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Most noise is generated when the natural frequency of the stator core coincides with or is close to the frequency of the magnetomotive force. To calculate the natural frequency of a stator core with windings, a stator core and end winding were modelled as double rings connected by springs. The energy of each ring was expressed by kinetic energy and potential energy equations. These energy equations were put into a Lagrange's equation. Using the orthogonal characteristics of a triangular function, a two-mass two-degrees-of-freedom system was derived for a double ring (stator core and end winding coupled with spring). The vibration-model equation yielded the natural frequency of the stator core with windings, with an accuracy within about 5% of measured values. The mechanical finite-element method yielded the vibration behaviour, the in-phase mode and the out-of-phase mode, which coincided with the experimental results. A practical and accurate method for calculating the natural frequency of a core with winding was derived from the Lagrange's equation.