TiKZ 图 x^a* cos(ln(x))

Question

我想要绘制函数 X^(-1.5)*cos(ln(X))，我可以成功完成 X^(1.5)*cos(ln(X))，但如果我输入负指数，代码就不起作用。

我想绘制一个函数，该函数在靠近墙壁时会增加，并且振荡波长也会增加。有人能帮忙吗？谢谢！

\draw[-stealth] (0,-2) -- (0,2);

\draw[-stealth] (0,0) -- (5,0);

\draw [scale=0.5,domain=10:0,smooth,variable=\x,blue]    plot (\x, { 0.1*cos(1200* ln(\x))*(\x)^(1.5) });

\draw [scale=0.5,domain=10:0,smooth,variable=\x,black]    plot (\x, {  0.1*\x^(1.5) });

\draw [scale=0.5,domain=10:0,smooth,variable=\x,black]    plot (\x, {  -0.1*\x^(1.5) });

Answer 1

您可以按照我上面的建议，使用 cos(ln(x))/x^(1.5) 修改 @marmot 代码。为了让图表看起来更美观，我使用了一个模板：

\documentclass{standalone}
\usepackage[dvipsnames]{xcolor}%declare color here to avoid color clash with tikz
\usepackage{pgfplots}% This uses tikz
\pgfplotsset{compat=newest}% use newest version
\pgfmathdeclarefunction{f}{1}{%
\pgfmathparse{.1/x^(1.5)}%
}
\pgfplotsset{compat=newest}% use newest version
\pgfmathdeclarefunction{g}{1}{%
\pgfmathparse{0.1*cos(1200*ln(x))/x^1.5}%
}
\pgfplotsset{compat=newest}% use newest version
\pgfmathdeclarefunction{h}{1}{%
\pgfmathparse{-.1/x^(1.5)}%
}
\tikzset{Line Style1/.style={smooth,thick, dashed,samples=400}}
\tikzset{Line Style2/.style={smooth,thick, samples=800}}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
    %grid = both,%grid for major ticks (every integer) and minor ticks
    minor tick num=4,% number of hor/vert lines in a box
    every major grid/.style={Red!30, opacity=1.0},%set the color for major grid
    every minor grid/.style={ForestGreen!30, opacity=1.0},%set the color for minor grid
    height= 1\textwidth,%compress height: eg height=0.5\textwidth
    width = 1\textwidth,%compress width: eg width=0.5\textwidth
    thick,
    black,%Set the color of the main axes and numbers
    scale=1.0,
    axis lines=center,
    domain=0:4
    samples=500,
    line join=bevel,
    xmin=0,
    xmax=2,
    ymin=-4,
    ymax=4,
    %xticklabels=\empty,% remove % at beginning of line to remove x labels
    %yticklabels=\empty,% remove % at beginning of line to remove x labels
    major tick length=0pt,% Increase number adds tick mark and increases distance of numbers from the x/y axis
    minor tick length=0pt,% Increase number adds minor tick marks
    %xtick=\empty,
    %ytick=\empty,
] 
\addplot[Line Style2, color=Peach, domain=.01:2] (\x,{f(\x)}); %color names determined by dvipsnames
\addplot[Line Style2, color=NavyBlue, domain=0.05:2] (\x,{g(\x)});% in the xcolor package
\addplot[Line Style2, color=Peach, domain=0.01:2] (\x,{h(\x)});
\end{axis}
\end{tikzpicture}
\end{document}

Gummi 中运行的输出如下所示：

当您从右侧接近 y 轴时，您需要调整域的值以使图看起来赏心悦目：越接近 0，图形就越混乱。以至于它看起来像一个纯蓝色区域，而不是曲线。设置为 .05 时，图形看起来还不那么混乱。

Answer 2

下面是一些生成该图的 pgfplots 代码。

\documentclass[tikz,border=3.14mm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.16}
\begin{document}
\begin{tikzpicture}
 \begin{axis}[domain=0.01:10,no marks,axis lines=middle,smooth,
 xmax=12,xlabel=$\eta$,xtick=\empty,ytick=\empty]
  \addplot[color=blue,samples=101]  {0.1*cos(1200*ln(x))*pow(x,1.5)}; %
  \addplot[color=black] { 0.1*pow(x,1.5) };
  \addplot[color=black] {-0.1*pow(x,1.5)};
  \end{axis} 
\end{tikzpicture}
\end{document}

也可以用 Ti 绘制钾Z，我认为@DJP 会给你提供一个代码。

如果你想让物体向墙壁变大，你可以使用

\documentclass[tikz,border=3.14mm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.16}
\begin{document}
\begin{tikzpicture}
 \begin{axis}[domain=0.01:10,no marks,axis lines=middle,smooth,
 xmax=12,xlabel=$\eta$,xtick=\empty,ytick=\empty,ymin=-4.5,ymax=4.5]
  \addplot[color=blue,samples=101]  {0.1*cos(1200*ln(10-x))*pow(10-x,1.5)}; %
  \addplot[color=black] { 0.1*pow(10-x,1.5) };
  \addplot[color=black] {-0.1*pow(10-x,1.5)};
  \end{axis} 
\end{tikzpicture}
\end{document}