A particle of mass m is attached to a massless spring of constant k on a frictionless horizontal plane. Starting from equilibrium at t=0 with velocity u₀, it collides elastically with a rigid wall when its speed is 0.5u₀. After collision:
Select all that apply

Question

A particle of mass m is attached to a massless spring of constant k on a frictionless horizontal plane. Starting from equilibrium at t=0 with velocity u₀, it collides elastically with a rigid wall when its speed is 0.5u₀. After collision:

Select all that apply

G1 Physics · Accepted Answer

Let Ω=√(k/m). The wall collision occurs when speed is 0.5u₀, so from v=u₀ cos(Ωt), cos(Ωt₁)=1/2 and Ωt₁=π/3. The elastic collision reverses velocity without changing energy. The particle returns to equilibrium with speed u₀, so A is true. Tracking the reflected phase gives the second equilibrium crossing at t=5π/(3Ω), so D is true; the times quoted in B and C are not the actual first-equilibrium and maximum-compression times. Correct answers: A, D.