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 the time period $T$ and amplitude $A$. When the mass is in an equilibrium position, as shown in the figure, another mass $m$ is gently fixed upon it. The new amplitude of oscillation will be :

• A. $A \sqrt{\frac{ M - m }{ M }}$
• B. $A \sqrt{\frac{ M }{ M + m }}$
• C. $A \sqrt{\frac{ M + m }{ M }}$
• D. $A \sqrt{\frac{M}{M-m}}$

Answer 1

Answer: (B)

$A \sqrt{\frac{ M }{ M + m }}$

Answer 2

The momentum of a system remains conserved.
$p_{i}=p_{f}$
$MA \omega=( m + M ) A ' \omega'$
$MA \sqrt{\frac{ k }{ M }}=( m + M ) A ' \sqrt{\frac{ k }{ m + M }}$
$A'= A \sqrt{\frac{ M }{ M + m }}$