A solid homogeneous cylinder of radius r and mass m rolls without slipping on the inside of a stationary larger cylinder of radius R.
(a) If the small cylinder starts at rest from an angle µo from the vertical, what is the total downward force it exerts on the outer cylinder as it passes through the lowest point?
(b) Determine the equation of motion of the inside cylinder using Lagrangian techniques.
(c) Find the period of small oscillations about the stable equilibrium position.