Formulae for errors for initial displacement and velocity problems using the Newmark method

A standard test of the Newmark method in structural dynamics is its application to the determination of the response of a damped or undamped single-degree-of-freedom system to a prescribed initial displacement or velocity. In this paper formulae for the error, Δ_j, in the response, after applying the Newmark method for j time-steps each of duration Δt, are proposed and their acceptable accuracy is demonstrated.