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26.( AIEEE 2003)

Two particles $A$ and $B$ of equal masses are suspended from two massless springs of spring of spring constant $k_{1}$ and $k_{2}$ , respectively. If the maximum velocities, during oscillation, are equal, the ratio of amplitude of $A$ and $B$ is :

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

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

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

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

Correct Answer is Option (C)

Maximum velocity during $S H M$ $= A ω = A \sqrt{\frac{k}{m}}$

$[$ $∴$ $ω = \sqrt{\frac{k}{m}}$ $]$

Here the maximum velocity is same and $m$ is also same

$∴$ $A_{1} \sqrt{k_{1}} = A_{2} \sqrt{k_{2}}$

$∴$ $\frac{A_{1}}{A_{2}} = \sqrt{\frac{k_{2}}{k_{1}}}$

Simple Harmonic Motion