A flywheel, with a mass of (50 mathrm{~kg}) and an eccentricity of (12 mathrm{~mm}), is mounted at
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A flywheel, with a mass of \(50 \mathrm{~kg}\) and an eccentricity of \(12 \mathrm{~mm}\), is mounted at the center of a steel shaft of diameter \(25 \mathrm{~mm}\). If the length of the shaft between the bearings is \(0.75 \mathrm{~m}\) and the rotational speed of the flywheel is \(1200 \mathrm{rpm}\), find (a) the critical frequency in rad/s, (b) the vibration amplitude of the rotor, and (c) the force transmitted to the bearing supports.
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