Noise levels in a vertical hydroelectric turbo-generator rotor bearing systems are often very high which may lead finally to catastrophic failures during critical operating regimes. Hydroelectric vertical rotor system contains a turbine runner shaft at lower end coupled to the generator rotor with various intermediate support bearings. The main center of noise is noticed at the generator, which is induced by the unbalance and magnetic pull-in loads along with other coupled system vibrations. Present work focuses on the dynamic analysis of the coupled rotor-bearing system subjected to important nonlinear forces. The equations of motion are formulated, and the transient vibration response is obtained numerically. Further, in order to minimize the vibrations and noise levels at the generator, a support system for the generator rotor is considered with linear spring elements. The resultant system analysis is conducted and effectiveness of the study is illustrated in detail.