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A universal and modular approach for synthesizing electromagnetically excited vibrations in electrical machines is presented. The synthesis process uses force responses, i.e., the normalized structural vibration responses for a machine's generic set of force excitation shapes. The responses are superposed after scaling by the operating point dependent force excitation amplitudes. This leads to a computationally efficient process. It allows to use detailed structural 3-D models and to synthesize the vibrations in the entire operating range of the machine. For validation, measured and synthesized vibration spectrograms of a run-up test of an interior permanent magnet traction motor are presented.