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  4. If displacement x and velocity v are related as 4 v2=25-x2 in a SHM Then time period of given SHM is (consider SI units)

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Q. If displacement $x$ and velocity $v$ are related as $4 v^{2}=25-x^{2}$ in a SHM Then time period of given SHM is (consider SI units)

Oscillations

Solution:

Given $4 v^{2}=25-x^{2}$
Differentiating with respect to $t$ on both sides,
$8\,v a=-2 \,x v \Rightarrow a=-\frac{x}{4}$
Motion is simple harmonic:
So, $\omega^{2}=\frac{1}{4}$ and $T=2 \pi \sqrt{4}=4 \pi$