Two bodies A and B of equal mass are suspended from two massless springs of spring constant and , respectively. If the bodies oscillate vertically such that their amplitudes are equal, the ratio of the maximum velocity of A to the maximum velocity of B i

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Solution

Q.
Two bodies A and B of equal mass are suspended from two massless springs of spring constant $k_{1}$ and $k_{2}$ , respectively. If the bodies oscillate vertically such that their amplitudes are equal, the ratio of the maximum velocity of A to the maximum velocity of B is [2025]

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

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

3 $\frac{k_{2}}{k_{1}}$

4 $\sqrt{\frac{k_{2}}{k_{1}}}$

Ans.
(1)

Here $ω = \sqrt{\frac{k}{m}}$ and maximum velocity $V = A ω = A \sqrt{\frac{k}{m}}$

So, $\frac{V_{A}}{V_{B}} = \sqrt{\frac{k_{1}}{k_{2}}}$

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