This article summarizes the work regarding the complex and viscous damping models of SDOF system. Through calculating dynamic equations based on harmonic excitation, the result is that: when the excitation's period is less than the structure natural period, the displacement, velocity, acceleration responses of the complex damping system are stronger than the latter. Further, the displacement and the velocity spectra of some representative earthquake records are provided of two models, which show the similar trend as harmonic excitation. But the absolute acceleration spectra values of the complex damping model are higher than the other one at most time. And generally with the growing damping ratio and structure natural period, the difference is more significant. Under certain earthquake records, the structure displacement spectra values may differ by 17%, the velocity values differ by 20%, the acceleration values differ by 15%.