Question

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

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

In case (ii), the springs are shown in the maximum compressed position. If the spring of spring constant $k_1$ is compressed by $x_1$ and that of spring constant $k_2$ is compressed by $x_2$ then

$x_1+x_2=A$ .....(i)

And $k_1{x}_1=k_2{x}_2\Rightarrow x_2=\frac{k_1{x}_1}{k_2}$ .......(ii)

From (i) & (ii)

$x_1+\frac{k_1{x}_1}{k_2}=A\Rightarrow x_1=\frac{k_{2}A}{k_2+k_1}$