We considered two kinds of numerical modeling techniques for the dynamic response of a structure subjected to ground acceleration. One of the techniques is based on the equation of motion relative to ground motion, and the other is based on the equation of absolute motion of the structure and the ground. The analytic background of the former is well established while the latter is not yet. The latter is called large mass technique, which allocates an appropriate large mass to the ground so that it can cause the ground to move according to a given acceleration time history. In this paper, employing a single degree-of-freedom spring-mass system, we analyzed the equations of motion of the two techniques and provided some theorems on the large mass technique. Using simple examples, we compared numerical results of two modeling techniques with analytic solutions. We have shown that the theorems give us a clear insight on the large mass technique through numerical tests.

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