In the given figure, a mass M is attached to a horizontal spring… | JEE Main 2021 (24 Feb, Shift 1)

Q75JEE Main 2021 · 24 FEB · SHIFT 1Medium

Spring Systems

In the given figure, a mass M is attached to a horizontal spring which is fixed on one side to a rigid support. The spring constant of the spring is k. The mass oscillates on a frictionless surface with time period T and amplitude A. When the mass is in equilibrium position, as shown in the figure, another mass m is gently fixed upon it. The new amplitude of oscillations will be:

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Answer: (d)

Momentum conserved at equilibrium: $Mv = (M+m)v'$ .
$A = \frac{v}{\omega} = \frac{p}{\sqrt{k\,(\text{mass})}}$ with $p$ unchanged.
$A' = A\sqrt{\frac{M}{M+m}}$ , so the answer is (d).

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Spring Systems question from JEE Main 2021 (24 Feb, Shift 1)

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