(a) A bead is free to slide along a smooth straight horizontal wire. One end of the wire is kept at a fixed point which one can take as the pole or origin and the wire is rotated around the origin in a horizontal plane at a constant angular velocity ω. Find the equation of the path of the bead.

(b) Suppose the bead is at the origin when t = 0 and the wire starts rotating at θ = 0. Describe the motion of the bead.