Question

A block $M$ shown in the figure oscillates in a simple harmonic motion with amplitude $A$. The amplitude of the point $P$ is

• A. $\frac{k_{1}A}{k_2}$
• B. $\frac{k_{2}A}{k_1}$
• C. $\frac{k_{1}A}{k_1+k_2}$
• D. $\frac{k_{2}A}{k_1+k_2}$

Answer 1

The correct option is D $\frac{k_{2}A}{k_1+k_2}$

The springs are in series, so restoring force is the same in both the springs.
Hence, $k_1{x}_1=k_2{x}_2$
Also, $x_1+x_2=A$
$\Rightarrow x_1+\frac{k_1}{k_2}{x}_1=A$
$\Rightarrow x_1\left(\frac{k_1+k_2}{k_2}\right)=A$
$\Rightarrow x_1=\frac{k_{2}A}{k_1+k_2}$
Option $d$ is correct.