\documentclass[tikz]{standalone}

\usepackage{pgfplots}

\pgfplotsset{compat=1.14}

\begin{document}

\begin{tikzpicture}
    \begin{axis}[xmin=0, xmax=1, ymin=0, ymax=1.1, xtick={0}, ytick={0,1}, yticklabels={0,$\sqrt{mg/\beta}$}, width=12cm, height=5cm, ymajorgrids]
        \addplot [domain=0:1,smooth, samples=25] {tanh(9.81*x)};
    \end{axis}
\end{tikzpicture}

\end{document}
