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This letter develops a fast analytical method for uncertainty quantification of electromechanical oscillation frequency due to varying generator dampings. By employing the techniques of matrix determinant reduction, two types of uncertainty analysis are investigated to quantify the impact of the generator damping on electromechanical oscillation frequency, i.e., interval analysis and probabilistic analysis. The proposed analytical frequency estimation formula is verified against conventional methods on two transmission system models. Then, Monte Carlo experiments and interval analysis are respectively conducted to verify the established lower/upper bound formulae and probability distribution formulae. Results demonstrate the accuracy and speed of the proposed method.