A rotor has a mass of \(10 \mathrm{~kg}\) and is mounted midway on a \(20 \mathrm{~mm}\) diameter horizontal shaft supported at the ends by two bearings \(1.2 \mathrm{~m}\) apart. The shaft rotates at \(2000 \mathrm{rpm}\). If the centre of rotor of the rotor is \(0.10 \mathrm{~mm}\) away from the geometric centre of the rotor due to certain manufacturing defect, determine

(a) the amplitude of the steady-state vibration, and

(b) the dynamic force transmitted to the bearing. For shaft material, \(E=200 \mathrm{GPa}\).