Some applications of Laplace transforms in models with impulses or discontinuous forcing functions

Commonly, in Ordinary Differential Equations courses, equations with impulses or discontinuous forcing functions are studied. In this context, the Laplace Transform of the Dirac delta function and unit step function is taught, which are used as forcing functions in theoretical equations. However, application in real situations is also an important part of the learning process. In this sense, most books are flawed regarding the practical applications of this type of equation. Therefore, the purpose of this work is to study the solution of differential equations under the action of discontinuous forcing functions or impulses, contextualized in Physics or Engineering problems, using Laplace transforms. For this, this article analyzes some physical systems that are not so explored in the literature, such as the galvanometer, a circuit used inside an ammeter or voltmeter to measure current or voltage. In addition, we also studied an R-L-C circuit (Resistor, Inductor and Capacitor), using the Laplace Transform to find the capacitor voltage, demonstrating an extremely useful way for solving electrical circuits in series or in parallel.

Keywords:
Differential equations; Laplace transforms; Mathematical modeling