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. 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)

Momentum of system remains conserved.
$p_i=p_f$
$MA\omega =(m+M)A^{\prime }{\omega }^{\prime }$
$MA\sqrt{\frac{k}{M}}=(m+M)A^{\prime }\sqrt{\frac{k}{m+M}}$
$A^{\prime }=A\sqrt{\frac{M}{M+m}}$