Abstract

VEGA, Salustiano et al. Solving the equation of dampening harmonic motion using some numerical methods. Rep. cient. FACEN [online]. 2023, vol.14, n.1, pp.91-97. ISSN 2222-145X.  https://doi.org/10.18004/rcfacen.2023.14.1.91.

The model of damped harmonic motion is one of the topics addressed in the area of mathematics and physics, its representation through differential equations is the main reason for its study. The simplest case is usually analyzed to obtain a real analytical solution, in which the usual resolution techniques taught to describe damped harmonic motion consider small damping intensities. However, analysis using certain numerical methods that approximate ordinary differential equations will allow us to solve this model numerically and provide different resolution techniques. In this work, the differential equation that describes the damped harmonic motion will be solved numerically. Some initial conditions for the differential equation will be proposed and the functions ODE23, ODE45 and ODE 113 of Matlab and some classical numerical algorithms will be implemented, such as the first-order Euler Back methods, the second-order Runge Kutta method, of Adams Moulton of the third order and de Runge Kutta of the fourth order. Finally, a comparison of the numerical algorithms and the implemented Matlab functions will be made with the exact analytical solution of the differential equation, as well as with the exact solution for the vertical velocity of the mass.

Keywords : Differential equations; Numerical methods; Algorithm.

        · abstract in Spanish     · text in Spanish     · Spanish ( pdf )