A block having mass $\mathrm{M}$ is placed on a horizontal frictionless surface. This mass is attached to one end of a spring having force constant $\mathrm{k}$. The other end of the spring is attached to a rigid wall. This system consisting of spring and mass $\mathrm{M}$ is executing SHM with amplitude $\mathrm{A}$ and frequency $\mathrm{f}$. When the block is passing through the mid-point of its path of motion, a body of mass $\mathrm{m}$ is placed on top of it, as a result of which its amplitude and frequency changes to $\mathrm{A}^{\prime}$ and $\mathrm{f}$.
The ratio of frequencies $(\mathrm{f} / \mathrm{f})=\ldots \ldots \ldots$
(A) $\sqrt{\{} \mathrm{M} /(\mathrm{m}+\mathrm{M})\}$
(B) $\sqrt{\{\mathrm{m} /(\mathrm{m}+\mathrm{M})\}}$
(C) $\sqrt{\{\mathrm{MA} / \mathrm{mA}}\}$
(D) $\sqrt{[}\{(\mathrm{M}+\mathrm{m}) \mathrm{A}\} / \mathrm{mA}]$