### 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 $\dot{x}(0)=0$.