This study presents a numerical investigation using the finite element method on the vibratory behavior of a single spool gas turbine designed for unmanned aerial vehicle applications. The shaft of the rotor-bearing system is supported on a front bearing composed of a deep groove ball bearing with a vibration absorber element and a rear squeeze film damper bearing. Three radial clearances for the squeeze film damper were analyzed to determine the best geometric configuration for the rear bearing, considering the rotordynamic performance of the entire system. Whirl speeds and unbalanced system responses were carefully evaluated to determine the best radial clearance for the squeeze film damper. After defining the best radial clearance, a transient analysis was performed to simulate the transition of the system through resonance, and a spectral map is presented to illustrate the vibratory behavior of the system considering the influence of all related important frequencies. The rotordynamic behavior of the system is predicted, and vibration problems are avoided. Its mechanical drawings were released to manufacturing, and the first prototype is in the experimental test phase, thus indicating that the numerical results presented in this study are consistent.