\begin{equation}
  \ddot{X}(t) + 2\zeta\omega_0\dot{X}(t) + \omega_0^2X(t) = W(t),
  \quad t \in [0, t_{\mathrm{end}}], \quad \dot{X}(0) = 0,\quad X(0) = 0\,,
  \label{eq:ex2_stochas_eq}
\end{equation}
