Frequency and time domain dynamic structural analysis: convergence and causality

Matrix formulations for the dynamic analysis of SDOF systems in frequency and time domain are presented in this paper. The strict correspondence between both types of analysis are discussed. A study of the convergence of the response obtained through the frequency domain is performed. This study indicates the presence of an imaginary term in the response when the number of sampling terms in the Fourier transforms is even. A proof of the important causality property of the response is developed and an eventual source of non-causality is indicated.