A wire is bent into the shape given by and oriented vertically, opening upward, in a uniform…

A wire is bent into the shape given by  and oriented vertically, opening upward, in a uniform gravitational field g. The wire rotates at a constant angular velocity w about the y axis, and a bead of mass m is free to slide on it without friction.

(a) Find the equilibrium height of the bead on the wire. Consider especially the case n = 2.

(b) Find the frequency of small vibrations about the equilibrium position.