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JEE Main 20249 AprilMorning Shift

Exam: JEE Main
Year: 2024
Date: 9 April
Shift: Morning Shift
Subject: Physics
Chapter: Oscillations

JEE Main 2024 · 9 April · Morning Shift · Physics · Oscillations

The position, velocity and acceleration of a particle executing...

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 ________

Correct answer

0

Step-by-step 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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