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Simple Harmonic Motion question

2016 · Shift 2 · Q37
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  5. /2016 · Shift 2 · Q37

Simple Harmonic Motion question

2016 · Shift 2 · Q37

JEE AdvancedPhysicsSimple Harmonic MotionMultiple correct+4 / −2
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 x0. Consider two cases: (i) when the block is at x0; and (ii) when the block is at x = x0 + A. In both cases, a particle with mass m( < M) is softly placed on the block after which they stick on each other. Which of the following statement(s) is(are) true about the motion after the mass m is placed on the mass M?
  1. A
    The amplitude of oscillation in the first case changes by a factor of Mm+M\sqrt {{M \over {m + M}}}m+MM​​, whereas in the second case it remains unchanged.
  2. B
    The final time period of oscillation in both the cases is same
  3. C
    The total energy decreases in both the cases
  4. D
    The instantaneous speed at x0 of the combined masses decreases in both the cases
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