An object of mass 0.2 kg executes simple harmonic motion along x axis with frequency of (25/π)Hz. At the position x = 0.04 m the object has kinetic energy 0.5 J and potential energy 0.4 J. The amplitude of oscillation is ________ cm. Numerical answer type. Work it out, then open the answer.

Answer: 6. ω = 2π × 25/π = 50 rad/s E = 0.5 + 0.4 = 0.9 J 0.9 = 1/2(0.2)(2500)A² = 250A² ⇒ A² = 0.0036 A = 0.06 m = 6 cm So the answer is 6 cm.

An object of mass 0.2 kg executes simple harmonic motion along x axis… | JEE Main 2024 (8 Apr, Shift 2)

Q30JEE Main 2024 · 8 APR · SHIFT 2Medium

Energy in SHM

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

Numerical answer type. Work it out, then open the answer.

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Answer: 6

$\omega = 2\pi \times \frac{25}{\pi} = 50$ rad/s
$E = 0.5 + 0.4 = 0.9$ J
$0.9 = \frac{1}{2}(0.2)(2500)A^2 = 250A^2 \Rightarrow A^2 = 0.0036$
$A = 0.06$ m $= 6$ cm
So the answer is 6 cm.

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