  We consider a Brans-Dicke scalar field stabilized by a general power law
potential with power index $n$ at a finite equilibrium value. Redshifting
matter induces oscillations of the scalar field around its equilibrium due to
the scalar field coupling to the trace of the energy momentum tensor. If the
stabilizing potential is sufficiently steep these high frequency oscillations
are consistent with observational and experimental constraints for arbitrary
value of the Brans-Dicke parameter $\omega$. We study analytically and
numerically the equation of state of these high frequency oscillations in terms
of the parameters $\omega$ and $n$ and find the corresponding evolution of the
universe scale factor. We find that the equation of state parameter can be
negative and less than -1 but it is not related to the evolution of the scale
factor in the usual way. Nevertheless, accelerating expansion is found for a
certain parameter range. Our analysis applies also to oscillations of the size
of extra dimensions (the radion field) around an equilibrium value. This
duality between self-coupled Brans-Dicke and radion dynamics is applicable for
$\omega= -1 + 1/D$ where D is the number of extra dimensions.
