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This paper introduces a frequency-domain approach for investigation of the phenomenon of torsional dynamics. The Nyquist criterion is adopted by the proposed method to identify stability regions with respect to torsional oscillations. This paper also introduces two performance indices to evaluate torsional dampings and propensity of the system to experience torsional oscillations. The proposed method is an alternative approach to the eigenvalue analysis method and the complex torque method for investigation of torsional dynamics. The salient features of the method as compared with the aforementioned two methods are: 1) its computational efficiency since it utilizes the open-loop transfer-function matrix of the system and inherently more advantages for large size systems; 2) its performance indices that readily reveal "damping of" and "propensity to" a torsional oscillatory mode; and 3) its capability to formulate a multimachine system which includes both induction and synchronous machines. The proposed method is applied to the First IEEE Benchmark Systems for SSR studies and the results are verified based on comparison with those obtained from eigenvalue studies and digital-computer time-domain simulation.