d
The net force becomes zero at the mean point. Therefore, linear momentum must be conserved.

\(\therefore \quad M v_{1}=(M+m) v_{2}\)

\(M A_{1} \sqrt{\frac{k}{M}}=(M+m) A_{2} \sqrt{\frac{k}{m+M}} \therefore \quad(V=A \sqrt{\frac{k}{M}})\)

\(A_{1} \sqrt{M}=A_{2} \sqrt{M+m} \quad \therefore \frac{A_{1}}{A_{2}}=\sqrt{\frac{m+M}{M}}\)