JEE Advanced 2016 Physics question

A block with mass is connected by a massless spring with stiffness constant to a rigid wall and moves without friction on a horizontal surface. The block oscillates with small amplitude about an equilibrium position . Consider two cases: (i) when the block is at ; and (ii) when the block is at . In both the cases, a particle with mass 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 is placed on the mass ?

• (A)The amplitude of oscillation in the first case changes by a factor of , whereas in the second case it remains unchangedCorrect
• (B)The final time period of oscillation in both the cases is sameCorrect
• (C)The total energy decreases in both the cases
• (D)The instantaneous speed at of the combined masses decreases in both the casesCorrect