Squeeze film damping systems and methods therefore are provided that include features for optimizing the damping response to vibrational loads experienced by a rotary component of a gas turbine engine. In one exemplary aspect, a damping system actively controls a dynamic sleeve to adjust the damping response. In particular, the dynamic sleeve is disposed within a chamber defined by a damper housing. The damping system controls the damper gap by translating the dynamic sleeve. When the dynamic sleeve is translated, a variable damper gap is varied, allowing for fluid to squeeze into or out of the damper gap, thereby adjusting the damping response to the vibration of the rotary component.