First slide

Simple hormonic motion

Question

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

Moderate

A

$π$
B

2 $π$
C

4 $π$
D

6 $π$

Solution

Given $4 v^{2} = 5 - x^{2}$
Differentiating with respect to t on both sides,
$8 va = - 2 xv \Rightarrow a = - \frac{x}{4}$
Motion is simple harmonic:
So, $ω^{2} = \frac{1}{4} a n d T = 2 π \sqrt{4} = 4 π$

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