Capability to capture dynamic loading in linear dynamic analysis of single degree of freedom systems

In this work, the importance of the capability to capture dynamic loading for an integration method is emphasized. In a step-by-step integration procedure, amplitude distortions in the transient and steady-state responses depend on the step discretization error of dynamic loading for each time step. Correlations between amplitude distortion and step discretization error for dynamic loadings are analytically established for a specified integration method. These correlations may be considered as the basic numerical properties in evaluating a step-by-step integration method. As a result, the superiority of the previously published algorithm (PPA) [S. Y. Chang, Int. J. Numer. Meth. Eng. 77(8) (2009) 1100-1120] over its modified form and the member of Newmark family method (MNM) with β = γ = 1/2 in capturing dynamic loading is analytically verified (even though the three algorithms have exactly the same characteristic equation).