The velocity of a particle executing SHM varies with displacement (x) as 4v² = 50 - x². The time period of oscillations is x/7 s. The value of x is ___________. ( Take π = 22/7) Numerical answer type. Work it out, then open the answer.

Answer: 88. v² = 1/4(50 - x²) compared with v² = ω²(A² - x²) gives ω = 1/2 rad/s. T = (2π)/(ω) = 4π = 88/7 s. x/7 = 88/7 ⇒ x = 88. Answer: 88.

The velocity of a particle executing SHM varies with displacement (x)… | JEE Main 2023 (30 Jan, Shift 2)

Q42JEE Main 2023 · 30 JAN · SHIFT 2Medium

Velocity & Acceleration in SHM

The velocity of a particle executing SHM varies with displacement $(x)$ as $4v^2 = 50 - x^2$ . The time period of oscillations is $\frac{x}{7}\text{ s}$ . The value of $x$ is ___________. $($ Take $\pi = \frac{22}{7})$

Numerical answer type. Work it out, then open the answer.

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Answer: 88

$v^2 = \frac{1}{4}(50 - x^2)$ compared with $v^2 = \omega^2(A^2 - x^2)$ gives $\omega = \frac{1}{2}$ rad/s.
$T = \frac{2\pi}{\omega} = 4\pi = \frac{88}{7}$ s.
$\frac{x}{7} = \frac{88}{7} \Rightarrow x = 88$ .
Answer: 88.

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