Without a sufficient level of "damping", it would be impossible for the rotating shaft to manage passing the critical rotation speeds (corresponding to the shaft natural frequencies) as shaft vibration would grow indefinitely. The damping coefficient in the equation of motion aggregates in fact many physical losses (in the shaft material, in the friction between the sub-assemblies of rotor parts, in the bearings, in the interacting fluids...) and thus depends on the construction details of the rotating machinery - meaning it has generally to be assessed experimentally