Physics - SHM Question with Solution | TestHub

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 k₁which is

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