Two identical point masses P and Q ,… - NEET UG 2025 Physics PYQ

NEET UG 2025 — Physics Waves & Oscillations

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Two identical point masses P and Q , suspended from two separate massless springs of spring constants $\mathrm{k}_1$ and $\mathrm{k}_2$ , respectively, oscillate vertically. If their maximum speeds are the same, the ratio $\left(A_Q / A_P\right)$ of the amplitude $A_Q$ of mass $Q$ to the amplitude $A_P$ of mass $P$ is :

Official previous-year question

Held on 30 Apr 2025 · Verified 9 Jul 2026.

Options

A
$\frac{\mathrm{k}_2}{\mathrm{k}_1}$
B
$\frac{\mathrm{k}_1}{\mathrm{k}_2}$
C
$\sqrt{\frac{\mathrm{k}_2}{\mathrm{k}_1}}$
D
$\sqrt{\frac{\mathrm{k}_1}{\mathrm{k}_2}}$

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Solution

$\begin{aligned} & \text { Given } \mathrm{m}_{\mathrm{P}}=\mathrm{m}_{\mathrm{Q}} \\ & \text { Also }\left(\mathrm{V}_{\max }\right)_{\mathrm{P}}=\left(\mathrm{V}_{\max }\right)_{\mathrm{Q}} \\ & \therefore \quad \mathrm{A}_{\mathrm{P}} \omega_{\mathrm{P}}=\mathrm{A}_{\mathrm{Q}} \omega_{\mathrm{Q}} \\ & \mathrm{A}_{\mathrm{P}} \sqrt{\frac{\mathrm{k}_1}{\mathrm{~m}_{\mathrm{P}}}}=\mathrm{A}_{\mathrm{Q}} \sqrt{\frac{\mathrm{k}_2}{\mathrm{~m}_{\mathrm{Q}}}}\left[\because \omega=\sqrt{\frac{\mathrm{k}}{\mathrm{m}}}\right] \\ & \therefore \frac{\mathrm{A}_{\mathrm{Q}}}{\mathrm{A}_{\mathrm{P}}}=\sqrt{\frac{\mathrm{k}_1}{\mathrm{k}_2}}\end{aligned}$

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