The study of the forced responses of material systems to various kinds of external excitation is usually the central object of modelling. Determination, or at least some global description, of such responses is clearly of major concern in many fields of physics and of mechanical engineering. In contrast to the vibration modes, which remain an abstract concept, forced responses are amenable to measurement. Furthermore, they control operating and mechanical integrity conditions of most material devices and structures. The problem of solving the equations of motion is often extremely difficult, requiring generally the use of advanced computational methods. This is mainly because of the presence of nonlinearities. However, linear Lagrange's equations may usually be solved analytically, provided that the coefficients are constant and that the excitation has a suitable analytical form. Here, we describe a general method for solving this kind of problems based on the Laplace transformation, which allows one to replace the time dependent differential equations by algebraic equations, expressed in terms of the Laplace variable. As will be shown, this method presents several advantages over the direct method of solving the differential equations in the time domain.