In various industrial applications there is a need for higher speed, yet reliably operating rotating machinery. A key factor in achieving this type of machinery continues to be the ability to accurately predict the dynamic response and stability of a rotor-bearing system. This thesis introduces and explains the nature of rotor dynamic phenomena from comparatively simple analytic models. Starting with the most simple rotor model that is supported in two rigid bearings at its ends, the more realistic and more involved cases are considered by incorporating the effects of flexible bearings. Knowledge of these phenomena is fundamental to an understanding of the behavior of complex models, which corresponds to the real model of turbo machines namely turbocharger, and determine the dynamic characteristics for it which is very important in its design.