Abstract
In this work we explore the technique of the inverse of the Laplace transform, which is known as the Fourier-Mellin transform, to solve, in a direct and rigorous way, the problem of a system that oscillates under the action of a periodic external force. We also present a model in which the external force is described in terms of a sequence of Dirac deltas. This model is pertinent to describe the classical problem of a child boosted in a park swing, usually described in terms of a sinusoidal function. We indicate our forced oscillator model as more realistic to the description of this kind of problem as it considers the action of the external force only during the very small time interval of contact between the child and the agent that applies the force. The principal result of this paper were obtained in the resonance regime, in which the average power transferred to the system presented a series of peaks, corresponding to the entire multiples of the natural frequency of oscillation, in contrast to what is obtained in the ordinary case in which the external force is described by a trigonometric function.
Keywords:
Classical mechanics; Fourier-Mellin transform; Forced oscillations
