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Question

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 then the new amplitude of oscillation will be :


A
AMM+m
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B
AMMm
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C
AMmM
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D
AM+mM
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Solution

The correct option is A AMM+m
Before placing the mass m, angular frequency,
ωi=kM

After placing the mass m, angular frequency,
ωf=kM+m

As there is no impulsive force, so, linear momentum will remain conserved.

pi=pf
MωiAi=(M+m)ωfAf

M×kM×A=(M+m)×kM+m×Af

Af=AMM+m

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