Oscillations

JEE Main level, single correct, medium

11 of 194

Question 11 of 194

Two bodies A and B of equal mass are suspended from two massless springs of spring constant k1k_1 and k2k_2, respectively. If the bodies oscillate vertically such that their amplitudes are equal, the ratio of the maximum velocity of AA to the maximum velocity of BB is

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Answer: (B) k1k2\sqrt{\frac{\mathrm{k}_1}{\mathrm{k}_2}}

V1=A1ω1 V2=A2ω2 A1=A2 V1 V2=ω1ω2=K1 m K2 m V1 V2=K1 K2\begin{aligned} & \mathrm{V}_1=\mathrm{A}_1 \omega_1 \\ & \mathrm{~V}_2=\mathrm{A}_2 \omega_2 \\ & \mathrm{~A}_1=\mathrm{A}_2 \\ & \frac{\mathrm{~V}_1}{\mathrm{~V}_2}=\frac{\omega_1}{\omega_2}=\frac{\sqrt{\frac{\mathrm{K}_1}{\mathrm{~m}}}}{\sqrt{\frac{\mathrm{~K}_2}{\mathrm{~m}}}} \\ & \frac{\mathrm{~V}_1}{\mathrm{~V}_2}=\sqrt{\frac{\mathrm{K}_1}{\mathrm{~K}_2}}\end{aligned}

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