First slide

Simple hormonic motion

Question

Two bodies M and N of equal masses are suspended from two separate massless springs of force constants $k_{1} and k_{2}$ respectively. If the two bodies oscillate vertically such that their maximum velocities are equal, the ratio of the amplitude M to that of N is

Moderate

A

$\frac{k_{1}}{k_{2}}$
B

$\sqrt{\frac{k_{1}}{k_{2}}}$
C

$\frac{k_{2}}{k_{1}}$
D

$\sqrt{\frac{k_{2}}{k_{1}}}$

Solution

Maximum velocity = $aω = a \sqrt{\frac{k}{m}}$
Given that $a_{1} \sqrt{\frac{K_{1}}{m}} = a_{2} \sqrt{\frac{K_{2}}{m}} \Rightarrow \frac{a_{1}}{a_{2}} = \sqrt{\frac{K_{2}}{K_{1}}}$

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