An extended version of a reduced order model called the Fundamental Mistuning Model (FMM) accurately predicts vibratory response and damping in a bladed disk system. The extended FMM software may describe the normal modes and natural frequencies of a mistuned bladed disk as well as damping in the disk using complex-valued inputs of its tuned system frequencies and the frequency mistuning of each blade/disk sector (i.e., the sector frequencies). The extended FMM system identification methods--basic and advanced extended FMM ID methods--also use complex mistuned modes and complex frequencies of the mistuned bladed disk as inputs. As a result, in extended FMM ID calculations, the tuned system frequencies and the mistuning frequency ratios are complex numbers. The real parts of frequencies relate to sector frequencies as well as tuned system frequencies. However, the imaginary part can be related to system damping. Thus, extended FMM ID methodology may be used to identify not only the frequencies of the individual sectors of the bladed disk, but also to identify damping in the bladed disk system. The extended FMM may predict how much the bladed disk will vibrate under the operating (rotating) conditions. Field calibration and testing of the blades may be performed using traveling wave analysis and extended FMM ID methods. The extended FMM model can be generated completely from experimental data. Because of extended FMM's simplicity, no special interfaces are required for extended FMM to be compatible with a finite element model. Because of the rules governing abstracts, this abstract should not be used to construe the claims.