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Eccentricity leading to unbalanced magnetic pull (UMP) in electrical machines is a significant concern in industry. The UMP is known to be composed of two components: A radial component and a tangential one. Models that are used in industry currently tend to include the radial component alone. In this study, a Jeffcott rotor model together with a new UMP model that incorporates both the radial and tangential UMP constituents is studied for an industrial hydropower generator. Characterising the UMP as springs permits the proposed model to inherit UMP stiffness contribution. It is shown firstly that the new UMP model is sensitive to forcing frequency in the rotor movements and secondly, that this sensitivity to forcing frequency increases with decreasing rotor system stiffness. Moreover, quasi-periodic motion in the rotor displacements is observed for some forcing frequencies and system stiffnesses. Eigenvalue-based stability analysis is performed and shows that damping and stiffness of the rotor and of the bearings are important when non-synchronous whirling of the rotor comes into play. Accounting for both UMP components is an important cornerstone in the generation of better rotor designs which can help to curb rotor-stator malfunction and can contribute in the design of long lasting rotors.