A first-of-its-kind forced-response system identification approach is introduced to measure rotordynamic damping of shaft modes in a full gas turbine aero-engine. The approach involves forced-response modal analysis in which the rotordynamic system is excited with an external shaker, and engine modal characteristics are extracted from rotor shaft response signals. A reduced-order modeling framework capturing full-engine dynamics and coupling between rotor shafts and support static structure was developed and implemented in a Pratt & Whitney Canada PW615 Turbofan engine. The framework was used to guide the design of forced-response system identification experiments. The design study shows that two orthogonal shakers are required to excite both forward- and backward-whirling shaft modes and that excessive forcing amplitudes that produce whirl over 0.4 of journal eccentricity ratio can yield up to 12% lower response magnitudes due to nonlinear bearing characteristics. A statistical analysis of virtual experiments under real engine operating conditions demonstrates feasibility and robustness of the approach, measuring rotordynamic damping for key shaft modes with an uncertainty of up to 15%. General applicability of the approach with similar error levels is suggested for multispool multiframe aero-engine architectures. Guidelines for experimental setup, data acquisition, and processing are established for full-engine forced-response system identification experiments. The new capability shows promise in supporting aero-engine diagnostics and prognostics to improve the life cycle operation of commercial and military engines.