A shaft \(15 \mathrm{~mm}\) diameter and \(1 \mathrm{~m}\) long is held in long bearings. The weight of the disc at the centre of the shaft is \(15 \mathrm{~N}\). The eccentricity of the centre of gravity of the disc from centre of rotor is \(0.3 \mathrm{~mm}\). The permissible stress in the shaft material is \(65 \mathrm{MPa}\) and its modulus of elasticity is \(200 \mathrm{GPa}\). Determine

(a) the critical speed of the shaft, and

(b) the range of speed over which it is unsafe to run the shaft.