“…If this factor β is positive, we deal with a nonlinear spring hardening system, if β is negative, it is a spring softening system. Unfortunately, such a system cannot be examined using the Laplace or Laplace-like transformation, such as [6], as this transformation can deal only with linear functions, respectively, nonlinear quadratic functions. For solving this nonlinear so-called Duffing DE, there are several methods available, such as averaging method or the harmonic balancing method.…”