Paragraph II: Two particles, 1 and 2, each of mass m, are connected by a massless spring, and are on a horizontal frictionless plane, as shown in the figure. Initially, the two particles, with their center of mass at x₀, are oscillating with amplitude a and angular frequency ω. Thus, their positions at time t are given by x₁(t) = (x₀ + d) + a sin ωt and x₂(t) = (x₀ − d) − a sin ωt, respectively, where d > 2a. Particle 3 of mass m moves towards this system with speed u₀ = aω/2, and undergoes instantaneous elastic collision with particle 2, at time t₀. Finally, particles 1 and 2 acquire a center of mass speed v_cm and oscillate with amplitude b and the same angular frequency ω. If the collision occurs at time t₀ = π/(2ω), then the value of 4b²/a² will be ________.