Oscillations

JEE Main level, single correct, medium

71 of 194

Question 71 of 194

Two particles A\mathrm{A} and B\mathrm{B} of equal masses are suspended from two massless springs of spring constant k1\mathrm{k}_1 and k2\mathrm{k}_2, respectively. If the maximum velocities, during oscillation, are equal, the ratio of amplitude of AA and BB is

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Answer: (C) k2k1\sqrt{\frac{\mathrm{k}_2}{\mathrm{k}_1}}

Vmax⁡=ωA=mω2I=k\mathrm{V}_{\max }=\omega \mathrm{A}=\mathrm{m} \omega^2 \mathrm{I}=\mathrm{k}
⇒ω2=km⇒ω=km⇒ω∝K\Rightarrow \omega^2=\frac{\mathrm{k}}{\mathrm{m}} \Rightarrow \omega=\sqrt{\frac{\mathrm{k}}{\mathrm{m}}} \quad \Rightarrow \omega \propto \sqrt{\mathrm{K}} \quad or ω1ω2=k1k2\quad \frac{\omega_1}{\omega_2}=\sqrt{\frac{\mathrm{k}_1}{\mathrm{k}_2}}
VAmax⁡=VBmax⁡⇒(k1 m)(A1)=(k2 m)(A2)⇒A1 A2=k2k1\mathrm{V}_{\mathrm{A}} \max =\mathrm{V}_{\mathrm{B}} \max \quad \Rightarrow\left(\sqrt{\frac{\mathrm{k}_1}{\mathrm{~m}}}\right)\left(\mathrm{A}_1\right)=\left(\sqrt{\frac{\mathrm{k}_2}{\mathrm{~m}}}\right)\left(\mathrm{A}_2\right) \Rightarrow \frac{\mathrm{A}_1}{\mathrm{~A}_2}=\sqrt{\frac{\mathrm{k}_2}{\mathrm{k}_1}}

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