\documentclass[tikz]{standalone}

\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[french]{babel}
\usepackage{pgfplots}
\usepackage{amssymb} 

\pgfplotsset{compat=1.14}

\begin{document}

\begin{tikzpicture}
    \begin{axis}[height=6cm, width=15cm, xmin=0, xmax=40, ymin=0, ymax=0.1, xmajorgrids, ytick={0}, xtick={0,5,...,40}, xlabel={$\omega\;(\mathrm{rad}\cdot\mathrm{s}^{-1})$}, ylabel={$Z (\mathrm m)$}]
        \addplot expression [color=blue, mark=none, domain=0:40, smooth, samples=35] {10/sqrt((400 - x^2)^2+(20*x/3)^2)};
        \addplot expression [color=blue, mark=none, domain=0:40, smooth, forget plot] {10/sqrt((400 - x^2)^2+(20*x/2)^2)};
        \addplot expression [color=brown, mark=none, domain=0:40, smooth] {10/sqrt((400 - x^2)^2+(20*x/(1/sqrt(2)))^2)};
        \addplot expression [color=brown, mark=none, domain=0:40, smooth] {10/sqrt((400 - x^2)^2+(20*x/0.2)^2)};
        \legend{$Q>\frac1{\sqrt2}$, $Q\leqslant \frac1{\sqrt2}$}
    \end{axis}
\end{tikzpicture}



\end{document}
