A method to distinguish between forced and natural oscillations using PMU data is proposed. In PMU measurements, forced and natural oscillations can appear very similar visually, but the remedial actions are very different for them. Therefore, it is important to be able to distinguish between them. Forced oscillations do not exhibit damping in the same way as natural oscillations which are governed by the electromechanical modes of the system. This fundamental difference between forced and natural oscillations is leveraged in this paper to distinguish them. The method fits a Least Squares Autoregressive Moving Average plus Sinusoid (LS-ARMA+S) model to the measurement data, which is used to extract damping ratios of the electromechanical modes from the colored background noise. The LS-ARMA+S method is selected because it can accurately separate an oscillation from the background noise without losing the modal information in the background noise at the oscillation frequency. The damping ratio is then used to classify the oscillation as forced or natural. The method is tested in two case studies; one simple transfer function system and one small test system with 4 generators. The results show that with careful selection of damping ratio threshold value, the method achieves more than 99 % correct classifications.