Modelagem matemática de oscilações com parâmetro de amortecimento transiente

Abstract

In this work we propose an alteration in the damping term of the damped harmonic oscillator equation, proposing that the resistance to motion term is not only proportional to velocity but a product between velocity and time, of the type γ(t)v(t) = αtv(t). In a broader aspect, the associated differential equation would no longer be constant coefficients, but variable coefficients. This changes the method of solution and the way of analyzing the phenomenon. Several methods were tested to solve this equation, but the one that proved to be more fruitful was the power series solution method, or Fröbenius method. To complement this study and test its physical feasibility, numerical computation methods using the Python language were employed. The results demonstrate physical consistency, but within a finite range of times.