  In this paper we explore the stability of an inverted pendulum with
generalized parametric excitation described by a superposition of $N$ sines
with different frequencies and phases. We show that when the amplitude is
scaled with the frequency we obtain the stabilization of the real inverted
pendulum, i.e., with values of $g$ according to planet Earth ($g\approx
9.8$m/s$^{2}$) for high frequencies. By randomly sorting the frequencies, we
obtain a critical amplitude in light of perturbative theory in classical
mechanics which is numerically tested by exploring its validity regime in many
alternatives. We also analyse the effects when different values of $N$ as well
as the pendulum size $l$ are taken into account.
