An object of mass 0.2 ~kg executes simple… - JEE Main 2024 Physics PYQ

JEE Main 2024 — Physics Waves & Oscillations

2024integereasy

An object of mass $0.2 \mathrm{~kg}$ executes simple harmonic motion along $\mathrm{x}$ axis with frequency of $\left(\frac{25}{\pi}\right) \mathrm{Hz}$ . At the position $x=0.04 \mathrm{~m}$ the object has kinetic energy $0.5 \mathrm{~J}$ and potential energy $0.4 \mathrm{~J}$ . The amplitude of oscillation is _____ $\mathrm{cm}$ .

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Held on 8 Apr 2024 · Verified 6 Jul 2026.

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Solution

$\begin{aligned} & \text { Total energy }=\text { K.E. }+ \text { P.E. } \\ & \text { at } x=0.04 \mathrm{~m}, \text { T.E. }=0.5+0.4=0.9 \mathrm{~J} \\ & \begin{aligned} \text { T.E } & =1 \mathrm{~m} \omega^2 \mathrm{~A}^2=0.9 \\ & =\frac{1}{2} \times 0.2\left(2 \pi \times \frac{25}{\pi}\right)^2 \times \mathrm{A}^2=0.9 \\ \Rightarrow \mathrm{A} & =0.06 \mathrm{~m} \\ \mathrm{~A} & =6 \mathrm{~cm}\end{aligned}\end{aligned}$

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