The velocity of a particle executing simple harmonic motion along x -axis is described as v² = 50 - x², where x represents displacement. If the time period of motion is x/7 s, the value of x is ______. Numerical answer type. Work it out, then open the answer.

Answer: 44. For SHM v² = ω²(A² - x²) = ω²A² - ω²x² Compare with v² = 50 - x²: ω² = 1 ⇒ ω = 1 rad/s T = (2π)/(ω) = 2π = 2×22/7 = 44/7 s x/7 = 44/7 ⇒ x = 44

The velocity of a particle executing simple harmonic motion along x… | JEE Main 2026 (4 Apr, Shift 1)

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Velocity & Acceleration in SHM

The velocity of a particle executing simple harmonic motion along $x$ -axis is described as $v^2 = 50 - x^2$ , where $x$ represents displacement. If the time period of motion is $\frac{x}{7}\text{ s}$ , the value of $x$ is ______.

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

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Answer: 44

For SHM $v^2 = \omega^2(A^2 - x^2) = \omega^2A^2 - \omega^2x^2$
Compare with $v^2 = 50 - x^2$ : $\omega^2 = 1 \Rightarrow \omega = 1$ rad/s
$T = \frac{2\pi}{\omega} = 2\pi = 2\times\frac{22}{7} = \frac{44}{7}$ s
$\frac{x}{7} = \frac{44}{7} \Rightarrow x = 44$

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