A block M on a frictionless surface oscillates with small amplitude A about equilibrium x₀. A particle m

Question

A block M on a frictionless surface oscillates with small amplitude A about equilibrium x₀. A particle m<M is softly placed on it and sticks, in two cases: (i) at x₀; (ii) at x₀+A. Which statements are true?

Select all that apply

G1 Physics · Accepted Answer

Case (i), mass m is added at equilibrium where the block has speed v. Momentum gives v′=Mv/(M+m); with new ω′=√[k/(M+m)], the new amplitude becomes A√[M/(M+m)], so A is true. Case (ii), mass is added at the extreme where v=0, so amplitude stays A. In both cases the final period depends only on M+m and k, so B is true. At the extreme no kinetic energy is lost, so C is false. The speed at equilibrium is smaller after adding mass in both cases, so D is true. Correct answers: A, B, D.