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A linear and respective nonlinear state space model of a linear permanent magnet oscillatory machine is defined and then its parameters are computed from tests. The experiments were performed on two linear machine prototypes, one with interior permanent magnets and flux concentration and the other with surface permanent magnets. The finite element method model, validated on the existing prototype, shows further improvement possibilities of the interior permanent magnet machine. Dynamic tests and simulations with mechanical coupling of the two machines are used to validate the model in motion and on load. Good agreement between theory and tests in terms of various variables, including the linear position measured with a Laser-based transducer, has been observed. Index Terms--Linear synchronous motor, nonlinear systems, oscillators.