Dynamic analyses of vertical hydro power plant rotors require the consideration of the non-linear bearing characteristics. This study investigates the vibrational behavior of a typical vertical machine using a time integration method that considers non-linear bearing forces. Thereby, the influence of support stiffness and unbalance magnitude is examined. The results show a rising influence of unbalance on resonance speed with increasing support stiffness. Furthermore, simulations reveal that the shaft orbit in the bearing is nearly circular for typical design constellations. This property is applied to derive a novel approximation procedure enabling the examination of non-linear resonance behavior, using linear rotor dynamic theory. The procedure considers the dynamic film pressure for determining the pad position. In addition, it is time-efficient compared to a time integration method, especially at high amplitudes when damping becomes small.