The kinetic and potential energies for the damped wave equation \begin{document} $ \begin{equation} u''+2Bu'+A^2u = 0 \;\;\;\;\;\;({\rm DWE})\end{equation} $ \end{document} are defined by \begin{document}$ K(t) = \Vert u'(t)\Vert^2,\, P(t) = \Vert Au(t)\Vert^2, $\end{document} where \begin{document}$ A,B $\end{document} are suitable commuting selfadjoint operators. Asymptotic equipartition of energy means \begin{document}$\begin{equation} \lim\limits_{t\to\infty} \frac{K(t)}{P(t)} = 1 \;\;\;\;\;\;({\rm AEE})\end{equation}$ \end{document} for all (finite energy) non-zero solutions of (DWE). The main result of this paper is the proof of a result analogous to (AEE) for a nonautonomous version of (DWE).