A body is performing simple harmonic with… - JEE Main 2022 Physics PYQ

JEE Main 2022 — Physics Waves & Oscillations

2022integermedium

A body is performing simple harmonic with an amplitude of $10\mathrm{cm}$ . The velocity of the body was tripled by air Jet when it is at $5\mathrm{cm}$ from its mean position. The new amplitude of vibration is $\sqrt{x}\mathrm{cm}$ . The value of $x$ is _____ .

Official previous-year question

Held on 29 Jun 2022 · Verified 6 Jul 2026.

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Solution

JEE Main 2022 Physics, Oscillations — solution figure

In SHM, velocity of the particle at any displacement, $x$ is given by, $v=\sqrt{{A}^{2}-{x}^{2}}$ .

Therefore,

$\Rightarrow \frac{v}{3v}=\frac{(\sqrt{{A}_{1}^{2}-25})}{\sqrt{{A}_{2}^{2}-25}}$ $\Rightarrow \sqrt{{A}_{2}^{2}-25}=3\times \sqrt{75}$

$\Rightarrow {A}_{2}^{2}=700$ $\Rightarrow {A}_{2}=\sqrt{700}\mathrm{cm}$

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