The position, velocity and acceleration of… - JEE Main 2024 Physics PYQ

JEE Main 2024 — Physics Waves & Oscillations

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The position, velocity and acceleration of a particle executing simple harmonic motion are found to have magnitudes of $4 \mathrm{~m}, 2 \mathrm{~ms}^{-1}$ and $16 \mathrm{~ms}^{-2}$ at a certain instant. The amplitude of the motion is $\sqrt{x}, \mathrm{~m}$ where $x$ is ________

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Held on 9 Apr 2024 · Verified 6 Jul 2026.

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Solution

$\begin{aligned} & x=4 \mathrm{~m}, V=2 \mathrm{~m} / \mathrm{s}, \mathrm{a}=16 \mathrm{~m} / \mathrm{s}^2 \\ & |\mathrm{a}|=\omega^2 \mathrm{x} \\ & \Rightarrow 16=\omega^2(4) \\ & \omega=2 \mathrm{rad} / \mathrm{s} \\ & \mathrm{v}=\omega \sqrt{\mathrm{A}^2-\mathrm{x}^2} \\ & A=\sqrt{\frac{\mathrm{v}^2}{\omega^2}+\mathrm{x}^2} \Rightarrow \mathrm{A}=\sqrt{\frac{4}{4}+16} \\ & A=\sqrt{17} \mathrm{~m}\end{aligned}$

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