A vertical steel shaft of 15mm diameter is held in long bearing 1m apart and carries at its middle a disc of mass 15 kg. The eccentricity of the centre of gravity of the disc from the centre of the shaft is 0.30mm. The modulus of elasticity for the shaft material is 200 GPa and the permissible stress is 70 MPa. Determine the critical speed of the shaft neglecting the mass of the shaft and the range of speed over which it is unsafe to run the shaft.