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JEE Main 2023 (29 Jan, Shift 2) · Velocity & Acceleration in SHM

Velocity & Acceleration in SHM question from JEE Main 2023 (29 Jan, Shift 2)

Q44JEE Main 2023 · 29 JAN · SHIFT 2Medium

Velocity & Acceleration in SHM

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

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

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Answer: 40

$F = -25x \Rightarrow k = 25$ N/m; $m = 0.25$ kg.
$\omega = \sqrt{\frac{k}{m}} = \sqrt{100} = 10$ rad/s.
$A = \frac{v_{max}}{\omega} = \frac{4}{10} = 0.4$ m.
Answer: 40 cm.

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