A system for damping machine-induced vibration in a workpiece includes a plurality of workpiece holders to hold the workpiece in a work cell. The system also includes a machine tool located in the work cell. The machine tool performs a machining operation on the workpiece while the workpiece is held by the plurality of workpiece holders. The system further includes a damping apparatus coupled to the workpiece. The damping apparatus controls machine-induced vibrations in the workpiece during the machining operation.