Mechanics maths-Wrk,power,energy

A small bead of mass m is threaded on a smooth wire in the form of a circle of radius a. The wire is fixed in a vertical plane & a light elastic string of natural length a & modulus 2mg joins the bead to the highest point of the wire. The bead is released from rest in a position where the string is just taut, & in the subsequent motion it passes through the lowest point of the wire with speed U. Using the principle of conservation of energy, or otherwise, find U in terms of g & a.