A frictionless circle of radius R is made out of a strip of metal and held fixed in the vertical plane. A massless spring with constant k and unstretched length l is attached to the bottom of the circle, as shown. The other end is attached to a mass m than can slide along the inside of the circle. The spring is compressed to zero length and released at time t = 0. What is the minimum vale of l for which the mass remains in contact with the circle at all times?