A block with mass M is connected by a massless spring with stiffness constant k to a rigid wall and moves without friction on a horizontal surface. The block oscillates with small amplitude A about an equilibrium position $x_0$. Consider two cases : (i) when the block is at $x_0\text{;}$ and (ii) when the block is at $x=x_0+\text{A}\text{.}$ In both the cases, a particle with mass m $\left(<\text{M}\right)$ is softly placed on the block after which they stick to each other. Which of the following statement(s) is(are) true about the motion after the mass m is placed on the mass M?

• Correct answer
  A

  The amplitude of oscillation in the first case changes by a factor of $\sqrt{\frac{\text{M}}{\text{m}+{\text{M}}^{\prime }}}$ whereas in the second case it remains unchanged
• Correct answer
  B

  The final time period of oscillation in both the cases is same
• C

  The total energy decreases in both the cases
• Correct answer
  D

  The instantaneous speed at $x_0$ of the combined masses decreases in both the cases.

Hence, the correct answer is options: 'A', 'B', 'D'.