Two particles execute SHM according to x₁ = A sinωt and x₂ = A sin(ωt+π/3). If the first positive time at which their velocities are exactly equal is 5T/N, find N.

Question

G1 Physics · Accepted Answer

Equal velocities require cosωt = cos(ωt+π/3). The first positive non-trivial solution gives ωt = 5π/6. Therefore, t = (5π/6)/(2π/T) = 5T/12. Comparing with 5T/N, we obtain N = 12.