垂直拉伸 tikz 图形

Question

遵循代码

\documentclass[11pt,
              a4paper,
              DIV=calc
            ]{scrartcl}
\usepackage[autooneside=false,automark,markcase=ignoreuppercase,headsepline,plainheadsepline]{scrlayer-scrpage}
\usepackage[left=2cm,right=2cm,top=2cm,bottom=3cm]{geometry}
\usepackage{amsmath,amssymb,amsthm}
\usepackage{pstricks}
\usepackage{pst-plot}
\usepackage{pst-pdf}
\usepackage{tikz}
% Zustandsgrößen
\newcommand{\uC}[1]{\mathrm{u_{C_{#1}}}}
\newcommand{\iL}{\mathrm{i_L}}
% Eingangsgrößen
\newcommand{\Uin}{\mathrm{U_{in}}}
\newcommand{\UD}[1]{\mathrm{U_{D_{#1}}}}
\newcommand{\Usboost}{\mathrm{U_{S_{boost}}}}
\newcommand{\UAC}{\mathrm{U_{AC}}}
\definecolor{tkblue}{rgb}{0,0.212,0.369}

\begin{document}
\begin{figure}[htbp]
   \centering
   \begin{tikzpicture}[domain=0:14]
     \draw[tkblue,thick] plot (\x,{1-exp(-0.6*\x)*(cos(deg(sqrt(1-0.3^2)*\x))+0.3/(sqrt(1-0.3^2))*sin(deg(sqrt(1-0.3^2)*\x)))}) node[right] {$f(\mathrm{x})$};
     \draw[very thin,gray] (0,-0.4) grid (14.1,2.4);
     \draw[->] (0,0) -- (14.2,0) node[right] {$x$};
     \draw[->] (0,-0.5) -- (0,2.5) node[above] {$y$};
     \draw[black,<->,thick] (0,2) -- (7,2);
     \draw[black,thick] (3.5,2.15) node{{\scriptsize $\mathrm{transienter} \mathrm{Zustand}$}};
     \draw[black,<-,thick] (7,2) -- (14,2);
     \draw[black,thick] (10.5,2.15) node{{\scriptsize $\mathrm{stationaerer} \mathrm{Zustand}$}};
     \draw[black,-,thick] (7,2.5) -- (7,0); 
     \end{tikzpicture}
     \caption{transienter- und stationärer Fall}
 \label{fig:test}
\end{figure}
\end{document}

生成：

如何垂直拉伸图形？它看起来有点被压缩了。

第二个问题是，如何在 \mathrm{} 内使用“ä”？

非常感谢您的帮助。