The velocity of a particle executing SHM varies with displacement as . The time period of oscillations is . The value of is _______. (Take ) [2023]

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Solution

Q.
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 _______. (Take $π = \frac{22}{7}$ ) [2023]

Ans.
(88)

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

$\Rightarrow v = \frac{1}{2} \sqrt{50 - x^{2}} \Rightarrow ω = \frac{1}{2}$

$T = \frac{2 π}{ω} = 4 π = \frac{88}{7}$

$\Rightarrow x = 88$

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