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PhysicsSHMMiscellaneousMedium2 minPYQ_2021

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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 oscillation will be:

Options:

Answer:

Solution:

Momentum of system remains conserved.

$p_{i} = p_{f}$

$M A ω = (m + M) A^{'} ω$

$M A \sqrt{\frac{k}{M}} = (m + M) A^{'} \sqrt{\frac{k}{m + M}}$

$A^{'} = A \sqrt{\frac{M}{M + m}}$

Stream:JEESubject:PhysicsTopic:SHMSubtopic:Miscellaneous

⏱ 2mℹ️ Source: PYQ_2021

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