Question

A mass $M$ attached to a horizontal spring, executes SHM with amplitude $A_1$. When the mass $M$ passes through its mean position then a smaller mass $m$ is placed over it and both of them move together with amplitude $A_2$. The ratio of $\left(\frac{A_1}{A_2}\right)$ is:

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

Answer 1

The correct option is D $\sqrt{\frac{M+m}{M}}$

Energy of simple harmonic oscillator is constant.
$\frac{1}{2}\times M{\omega }^2{A}_1^2=\frac{1}{2}(m+M){\omega }^2{A}_2^2$
$\frac{A_1^2}{A_2^2}=\frac{M+m}{M}$
$\frac{A_1}{A_2}=\sqrt{\frac{M+m}{M}}$