Damped oscillators: A continuous model for velocity dependent drag

We study a continuous model which describes the action of a velocity dependent drag on an oscillatory system. The solution of the resulting differential equation turns out to be asymptotic to a function which is expressible by means of the gamma and the hypergeometric functions. Among the applications, we consider that to the free oscillations around the fixed point which are ruled by van der Pol’s equation. A section is devoted to computational procedures and simulations.