A particle of mass 250g executes a simple… - JEE Main 2023 Physics PYQ

JEE Main 2023 — Physics Waves & Oscillations

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A particle of mass $250g$ executes a simple harmonic motion under a periodic force $F=(–25x)N$ . The particle attains a maximum speed of $4m{s}^{-1}$ during its oscillation. The amplitude of the motion is ______ $\mathrm{cm}$ .

Official previous-year question

Held on 29 Jan 2023 · Verified 6 Jul 2026.

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Solution

Given, force $F=(–25x)N$

$\Rightarrow 0.25a=-25x$

$\Rightarrow a=-100x$

Now comparing it with standard equation, $a=-{\omega }^{2}x$ we get

$\omega =10$ .

Now, ${v}_{max}=\omega A$

$\Rightarrow \omega A=4$

$\Rightarrow A=\frac{4}{10}=0.4m$

$\Rightarrow A=40\mathrm{cm}$ .

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