1. Introduction

When calculating an oscillator spectrum, it is necessary to solve a second-order differential equation whose solution is a Duhamel integral.

If this integral can be calculated exactly using the Laplace transform for some simple analytic functions (Dirac, sine, cosine, Heaviside, see [bib1]), it must be integrated numerically in the general case.

This document provides an effective method for dealing with this problem.

This method is implemented in*code_aster*, in operator CALC_FONCTION, keyword factor SPEC_OSCI.