Problem

As part of a manufacturing proceass, a uniform bar is placed on a centering device consist...

As part of a manufacturing proceass, a uniform bar is placed on a centering device consisting of two counter-rotating drums A and B and a frictional slider C that provides light damping. When the bar is placed off-center on the two counter-rotating drums, it oscillates back and forth due to the sliding friction between each drum and the bar, and it eventually settles into the centered position due to the damper C. Once the bar has been centered, the next step in the manufacturing process can begin.

Assume that the steel bar has length L = 1.2 m, radius r = 22.5 mm, and density ρ = 7.85 g/cm3. Assuming that the initial misalignment (i.e., the initial distance between G and C) of each bar can be up to 0.25 m and that sliding between the drums and the bar never ceases, design the drums (i.e., their radius and what they are made of) and determine their placement so that sliding is maintained for the entire range of motion. Since the damping is light, it can be neglected. In addition, assume that you want to drive each drum with a constant angular speed ω0.