pi}{\omega}=4 \pi=\frac{88}{7}$
$x =88$
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