![我如何表示以下弹簧质量系统](https://linux22.com/image/382989/%E6%88%91%E5%A6%82%E4%BD%95%E8%A1%A8%E7%A4%BA%E4%BB%A5%E4%B8%8B%E5%BC%B9%E7%B0%A7%E8%B4%A8%E9%87%8F%E7%B3%BB%E7%BB%9F.png)
我该如何表示以下弹簧质量系统?
[
答案1
欢迎来到 TeX.SE!我想做广告3D 线圈为了那个原因。
\documentclass[tikz,border=3.14mm]{standalone}
\usetikzlibrary{decorations.pathmorphing,patterns}
\makeatletter
\newif\ifcoil@closed
\pgfkeys{%
/pgf/decoration/.cd,
3d coil color/.store in=\TDCoilColor,
3d coil color/.initial=black,
3d coil color=black,
3d coil width/.store in=\TDCoilWidth,
3d coil width/.initial=0.4pt,
3d coil width=0.4pt,
3d coil dist/.store in=\TDCoilDist,
3d coil dist/.initial=0.6pt,
3d coil dist=0.6pt,
3d coil opacity/.store in=\TDCoilOpacity,
3d coil opacity/.initial=1,
3d coil opacity=1,
3d coil closed/.code=\coil@closedtrue
}
% https://tex.stackexchange.com/a/219088/121799
\tikzset{get stroke color/.code={%
\expandafter\global% Jump over, now we have \global
\expandafter\let% Jump over now we have \global\let
\expandafter\pgfsavedstrokecolor% Jump we have \global\let\pgf...
\csname\string\color@pgfstrokecolor\endcsname% Finally expand this and put it at the end
}, % \global\let\pgf...{} in expanded form
restore stroke color/.code={\pgf@setstrokecolor#1},
}
\def\pgfpoint@onthreedcoil#1#2#3{%
\pgf@x=#1\pgfdecorationsegmentamplitude%
\pgf@x=\pgfdecorationsegmentaspect\pgf@x%
\pgf@y=#2\pgfdecorationsegmentamplitude%
\pgf@xa=0.083333333333\pgfdecorationsegmentlength%
\advance\pgf@x by#3\pgf@xa%
\advance\pgf@x by-\generaloffset pt%
}
% coil decoration
%
% Parameters: \pgfdecorationsegmentamplitude, \pgfdecorationsegmentlength,
\pgfdeclaredecoration{3d complete coil}{initial}
{
\state{initial}[width=0.5*\pgfdecorationsegmentlength,
next state=coil, persistent precomputation={% from https://tex.stackexchange.com/a/25689/121799
\pgfmathsetmacro\matchinglength{\pgfdecoratedinputsegmentlength / int(\pgfdecoratedinputsegmentlength/\pgfdecorationsegmentlength)}
\setlength{\pgfdecorationsegmentlength}{\matchinglength pt}
\tikzset{get stroke color}
\pgfmathsetmacro{\generaloffset}{\pgfdecorationsegmentlength}
\pgfmathsetmacro{\initialoffset}{1.5*\pgfdecorationsegmentlength}
\pgfmathsetmacro{\auxoffset}{2.5*\pgfdecorationsegmentlength}
}] {
% line in the back
%
\pgfsetstrokecolor{\TDCoilColor}
\pgfsetfillcolor{\TDCoilColor}
\pgfsetstrokeopacity{\TDCoilOpacity}
\pgfsetlinewidth{\TDCoilWidth}
\ifcoil@closed
\begingroup
\def\generaloffset{\auxoffset}
\pgfpathmoveto{\pgfpoint@onthreedcoil{1 }{ 1 }{15}}
\pgfpathcurveto
{\pgfpoint@onthreedcoil{1.555}{ 1 }{16}}
{\pgfpoint@onthreedcoil{2 }{ 0.555}{17}}
{\pgfpoint@onthreedcoil{2 }{ 0 }{18}}
\pgfcoordinate{TD@coilast}{\pgfpoint@onthreedcoil{2 }{ 0 }{18}}
\pgfcoordinate{TD@coilfirst}{\pgfpoint@onthreedcoil{1 }{ 1 }{15}}
\pgfusepath{stroke}
\pgfsetstrokecolor{\TDCoilColor}
\endgroup
\fi
\begingroup %
\def\generaloffset{\initialoffset}
\ifcoil@closed
\pgfpathmoveto{\pgfpointanchor{TD@coilast}{center}}
\else
\pgfpathmoveto{\pgfpointorigin}
\fi
\pgfpathcurveto
{\pgfpoint@onthreedcoil{2 }{-0.555}{7}}
{\pgfpoint@onthreedcoil{1.555}{-1 }{8}}
{\pgfpoint@onthreedcoil{1 }{-1 }{9}}
\pgfusepath{stroke}
%
% white background for front thick part
%
\pgfsetstrokeopacity{1}
\pgfsetstrokecolor{white}
\pgfsetfillcolor{white}
\pgfsetlinewidth{1.5*\TDCoilWidth+1.5*\TDCoilDist}
\pgfpathmoveto{\pgfpoint@onthreedcoil{1 }{-1 }{9}}
% draw forward
\pgfpathcurveto
{\pgfpoint@onthreedcoil{0.445}{-1 }{10}}
{\pgfpoint@onthreedcoil{0 }{-0.555}{11.25}}
{\pgfpoint@onthreedcoil{0 }{ 0 }{12.5}}
\pgfpathcurveto
{\pgfpoint@onthreedcoil{0 }{ 0.555}{13.25}}
{\pgfpoint@onthreedcoil{0.445}{ 1 }{14.25}}
{\pgfpoint@onthreedcoil{1 }{ 1 }{15}}
% draw the curve back
\pgfpathcurveto
{\pgfpoint@onthreedcoil{0.445}{ 1 }{14}}
{\pgfpoint@onthreedcoil{0 }{ 0.555}{12.75}}
{\pgfpoint@onthreedcoil{0 }{ 0 }{11.5}}
\pgfpathcurveto
{\pgfpoint@onthreedcoil{0 }{-0.555}{10.75}}
{\pgfpoint@onthreedcoil{0.445}{-1 }{10}}
{\pgfpoint@onthreedcoil{1 }{-1 }{9}}
\pgfusepath{stroke,fill}
%
% draw the thick foreground path
%
\pgfsetstrokecolor{\TDCoilColor}
\pgfsetfillcolor{\TDCoilColor}
\pgfsetstrokeopacity{\TDCoilOpacity}
\pgfpathmoveto{\pgfpoint@onthreedcoil{1 }{ 1 }{3}}
\pgfsetlinewidth{\TDCoilWidth}
% forward shifted +
\pgfpathmoveto{\pgfpoint@onthreedcoil{1 }{-1 }{9}}
\pgfpathcurveto
{\pgfpoint@onthreedcoil{0.445}{-1 }{10}}
{\pgfpoint@onthreedcoil{0 }{-0.555}{11.25}}
{\pgfpoint@onthreedcoil{0 }{ 0 }{12.5}}
\pgfpathcurveto
{\pgfpoint@onthreedcoil{0 }{ 0.555}{13.25}}
{\pgfpoint@onthreedcoil{0.445}{ 1 }{14.25}}
{\pgfpoint@onthreedcoil{1 }{ 1 }{15}}
% draw the curve back shfted -
\pgfpathcurveto
{\pgfpoint@onthreedcoil{0.445}{ 1 }{14}}
{\pgfpoint@onthreedcoil{0 }{ 0.555}{12.75}}
{\pgfpoint@onthreedcoil{0 }{ 0 }{11.5}}
\pgfpathcurveto
{\pgfpoint@onthreedcoil{0 }{-0.555}{10.75}}
{\pgfpoint@onthreedcoil{0.445}{-1 }{10}}
{\pgfpoint@onthreedcoil{1 }{-1 }{9}}
\pgfusepath{stroke,fill}
\pgfpathmoveto{\pgfpoint@onthreedcoil{1 }{ 1 }{15}}
\pgfpathcurveto
{\pgfpoint@onthreedcoil{1.555}{ 1 }{16}}
{\pgfpoint@onthreedcoil{2 }{ 0.555}{17}}
{\pgfpoint@onthreedcoil{2 }{ 0 }{18}}
\pgfcoordinate{TD@coilast}{\pgfpoint@onthreedcoil{2 }{ 0 }{18}}
\pgfusepath{stroke}
\endgroup
}
\state{coil}[switch if less than=%
1.9*\pgfdecorationsegmentlength to last,
width=+\pgfdecorationsegmentlength]
{ % line in the back
%
\pgfsetstrokecolor{\TDCoilColor}
\pgfsetfillcolor{\TDCoilColor}
\pgfsetstrokeopacity{\TDCoilOpacity}
\pgfpathmoveto{\pgfpointanchor{TD@coilast}{center}}
\pgfsetlinewidth{\TDCoilWidth}
\pgfpathcurveto
{\pgfpoint@onthreedcoil{2 }{-0.555}{7}}
{\pgfpoint@onthreedcoil{1.555}{-1 }{8}}
{\pgfpoint@onthreedcoil{1 }{-1 }{9}}
\pgfusepath{stroke}
%
% white background for front thick part
%
\pgfsetstrokeopacity{1}
\pgfsetstrokecolor{white}
\pgfsetfillcolor{white}
\pgfsetlinewidth{1.5*\TDCoilWidth+1.5*\TDCoilDist}
\pgfpathmoveto{\pgfpoint@onthreedcoil{1 }{ 1 }{3}}
\pgfpathmoveto{\pgfpoint@onthreedcoil{1 }{-1 }{9}}
% draw forward
\pgfpathcurveto
{\pgfpoint@onthreedcoil{0.445}{-1 }{10}}
{\pgfpoint@onthreedcoil{0 }{-0.555}{11.25}}
{\pgfpoint@onthreedcoil{0 }{ 0 }{12.5}}
\pgfpathcurveto
{\pgfpoint@onthreedcoil{0 }{ 0.555}{13.25}}
{\pgfpoint@onthreedcoil{0.445}{ 1 }{14.25}}
{\pgfpoint@onthreedcoil{1 }{ 1 }{15}}
% draw the curve back
\pgfpathcurveto
{\pgfpoint@onthreedcoil{0.445}{ 1 }{14}}
{\pgfpoint@onthreedcoil{0 }{ 0.555}{12.75}}
{\pgfpoint@onthreedcoil{0 }{ 0 }{11.5}}
\pgfpathcurveto
{\pgfpoint@onthreedcoil{0 }{-0.555}{10.75}}
{\pgfpoint@onthreedcoil{0.445}{-1 }{10}}
{\pgfpoint@onthreedcoil{1 }{-1 }{9}}
\pgfusepath{stroke,fill}
%
% draw the thick foreground path
%
\pgfsetstrokecolor{\TDCoilColor}
\pgfsetfillcolor{\TDCoilColor}
\pgfsetstrokeopacity{\TDCoilOpacity}
\pgfpathmoveto{\pgfpoint@onthreedcoil{1 }{ 1 }{3}}
\pgfsetlinewidth{\TDCoilWidth}
% forward shifted +
\pgfpathmoveto{\pgfpoint@onthreedcoil{1 }{-1 }{9}}
\pgfpathcurveto
{\pgfpoint@onthreedcoil{0.445}{-1 }{10}}
{\pgfpoint@onthreedcoil{0 }{-0.555}{11.25}}
{\pgfpoint@onthreedcoil{0 }{ 0 }{12.5}}
\pgfpathcurveto
{\pgfpoint@onthreedcoil{0 }{ 0.555}{13.25}}
{\pgfpoint@onthreedcoil{0.445}{ 1 }{14.25}}
{\pgfpoint@onthreedcoil{1 }{ 1 }{15}}
% draw the curve back shfted -
\pgfpathcurveto
{\pgfpoint@onthreedcoil{0.445}{ 1 }{14}}
{\pgfpoint@onthreedcoil{0 }{ 0.555}{12.75}}
{\pgfpoint@onthreedcoil{0 }{ 0 }{11.5}}
\pgfpathcurveto
{\pgfpoint@onthreedcoil{0 }{-0.555}{10.75}}
{\pgfpoint@onthreedcoil{0.445}{-1 }{10}}
{\pgfpoint@onthreedcoil{1 }{-1 }{9}}
\pgfusepath{stroke,fill}
\pgfpathmoveto{\pgfpoint@onthreedcoil{1 }{ 1 }{15}}
\pgfpathcurveto
{\pgfpoint@onthreedcoil{1.555}{ 1 }{16}}
{\pgfpoint@onthreedcoil{2 }{ 0.555}{17}}
{\pgfpoint@onthreedcoil{2 }{ 0 }{18}}
\pgfusepath{stroke}
\pgfcoordinate{TD@coilast}{\pgfpoint@onthreedcoil{2 }{ 0 }{18}}
}
\state{last}[next state=final]
{ % line in the back
%
\pgfsetstrokecolor{\TDCoilColor}
\pgfsetfillcolor{\TDCoilColor}
\pgfsetstrokeopacity{\TDCoilOpacity}
\pgfpathmoveto{\pgfpointanchor{TD@coilast}{center}}
\pgfsetlinewidth{\TDCoilWidth}
\pgfpathcurveto
{\pgfpoint@onthreedcoil{2 }{-0.555}{7}}
{\pgfpoint@onthreedcoil{1.555}{-1 }{8}}
{\pgfpoint@onthreedcoil{1 }{-1 }{9}}
\pgfusepath{stroke}
%
% draw the thick foreground path
%
\ifcoil@closed %\pgfpointanchor{TD@coilfirst}{center}
%
% white background for front thick part
%
\pgfsetstrokeopacity{1}
\pgfsetstrokecolor{white}
\pgfsetfillcolor{white}
\pgfsetlinewidth{1.5*\TDCoilWidth+1.5*\TDCoilDist}
\pgfpathmoveto{\pgfpoint@onthreedcoil{1 }{ 1 }{3}}
\pgfpathmoveto{\pgfpoint@onthreedcoil{1 }{-1 }{9}}
% draw forward
\pgfpathcurveto
{\pgfpoint@onthreedcoil{0.445}{-1 }{10}}
{\pgfpoint@onthreedcoil{0 }{-0.555}{11.25}}
{\pgfpoint@onthreedcoil{0 }{ 0 }{12.5}}
\pgfpathcurveto
{\pgfpoint@onthreedcoil{0 }{ 0.555}{13.25}}
{\pgfpoint@onthreedcoil{0.445}{ 1 }{14.25}}
{\pgfpointanchor{TD@coilfirst}{center}}
% draw the curve back
\pgfpathcurveto
{\pgfpoint@onthreedcoil{0.445}{ 1 }{14}}
{\pgfpoint@onthreedcoil{0 }{ 0.555}{12.75}}
{\pgfpoint@onthreedcoil{0 }{ 0 }{11.5}}
\pgfpathcurveto
{\pgfpoint@onthreedcoil{0 }{-0.555}{10.75}}
{\pgfpoint@onthreedcoil{0.445}{-1 }{10}}
{\pgfpoint@onthreedcoil{1 }{-1 }{9}}
\pgfusepath{stroke,fill}
\pgfsetstrokecolor{\TDCoilColor}
\pgfsetfillcolor{\TDCoilColor}
\pgfsetstrokeopacity{\TDCoilOpacity}
\pgfpathmoveto{\pgfpoint@onthreedcoil{1 }{ 1 }{3}}
\pgfsetlinewidth{\TDCoilWidth}
% forward shifted +
\pgfpathmoveto{\pgfpoint@onthreedcoil{1 }{-1 }{9}}
\pgfpathcurveto
{\pgfpoint@onthreedcoil{0.445}{-1 }{10}}
{\pgfpoint@onthreedcoil{0 }{-0.555}{11.25}}
{\pgfpoint@onthreedcoil{0 }{ 0 }{12.5}}
\pgfpathcurveto
{\pgfpoint@onthreedcoil{0 }{ 0.555}{13.25}}
{\pgfpoint@onthreedcoil{0.445}{ 1 }{14.25}}
{\pgfpointanchor{TD@coilfirst}{center}}
% draw the curve back shifted
\pgfpathcurveto
{\pgfpoint@onthreedcoil{0.445}{ 1 }{14}}
{\pgfpoint@onthreedcoil{0 }{ 0.555}{12.75}}
{\pgfpoint@onthreedcoil{0 }{ 0 }{11.5}}
\pgfpathcurveto
{\pgfpoint@onthreedcoil{0 }{-0.555}{10.75}}
{\pgfpoint@onthreedcoil{0.445}{-1 }{10}}
{\pgfpoint@onthreedcoil{1 }{-1 }{9}}
\pgfusepath{stroke,fill}
\else
%
% white background for front thick part
%
\pgfsetstrokeopacity{1}
\pgfsetstrokecolor{white}
\pgfsetfillcolor{white}
\pgfsetlinewidth{1.5*\TDCoilWidth+1.5*\TDCoilDist}
\pgfpathmoveto{\pgfpoint@onthreedcoil{1 }{ 1 }{3}}
\pgfpathmoveto{\pgfpoint@onthreedcoil{1 }{-1 }{9}}
% draw forward
\pgfpathcurveto
{\pgfpoint@onthreedcoil{0.445}{-1 }{10}}
{\pgfpoint@onthreedcoil{0 }{-0.555}{11.25}}
{\pgfpoint@onthreedcoil{0 }{ 0 }{12.5}}
\pgfpathcurveto
{\pgfpoint@onthreedcoil{0 }{ 0.555}{13.25}}
{\pgfpoint@onthreedcoil{0.445}{ 1 }{14.25}}
{\pgfpoint@onthreedcoil{1 }{ 1 }{15}}
% draw the curve back
\pgfpathcurveto
{\pgfpoint@onthreedcoil{0.445}{ 1 }{14}}
{\pgfpoint@onthreedcoil{0 }{ 0.555}{12.75}}
{\pgfpoint@onthreedcoil{0 }{ 0 }{11.5}}
\pgfpathcurveto
{\pgfpoint@onthreedcoil{0 }{-0.555}{10.75}}
{\pgfpoint@onthreedcoil{0.445}{-1 }{10}}
{\pgfpoint@onthreedcoil{1 }{-1 }{9}}
\pgfusepath{stroke,fill}
\pgfsetstrokecolor{\TDCoilColor}
\pgfsetfillcolor{\TDCoilColor}
\pgfsetstrokeopacity{\TDCoilOpacity}
\pgfpathmoveto{\pgfpoint@onthreedcoil{1 }{ 1 }{3}}
\pgfsetlinewidth{\TDCoilWidth}
% forward shifted +
\pgfpathmoveto{\pgfpoint@onthreedcoil{1 }{-1 }{9}}
\pgfpathcurveto
{\pgfpoint@onthreedcoil{0.445}{-1 }{10}}
{\pgfpoint@onthreedcoil{0 }{-0.555}{11.25}}
{\pgfpoint@onthreedcoil{0 }{ 0 }{12.5}}
\pgfpathcurveto
{\pgfpoint@onthreedcoil{0 }{ 0.555}{13.25}}
{\pgfpoint@onthreedcoil{0.445}{ 1 }{14.25}}
{\pgfpoint@onthreedcoil{1 }{ 1 }{15}}
% draw the curve back shifted
\pgfpathcurveto
{\pgfpoint@onthreedcoil{0.445}{ 1 }{14}}
{\pgfpoint@onthreedcoil{0 }{ 0.555}{12.75}}
{\pgfpoint@onthreedcoil{0 }{ 0 }{11.5}}
\pgfpathcurveto
{\pgfpoint@onthreedcoil{0 }{-0.555}{10.75}}
{\pgfpoint@onthreedcoil{0.445}{-1 }{10}}
{\pgfpoint@onthreedcoil{1 }{-1 }{9}}
\pgfusepath{stroke,fill}
\fi
\pgfpathmoveto{\pgfpoint@onthreedcoil{1 }{ 1 }{15}}
\ifcoil@closed %TD@coilfirst
\else
\pgfpathcurveto
{\pgfpoint@onthreedcoil{1.555}{ 1 }{16}}
{\pgfpoint@onthreedcoil{2 }{ 0.555}{17}}
{\pgfpoint@onthreedcoil{2 }{ 0 }{18}}
\fi
\pgfusepath{stroke}
%\pgfcoordinate{TD@coilast}{\pgfpoint@onthreedcoil{2 }{ 0 }{18}}
}
\state{final}
{
\pgfpathmoveto{\pgfpointdecoratedpathlast}
\tikzset{restore stroke color/.expand once=\pgfsavedstrokecolor}
}
}
\makeatother
\begin{document}
\begin{tikzpicture}[decoration={3d coil color=black,aspect=0.35, segment length=3mm,
amplitude=3mm,3d complete coil},thick,font=\sffamily]
% left
\fill[pattern=north east lines] (-1,7) rectangle (1,7.5);
\draw[very thick] (-1,7) -- (1,7);
\node[anchor=south] at (0,7.5) {Equilibrium};
\draw (0,4) -- (0,5) coordinate[midway](m1);
\draw (0,1) -- (0,0.5) coordinate(m2);
\fill (m1) circle (2pt) node[left] {$m_1$};
\fill (m2) circle (2pt) node[left] {$m_2$};
\draw[decorate,segment length=2mm] (0,5) -- (0,7);
\draw[decorate,segment length=3mm] (0,1) -- (0,4.1);
% right
\fill[pattern=north east lines] (2,7) rectangle (4,7.5);
\draw[very thick] (2,7) -- (4,7);
\node[anchor=south] at (3,7.5) {Motion};
\draw (3,3) -- (3,4) coordinate[midway](m1');
\draw (3,0) -- (3,-0.5) coordinate(m2');
\fill (m1') circle (2pt) (m2') circle (2pt);
\draw[decorate,segment length=3mm] (3,4) -- (3,7);
\draw[decorate,segment length=3mm] (3,0) -- (3,3);
% middle
\draw[dashed] (m1) -- (2.8,0 |- m1) coordinate[pos=0.9] (x1top);
\draw[-latex] (x1top) -- (x1top |-m1') node[left]{$x_1$};
\draw[dashed] (m2) -- (2.8,0 |- m2) coordinate[pos=0.9] (x2top);
\draw[-latex] (x2top) -- (x2top |-m2') node[left]{$x_2$};
\end{tikzpicture}
\end{document}
答案2
受@marmot 回答启发而来的一个不太复杂的解决方案:
\documentclass[tikz,border=3.14mm]{standalone}
\usetikzlibrary{decorations.pathmorphing,patterns}
\tikzset{
spring/.style={very thick,
decorate,
decoration={coil,
amplitude=1.5mm,
segment length=2mm,
pre length=3mm,
post length=3mm,
aspect=0.6,
}},
%
equilibrium state/.style={spring},
%
motion state/.style={spring,/pgf/decoration/segment length=2.5mm},
%
ground/.style={pattern=north east lines},
}
\begin{document}
\begin{tikzpicture}
% left
\fill[ground] (-1,7) rectangle (1,7.5);
\draw[very thick] (-1,7) -- (1,7);
\node[anchor=south] at (0,7.5) {Equilibrium};
\draw[ equilibrium state] (0,4)coordinate(m1) -- (0,7);
\draw[ equilibrium state] (0,1)coordinate(m2) -- (m1);
\fill (m1) circle (2pt) node[left] {$m_1$};
\fill (m2) circle (2pt) node[left] {$m_2$};
% right
\fill[ground] (2,7) rectangle (4,7.5);
\draw[very thick] (2,7) -- (4,7);
\node[anchor=south] at (3,7.5) {Motion};
\draw[ motion state] (3,3.5)coordinate(m'1) -- (3,7);
\draw[ motion state] (3,0)coordinate(m'2) -- (m'1);
\fill (m'1) circle (2pt) node[right] {$m_1$};
\fill (m'2) circle (2pt) node[right] {$m_2$};
% middle
\draw[dashed] (m1) -- (2.8,0 |- m1) coordinate[pos=0.9] (x1top);
\draw[-latex] (x1top) -- (x1top |-m'1) node[left]{$x_1$};
\draw[dashed] (m2) -- (2.8,0 |- m2) coordinate[pos=0.9] (x2top);
\draw[-latex] (x2top) -- (x2top |-m'2) node[left]{$x_2$};
\end{tikzpicture}
\end{document}