A flywheel, with a weight of 100 lb and an eccentricity of 0.5 in., is mounted at the center of a steel shaft of diameter 1 in. If the length of the shaft between the bearings is 30 in. and the rotational speed of the flywheel is 1200 rpm, find
(a) the critical speed,
(b) the vibration amplitude of the rotor, and
(c) the force transmitted to the bearing supports