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| -rw-r--r-- | buch/chapters/110-elliptisch/uebungsaufgaben/anharmonisch.tex | 62 |
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diff --git a/buch/chapters/110-elliptisch/uebungsaufgaben/anharmonisch.tex b/buch/chapters/110-elliptisch/uebungsaufgaben/anharmonisch.tex new file mode 100644 index 0000000..a00c393 --- /dev/null +++ b/buch/chapters/110-elliptisch/uebungsaufgaben/anharmonisch.tex @@ -0,0 +1,62 @@ +% +% anharmonisch.tex -- Potential einer anharmonischen Schwingung +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{txfonts} +\usepackage{pgfplots} +\usepackage{csvsimple} +\usetikzlibrary{arrows,intersections,math} +\begin{document} +\def\skala{1} +\definecolor{darkgreen}{rgb}{0,0.6,0} +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +\def\E{3} +\def\K{0.2} +\def\D{0.0025} + +\pgfmathparse{sqrt(\K/\D)} +\xdef\xnull{\pgfmathresult} + +\pgfmathparse{sqrt((\K+sqrt(\K*\K-4*\E*\D))/\D)} +\xdef\xplus{\pgfmathresult} +\pgfmathparse{sqrt((\K-sqrt(\K*\K-4*\E*\D))/\D)} +\xdef\xminus{\pgfmathresult} + +\def\xmax{13} + +\fill[color=darkgreen!20] (0,-1.5) rectangle (\xminus,4.7); +\node[color=darkgreen] at ({0.5*\xminus},4.7) [below] {anziehende Kraft\strut}; + +\fill[color=orange!20] (\xplus,-1.5) rectangle (\xmax,4.7); +\node[color=orange] at ({0.5*(\xplus+\xmax)},4.7) [below] {abstossende\strut}; +\node[color=orange] at ({0.5*(\xplus+\xmax)},4.3) [below] {Kraft\strut}; + +\node[color=gray] at (\xnull,4.7) [below] {verbotener Bereich\strut}; + +\draw (-0.1,\E) -- (0.1,\E); +\node at (-0.1,\E) [left] {$E$}; + +\draw[color=red,line width=1pt] + plot[domain=0:13,samples=100] + ({\x},{\E-(0.5*\K-0.25*\D*\x*\x)*\x*\x}); + +\draw[->] (-0.1,0) -- ({\xmax+0.3},0) coordinate[label={$x$}]; +\draw[->] (0,-1.5) -- (0,5) coordinate[label={right:$f(x)$}]; + +\fill[color=blue] (\xminus,0) circle[radius=0.08]; +\node[color=blue] at (\xminus,0) [below left] {$x_-\mathstrut$}; + +\fill[color=blue] (\xplus,0) circle[radius=0.08]; +\node[color=blue] at (\xplus,0) [below right] {$x_+\mathstrut$}; + +\fill[color=blue] (\xnull,0) circle[radius=0.08]; +\node[color=blue] at (\xnull,0) [below] {$x_0\mathstrut$}; + +\end{tikzpicture} +\end{document} + |