Question

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 $\left.\pi=\frac{22}{7}\right)$

Answer 1

$4 v ^2=50- x ^2 $
$ \Rightarrow v =\frac{1}{2} \sqrt{50- x ^2} $
$ \omega=\frac{1}{2} $
$ T =\frac{2 \pi}{\omega}=4 \pi=\frac{88}{7} $
$ x =88$