Rigid Body

A uniform thin rigid rod of mass M is supported by two rotating rollers
whose axes are separated by a fixed distance a. The rod is initially placed
at rest asymmetrically.
1. Assume that the rollers rotate in opposite directions. The coefficient
of kinetic friction between the bar and the rollers is \mu. Write the
equation of motion of the bar and solve for the displacement x(t) of the center of the bar from roller (1),
assuming x(0)=x_0 and \dot{x}(0)=0.

2. Now consider the case in which the directions of rotation of the rollers
are reversed, calculate the displacement x(t),assuming x(0)=x_0 and \dot{x}(0)=0.