Question:
Two particles $A$ and $B$ of equal masses are suspended from two massless springs of spring constants $\mathrm{K}_{1}$ and $\mathrm{K}_{2}$ respectively.If the maximum velocities during oscillations are equal, the ratio of the amplitude of $\mathrm{A}$ and $\mathrm{B}$ is
Correct Option: , 4
Solution:
(4)
$\mathrm{A}_{1} \omega_{1}=\mathrm{A}_{2} \omega_{2}$
$\mathrm{A}_{1} \sqrt{\frac{\mathrm{k}_{1}}{\mathrm{~m}}}=\mathrm{A}_{2} \sqrt{\frac{\mathrm{k}_{2}}{\mathrm{~m}}}$
$\frac{\mathrm{A}_{1}}{\mathrm{~A}_{2}}=\sqrt{\frac{\mathrm{k}_{2}}{\mathrm{k}_{1}}}$