Consider a rotor on a massless and rigid shaft, which is supported by ball bearings at the ends (Figure P2.5).

Figure P2.5 

The mass of the rotor is \(10 \mathrm{~kg}\) and the eccentricity is \(0.5 \mathrm{~cm}\). If the operating speed of the rotor is \(4,200 \mathrm{rpm}\), what should be the stiffnesses of the bearings such that the amplitude of rotor vibration does not exceed \(0.05 \mathrm{~cm}\) ?

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k 22 012 Bearing Rotor with mass = m and eccentricity = e Bearing Massless and rigid shaft