Two identical point masses P and Q , suspended from two separate massless springs of spring constants k_1 and k_2 , respectively, oscillate vertically. If their maximum speeds are the same, the ratio (A_Q / A_P) of the

Correct answer: D. k_1 k_2 aligned & Given m_ P =m_ Q & Also (V_ )_ P =(V_ )_ Q & A_ P ω_ P =A_ Q ω_ Q & A_ P k_1 m_ P =A_ Q k_2 m_ Q [ ω= k m ] & A_ Q A_ P = k_1 k_2 aligned

NEET 2025

Exam: NEET
Year: 2025
Subject: Physics
Chapter: Oscillations

NEET 2025 · Physics · Oscillations

Two identical point masses P and Q , suspended from two separate...

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 :

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 $\sqrt{\frac{\mathrm{k}_1}{\mathrm{k}_2}}$

Correct answer

D. $\sqrt{\frac{\mathrm{k}_1}{\mathrm{k}_2}}$

Step-by-step 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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