A particle is constrained to move (without friction) on a circular wire rotating by constant angular speed ω about a vertical diameter. Discover the equilibrium position of the particle, and compute the frequency of small oscillations around this position. Discover and interpret physically a critical angular velocity ω=ωc that divides the particle's motion into two distinct types. Construct phase diagrams for the two cases ω<ωc and ω>ωc.