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A mass \( M \), attached to a horizontal spring, executes \( \mathrm{SHM} \) with an amplitude \( A_{1} \). When the mass \( M \) passes through its
\( \mathrm{P} \) mean position then a smaller mass \( m \) is placed over it and W both of them move together with an amplitude \( A_{2} \). The ratio of \( \left(\frac{A_{1}}{A_{2}}\right) \) is
[AIEEE 2011]
(a) \( \frac{M}{M+m} \)
(b) \( \frac{M+m}{M} \)
(c) \( \left(\frac{M}{M+m}\right)^{1 / 2} \)
(d) \( \left(\frac{M+m}{M}\right)^{1 / 2} \)
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