Question

The mass M shown in the figure oscillates in 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

$\frac{k_{2}A}{k_1+k_2}$

At the maximum displacement of the block, let extension in first spring be $x_1$ and that in second spring be $x_2$.
So, $k_1{x}_1=k_2{x}_2\Rightarrow x_2=\frac{k_1}{k_2}{x}_1$
Now, $x_1+x_2=A\Rightarrow x_1+\frac{k_1}{k_2}{x}_1=A\therefore x_1=\frac{k_{2}A}{k_1+k_2}$