Awire has a shape given by the equation y = a 2", n > 2 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) use the lagrangian approach to find the equilibrium height of the bead on the wire for general n > 2. then analyze the special case n = 2. (b) find the frequency of small vibrations about the equilibrium position.