A mass M is attached to a horizontal spring of force constant,k fixed one side to a rigid support as shown in fig. (13). The mass oscillates on a friction less surface 

with time period T and amplitude A. When the mass is in equilibrium position another mass m is gently placed on it. What will be the new time period of
oscillations ?

• A

  $2\mathrm{\pi }\sqrt{\left(\frac{\mathrm{M}+\mathrm{m}}{\mathrm{k}}\right)}$

• B

  $2\mathrm{\pi }\sqrt{\left(\frac{\mathrm{M}-\mathrm{m}}{\mathrm{k}}\right)}$

• C

  $2\mathrm{\pi }\sqrt{\left(\frac{\mathrm{M}+\mathrm{m}}{2\mathrm{k}}\right)}$

• D

  $2\mathrm{\pi }\sqrt{\left(\frac{\mathrm{M}-\mathrm{m}}{2\mathrm{k}}\right)}$