\begin{equation}\label{EqMagnitudeHXi}
\displaystyle \frac{\partial |\widetilde{H}|^{2}}{\partial \omega} = \frac{-1/k^{2}\left(2\left(\displaystyle -2\frac{\omega}{\omega_{0}^2}\right)\left(\displaystyle 1-\left(\frac{\omega}{\omega_{0}}\right)^{2}\right)
+\displaystyle 8\xi^{2}\frac{\omega}{\omega_{0}^{2}}\right)}
{\left[\displaystyle \left(1-\left(\frac{\omega}{\omega_{0}}\right)^{2}\right)^{2}+4\xi^{2}\left(\frac{\omega}{\omega_{0}}\right)^{2}\right]^2}
\end{equation}