  In this paper, we analyse the basic ideas of Vibrodynamics and the two-timing
method. To make our analysis most instructive, we have chosen the Newton's
equation with a general oscillating force. We deal with its asymptotic
solutions in the high frequency limit. Our treatment is simple but general. The
targets of our study are \emph{the distinguished limits} and \emph{the
universal vibrogenic force}. The aim of \emph{the distinguished limit
procedure} is to identify how the small parameter can appear in an equation.
The proper appearance of a small parameter leads to \emph{valid successive
approximations}, and, in particular, to closed systems of averaged equations.
We show, that there are only two distinguished limits. This means that Newton's
equation, with high-frequency forcing, has two types of interesting asymptotic
solutions. The key item in the averaged equations for all distinguished limits
is \emph{the unique vibrogenic force}. The current state-of-the-art in this
area is: a large number of particular examples are well-known, effective and
advanced general methods (like the Krylov-Bogolyubov approach) are well
developed. However, the presented general and simple analysis of distinguished
limits and the vibrogenic force, formulated as a compact practical guide, is
novel. An advantage of our treatment is the possibility of its straightforward
use for various ODEs and PDEs with oscillating coefficients.
