This is the equation of motion governing the deformation u(t) of the idealized structural system of Fig. 6a subjected to earth• quake ground acceleration iig(t).
Comparison of Eqs. 3 and 7 shows that the equations of mo• tion for the structure subjected to two excitations-ground ac• celeration = iig(t) and external force = -mtig(t)-are one and the same. The deformation response u(t) of the structure to ground acceleration iig(t) will be identical to the response of the structure on fixed base due to an external force equal to mass times the
ground acceleration, acting opposite to the sense of acceleration. As shown in Fig. 7, the ground motion can therefore be replaced
by an effective force = -muit).