\documentclass{standalone}

\usepackage{pgfplots,mathtools}
\pgfplotsset{compat=newest}

\begin{document}
\begin{tikzpicture}
  \begin{axis}[
      xlabel = $\omega = \sqrt{k/m}$,
      ylabel = $\langle E\rangle/k_\text{B} T$,
      domain = 0.01:11,
      ymin = 0,
      smooth,thick,
      axis lines = center,
      every tick/.style = thick]

    \def\h{1}
    \def\b{1}
    \def\eev{1/2*\h*x*(1 + 4/(e^(\b*\h*x) - 1))}
    \addplot[color=blue]{\eev};

  \end{axis}
\end{tikzpicture}
\end{document}