Damping systems and engines including the damping systems are provided. In one embodiment, and by way of example only, the damping system includes a rotor, a bearing assembly mounted to the rotor, a spring cage disposed around the bearing assembly, an axially-extending housing surrounding the spring cage, a first squeeze film damper formed between the bearing assembly and the spring cage, and a second squeeze film damper formed between the spring cage and the axially-extending housing.