Despite the great utility, ordinary differential equations sometimes don’t have analytical solution and therefore require a numerical approach. One of the most used numerical methods is the Runge-Kutta 4th order, and in this work, its efficiency is analyzed when comparing its results with those obtained analytically. For this, a bibliographic research was carried out to elucidate the relevant fundamental contents, for the study of oscillations in three cases, the simple harmonic oscillator, the series RLC circuit and the damped and driven pendulum, and a computational and numerical treatment of these systems was, then, done. From the comparison between the numerical and analytical results, it can be concluded that the RungeKutta method presents efficacy and robustness for these cases and its computational implementation provides reliable results even in situations where analytical solutions do not apply (damped and driven pendulum), where the solution is chaotic in some cases.
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