We have recently developed a software to simulate a given physical phenomenon, without the need of knowing its corresponding equation of motion. This procedure is actually intended to illustrate the behavior of dynamical variables of interest, such as position, velocity, acceleration and energy. In our work, we present analytical solutions for each case under consideration; numerical solutions carried out by means of the finite difference method are presented as well. The harmonic oscillator is a moving periodical system, with a well-defined equilibrium position. We shall here present an overview of the general problem to be solved and a number of special cases shall be worked out in details. As one of the purposes of this article is to encourage readers to use numerical approaches to inspect physical problems, we shall discuss in a simple and direct way the numerical solutions of a mechanical oscillator. We also contemplate the behavior of the energy function and point out under which particular situations it is conserved. To validate the numerical method implemented in our paper, we compare the analytical solutions we derive with the results obtained by numerical computations.
Keywords:
mechanical harmonic oscillator; mechanical energy; external forces; finite difference method and dissipative forces
