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Get Answers to all your Questions
Q.23) 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 $\left(A_Q /A_P\right)$ of the amplitude $A_Q$ of mass $Q$ to the amplitude $A_P$ of mass $P$ is:
A) $\sqrt{\frac{k_1}{k_2}}$
B) $\frac{k_2}{k_1}$
C) $\frac{k_1}{k_2}$
D) $\sqrt{\frac{k_2}{k_1}}$
Answers (1)
In SHM , maximum speed $v_{\max }=A \omega=A \sqrt{\frac{k}{m}}$
Given $v_{\text {max }}$ is same for both:
$$
A_P \sqrt{k_1}=A_Q \sqrt{k_2} \Rightarrow \frac{A_Q}{A_P}=\sqrt{\frac{k_1}{k_2}}
$$
Answer: (1) $\sqrt{\frac{k_1}{k_2}}$.
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