  In this paper, we model, classify and investigate the solutions of
(normalized) second order ode's with \emph{nonconstant continuous
coefficients}. We introduce a generalized \emph{frequency function} as the
solution of a \emph{nonlinear integro-differential equation}, show its
existence and then derive a representation formula for (all) solutions of
(normalized) second order ode's with \emph{nonconstant continuous
coefficients}. Because this formula specifies the interplay between the
coefficients of the ode, the \emph{relaxation function} ("strongly" decreasing
positive function) and the frequency function of the oscillation, it can be
applied to design models of dissipative oscillations. As an application, we
present and discuss some oscillation models that stop within a finite time
period. Moreover, we demonstrate that a large class of oscillations can be used
to design and analyze dissipative waves. In particular, it is easy to model
dissipative waves that cause in each point of space an oscillation that stops
after a finite time period.
