In this paper, the aim is to investigate the frequency response of a rotor-disk system under rotation in the presence of unbalance. Rotating systems are among the most essential components in mechanical machinery and are widely used in most mechanical systems. Rotor-disk assemblies serve as key parts of engines and propulsion systems in aircraft and helicopters. Since these systems operate at high speeds, even the slightest imbalance can affect their performance. Therefore, forced vibrations of a rotor-disk-bearing system in the presence of internal damping are analyzed here. A mass imbalance is introduced on the disk to generate forced vibrations. The main shaft is composed of four smaller shafts with different cross-sections. Bearings are modeled using a viscoelastic foundation. The Timoshenko beam theory is employed to derive the equations of motion. The effects of internal damping, gyroscopic effects, bearing stiffness, loss factor of the viscoelastic foundation, and other parameters on the system’s vibrations are investigated. It is shown that increasing both bearing stiffness and internal damping reduces the displacement amplitude of the system.