Question

Two bodies A and B of equal mass are suspended from two separate massless springs of spring constant $k_{1}and{k}_2$ respectively. If the bodies oscillate vertically such that their maximum velocities are equal, the ratio of the amplitude of A to that of B is

• A. $\frac{k_1}{k_2}$
• B. $\sqrt{\frac{k_1}{k_2}}$
• C. $\frac{k_2}{k_1}$
• D. $\sqrt{\frac{k_2}{k_1}}$

Answer 1

The correct option is D

$\sqrt{\frac{k_2}{k_1}}$

Hanging spring block system

$\omega =\sqrt{\frac{k}{m}}$

for SHM, basic equations are

$x=Asin\omega t$

$v=A\omega cos\omega t$

so if $cos\omega t=1$

$vismaxi.e.,v=A\omega$

given $v_{1}max=v_{2}max$

$\Rightarrow A_1{\omega }_1=A_2{\omega }_2$
$\Rightarrow A_1\sqrt{\frac{k_1}{m}}=A_2\sqrt{\frac{k_2}{m}}$
$\Rightarrow \frac{A_1}{A_2}=\sqrt{\frac{k_2}{k_1}}$