Two particles $A$ and $B$ of equal masses are suspended from two massless springs of spring constants $k_{1}\ and\ k_{2}$, respectively. If the maximum velocities, during oscillations are equal, the ratio of amplitudes of $A$ and $B$ is

Question

Dr. Abubacker · Accepted Answer

(c) $v_{\max} = a\omega = a\frac{2\pi}{T} = \frac{2\pi a}{2\pi\sqrt{\frac{m}{k}}} = a\sqrt{\frac{k}{m}}$
Hence, $\frac{v_{max1}}{v_{max2}} = \frac{a_{1}}{a_{2}}\sqrt{\frac{k_{1}}{k_{2}}}$
$\because$ $v_{max1} = v_{max2}$ (given)
$\frac{a_{1}}{a_{2}} = \sqrt{\frac{k_{2}}{k_{1}}}$

Q. Two particles $A$ and $B$ of equal masses are suspended from two massless springs of spring constants $k_{1}\ and\ k_{2}$, respectively. If the maximum velocities, during oscillations are equal, the ratio of amplitudes of $A$ and $B$ is

Explanation

Reviewed by Dr. Abubacker

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