Quick Algorithms for Computing Either Displacement, Velocity or Acceleration of an Oscillator

Abstract

Accurate and efficient algorithms are derived for computing any desired response quantity of a single-degree-of-freedom linear oscillator subjected to an arbitrary forcing function. These algorithms are based on linear interpolation of the excitation between discrete points sampled uniformly in time. In the special case of the undamped oscillator, the displacement algorithm is equivalent to a previously published algorithm for this situation which was derived using a finite element approach. However, contrary to the claim made by the authors of this latter algorithm, it does not give an exact solution of the equation of undamped motion for an arbitrary forcing function.