Following this Method of averaging wiki i understand that Method of Averaging is a useful tool in dynamical systems, where time-scales in a differential equation are separated between a fast oscillation and slower behavior.
Even the example that wiki has, show that Average method is useful to know the qualitative behaviour of the original problem.
I know it is easier to study the average system, but my question goes on why is it dificult to study this original problem when fast oscillations are involved, why do we care about method of averaging.
Thank you in advance