[Tex/LaTex] Plotting a graph with several values of a parameter

pgfplotsplottikz-pgf

I'm trying to plot the function q(t) = (4.9/ (w^2))*(cosh(w*t)-cos(w*t)) for several values of the parameter w. That is, I want to plot whole graphs of q vs t, where I plug in say w=1, w=2, w=100, or whatever to see how the plot changes as I change the parameter.

Here's a minimal working example using TikZ:

\documentclass{minimal}
\usepackage{tikz}
\usetikzlibrary{calc}
\begin{document}
\begin{tikzpicture}
\draw[thick,->] (-2,0) -- (2,0) node[right]{$t$};
\draw[thick,->] (0,0) -- (0,5) node[above]{$q$};
\draw[blue,domain=-1:1] plot (\x,{(2.45/(3^2))*(exp(3*\x)+exp(-3*    \x)-2*cos(3*\x))});
\draw[violet,domain=-1.3:1.3] plot (\x,{(2.45/(1^2))*(exp(1*\x)+exp(-1*\x)-2*cos(1*\x))});
\draw[red,domain=-1.4:1.4] plot (\x,{(2.45/(0.1^2))*(exp(0.1*\x)+exp(-0.1*\x)-2*cos(0.1*\x))});
\end{tikzpicture}
\end{document}

And here's one using PGFplots:

\documentclass{minimal}
\usepackage{pgfplots}
\begin{document}
\begin{tikzpicture} 
\begin{axis}[xmin=-5,xmax=5,ymin=-0.5,ymax=100,no markers, grid=both]
\addplot {(2.45/(0.1^2))*(exp(0.1*x)+exp(-0.1*x)-2*cos(0.1*x))};
\addplot {(2.45/(0.5^2))*(exp(0.5*x)+exp(-0.5*x)-2*cos(0.5*x))};
\addplot {(2.45/(1^2))*(exp(1*x)+exp(-1*x)-2*cos(1*x))};
\end{axis}
\end{tikzpicture}
\end{document}

enter image description here

What I'd like to be able to do with this is

  1. plot several values of the parameter w (probably about 20) without typing out a separate \draw or \addplot line for each.
  2. color each of the different plots with a slightly different color and add a legend which will let the reader know roughly what value of the parameter each plot is based on the color.
  3. (TikZ plot only) use the range instead of the domain of the function so that every plot looks about the same — I tried just replacing domain=-1:1 with say range=0:5 but that didn't work.

I don't have a lot of experience with making plots in LaTeX, but I'd prefer an answer using either TikZ or pgfplots as I've at least used those a couple of times before.

Best Answer

I suspect this was the desired result? Large values of \w will cause your function to blow up, and will return an error message.

enter image description here

\documentclass{standalone}
\usepackage{pgfplots}

\def\mycolone{yellow}
\def\mycoltwo{green}

\pgfplotsset{every axis legend/.append style={
at={(.5,-.2)},
anchor=north}} 

\begin{document}
\begin{tikzpicture} 
\begin{axis}[xmin=-5,xmax=5,ymin=-0.5,ymax=100,no markers, grid=both]
\foreach \w in {5,10,...,100} {
\edef\tmp{\noexpand\addplot[\mycolone!\w!\mycoltwo]}
\pgfmathparse{\w/100}
\edef\x{\pgfmathresult}
\tmp{(4.9/((\w/100)^2))*(cosh(\w*x/100)-cos(\w*x/100))};
\edef\legendentry{\noexpand\addlegendentry{$\omega =
\noexpand\pgfmathprintnumber[fixed,fixed zerofill, precision=2]{\x}$}};
       \legendentry
}
\end{axis}
\end{tikzpicture}
\end{document}
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