The velocity of a particle executing SHM varies with displacement (...

Given:

$4{v}^{2} = 50 - {x}^{2}$

$⇒ v = \dfrac{1}{2}\sqrt{50 - {x}^{2}}$

Comparing with standard equation of SHM, $v = \omega\sqrt{{A}^{2} - {x}^{2}}$, we get

$\omega = \dfrac{1}{2}$

Now,

$T = \dfrac{2\pi}{\omega} = 4\pi = \dfrac{88}{7}$

Hence, required $x = 88$.