The single degree of freedom (SDF) system presents a simple case of structures; but in reality, there are structures which can be simulated as a SDF system in our life such that the single floor houses or some towers. The Duhamel’s integral which presents the particular response of a SDF system subjected to an arbitrary loading function cannot be determined theoretically in all cases. The present approach is occupied by the numerical integration of the Duhamel’s integral using the three points Gauss Quadrature, which presents a good accuracy and exactitude even when the step of time is sufficiently small. After the formulation of the expressions and the steps of the algorithm, three examples were being presented to compare the exact responses with those deducted from the present algorithm; such that we can see the excellent agreement between the results deducted by the presented approximate algorithm with those of the exact solutions. The present algorithm too, is very useful for the engineer or a designer, and very simple for computer programming.

numerical algorithm, SDF systems, equilibrium dynamic equation, arbitrary loading, Gauss Quadrature.