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Control design for linear, time-invariant mechanical systems typically requires an accurate low-order approximation in the low frequency range. For example a series expansion of the transfer function around zero consisting of a mass, velocity, and compliance term. Because computing such a series expansion of the transfer function can be cumbersome, a new method to compute low-order approximations of mechanical systems is developed in this paper. The method does not require an explicit expression for the transfer function, which is not always available for infinite-dimensional systems. The advantages of the proposed method is demonstrated in three examples., Comment: 32 pages, 7 figures