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Q.

A mass 0.9 kg. attached to a horizontal spring, executes SHM with an amplitude $A_{1}$ . When this mass passes through its mean position, then a smaller mass of 124 g is place over it and both masses move together with amplitude $A_{2}$ . If the ratio $\frac{A_{1}}{A_{2}}$ is $\frac{α}{α - 1}$ , then the value of $α$ will be ______.

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answer is 16.

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Detailed Solution

$\frac{1}{2} k A^{2} = \frac{1}{2} m v_{\max}^{2} \Rightarrow \frac{1}{2} k A^{2} = \frac{{(m v_{\max})}^{2}}{2 m} \Rightarrow \frac{1}{2} k A^{2} = \frac{p^{2}}{2 m} \Rightarrow {(\frac{A_{1}}{A_{2}})}^{2} = \frac{m_{2}}{m_{1}} = \frac{1024}{900} \Rightarrow \frac{A_{1}}{A_{2}} = \frac{32}{30} = \frac{16}{15} = \frac{16}{16 - 1} ∴ α = 16$

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A mass 0.9 kg. attached to a horizontal spring, executes SHM with an amplitude A1. When this mass passes through its mean position, then a smaller mass of 124 g is place over it and both masses move together with amplitude A2. If the ratio A1A2 is αα−1, then the value of α will be ______.