Two identical point masses $P$ and $Q$, suspended from two separate massless springs of spring const

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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 amplitude $A_{Q}$ of mass $Q$ to the amplitude $A_{P}$ of mass $P$ is

Accepted Answer

Maximum velocity $V = A\omega$$$\begin{matrix} & v_{P} = v_{Q} \ & A_{P}\omega_{P} = A_{Q}\omega_{Q} \ & \frac{A_{Q}}{A_{P}} = \frac{\omega_{P}}{\omega_{Q}}\ \left( \omega = \sqrt{\frac{k}{m}} ight) \ & \ = \sqrt{\frac{k_{P}}{m_{P}}\frac{m_{Q}}{k_{Q}}} \ & \ = \sqrt{\frac{k_{1}}{k_{2}}} \end{matrix}$$

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