The mass $M$ shown in figure oscillates in simple harmonic motion with amplitude $A$. The amplitude of the point $\mathrm{P}$ is          
 

If a force $F$ is applied to $M$, say to the right, let A be the distance moved by $M$. If the system is released, it executes simple harmonic motion of amplitude $A$. If $A_1$ and $A_2$ ae the extensions in springs $k_1$ and $k_2$ then $A=(A_1 + A_2)$ and

$F=k_1{A}_1=k_2{A}_2$

$\Rightarrow A_1=\frac{F}{k_1}{\text{ and A}}_2=\frac{F}{k_2}$ 

$\therefore A=A_1+A_2=F\left(\frac{1}{k_1}+\frac{1}{k_2}\right)$

                 $=\frac{F\left(k_1+k_2\right)}{k_1{k}_2}$

 $\Rightarrow F=\frac{k_1{k}_{2}A}{\left(k_1+k_2\right)}$

The amplitude of point P = amplitude of oscillation of spring k₁ which is

$A_1=\frac{F}{k_1}=\frac{k_{2}A}{\left(k_1+k_2\right)}$