A pendulum is constructed by attaching a very light-weight string to a cylinder of radius R and wrapping the string around the cylinder so that a mass m at the end of the string forms a pendulum in a plane perpendicular to the axis of the cylinder. Assume that the unwrapped part of the string remains straight. What is the equation of motion? What quantities are conserved? What is the frequency of small oscillations? Around which angle are the oscillations equal in angular amplitude?