Some diagrams of basic physics problems involving masses and springs, hanging both horizontally and vertically, as well as a mass connected to two springs, to study Hooke’s law and simple harmonic oscillations.
For more related figures, please see the “forces” or “Newton’s laws” tag.
Horizontal spring
Vertical spring
Double spring
Edit and compile if you like:
% Author: Izaak Neutelings (September 2020)
\documentclass[border=3pt,tikz]{standalone}
\usepackage{physics}
\usepackage{tikz}
\usepackage[outline]{contour} % glow around text
\usetikzlibrary{patterns,snakes}
\usetikzlibrary{arrows.meta} % for arrow size
\contourlength{0.4pt}
\colorlet{xcol}{blue!70!black}
\colorlet{darkblue}{blue!40!black}
\colorlet{myred}{red!65!black}
\tikzstyle{mydashed}=[xcol,dashed,line width=0.25,dash pattern=on 2.2pt off 2.2pt]
\tikzstyle{axis}=[->,thick] %line width=0.6
\tikzstyle{ell}=[{Latex[length=3.3,width=2.2]}-{Latex[length=3.3,width=2.2]},line width=0.3]
\tikzstyle{dx}=[-{Latex[length=3.3,width=2.2]},darkblue,line width=0.3]
\tikzstyle{ground}=[preaction={fill,top color=black!10,bottom color=black!5,shading angle=20},
fill,pattern=north east lines,draw=none,minimum width=0.3,minimum height=0.6]
\tikzstyle{mass}=[line width=0.6,red!30!black,fill=red!40!black!10,rounded corners=1,
top color=red!40!black!20,bottom color=red!40!black!10,shading angle=20]
\tikzstyle{spring}=[line width=0.8,blue!7!black!80,snake=coil,segment amplitude=5,segment length=5,line cap=round]
\tikzset{>=latex} % for LaTeX arrow head
\tikzstyle{force}=[->,myred,very thick,line cap=round]
\def\tick#1#2{\draw[thick] (#1)++(#2:0.1) --++ (#2-180:0.2)}
\begin{document}
% HORIZONTAL spring
\begin{tikzpicture}
\def\H{1} % wall height
\def\T{0.3} % wall thickness
\def\W{2.6} % ground length
\def\D{0.25} % ground depth
\def\h{0.6} % mass height
\def\w{0.7} % mass width
\def\x{1.6} % mass x position
\draw[spring] (0,\h/2) --++ (\x,0);
\draw[ground] (0,0) |-++ (-\T,\H) |-++ (\T+\W,-\H-\D) -- (\W,0) -- cycle;
\draw (0,\H) -- (0,0) -- (\W,0);
\draw[mass] (\x,0) rectangle++ (\w,\h) node[midway] {$m$};
\end{tikzpicture}
% HORIZONTAL spring - axis, rest position
\begin{tikzpicture}
\def\H{1.1} % wall height
\def\T{0.3} % wall thickness
\def\W{3.7} % ground length
\def\D{0.25} % ground depth
\def\h{0.7} % mass height
\def\w{0.8} % mass width
\def\x{2.0} % mass x position
\def\y{1.22*\H} % x axis y position
% AXIS
\draw[mydashed] (\x,0.9*\h) --++ (0,\y-0.9*\h);
\draw[axis] (\x-0.4*\W,\y) -- (\x+0.4*\W,\y) node[right] {$x$};
\tick{\x,\y}{-90} node[scale=0.8,above=-1] {$0$};
\draw[ell] (0,1.3*\h) --++ (\x,0) node[midway,fill=white,inner sep=0] {$\ell_0$};
% SPRING & MASS
\draw[spring] (0,\h/2) --++ (\x,0);
\draw[ground] (0,0) |-++ (-\T,\H) |-++ (\T+\W,-\H-\D) -- (\W,0) -- cycle;
\draw (0,\H) -- (0,0) -- (\W,0);
\draw[mass] (\x,0) rectangle++ (\w,\h) node[midway] {$m$};
\end{tikzpicture}
% HORIZONTAL spring - axis, extended
\begin{tikzpicture}
\def\H{1.1} % wall height
\def\T{0.3} % wall thickness
\def\W{3.9} % ground length
\def\D{0.25} % ground depth
\def\h{0.7} % mass height
\def\w{0.8} % mass width
\def\x{2.0} % mass x position
\def\dx{0.8} % extension
\def\y{1.22*\H} % x axis y position
\def\F{0.8} % force
% AXIS
\draw[mydashed] (\x,0) --++ (0,\y) (\x+\dx,0) --++ (0,1.1*\y);
\draw[axis] (\x-0.4*\W,\y) -- (\x+0.4*\W,\y) node[right] {$x$};
\tick{\x,\y}{-90} node[scale=0.8,above=-1] {$0$};
\draw[ell] (0,1.3*\h) --++ (\x,0) node[midway,fill=white,inner sep=0] {$\ell_0$};
\draw[dx] (\x,1.6*\h) --++ (\dx,0) node[pos=0.45,fill=white,inner sep=0] {$x$};
% SPRING & MASS
\draw[spring,segment length=7.5] (0,\h/2) --++ (\x+\dx,0);
\draw[ground] (0,0) |-++ (-\T,\H) |-++ (\T+\W,-\H-\D) -- (\W,0) -- cycle;
\draw (0,\H) -- (0,0) -- (\W,0);
\draw[mass] (\x+\dx,0) rectangle++ (\w,\h) node[midway] {$m$};
\draw[force] (\x+\dx+0.2*\w,0.9*\h) --++ (-\F,0) node[midway,right=1,above=-1] {$\vb{F}$};
\end{tikzpicture}
% HORIZONTAL spring - axis, compressed
\begin{tikzpicture}
\def\H{1.1} % wall height
\def\T{0.3} % wall thickness
\def\W{3.9} % ground length
\def\D{0.2} % ground depth
\def\h{0.7} % mass height
\def\w{0.8} % mass width
\def\x{2.0} % mass x position
\def\dx{0.9} % extension
\def\y{1.22*\H} % x axis y position
\def\F{0.8} % force
% AXIS
\draw[mydashed] (\x,0) --++ (0,\y) (\x-\dx,0) --++ (0,1.1*\y);
\draw[axis] (\x-0.4*\W,\y) -- (\x+0.4*\W,\y) node[right] {$x$};
\tick{\x,\y}{-90} node[scale=0.8,above=-1] {$0$};
\draw[ell] (0,1.3*\h) --++ (\x,0) node[pos=0.4,fill=white,inner sep=0] {$\ell_0$};
\draw[dx] (\x,1.6*\h) --++ (-\dx,0)
node[pos=0.45,fill=white,inner sep=0,scale=0.9] {$x$};
% SPRING & MASS
\draw[spring,segment length=2.9] (0,\h/2) --++ (\x-\dx,0);
\draw[ground] (0,0) |-++ (-\T,\H) |-++ (\T+\W,-\H-\D) -- (\W,0) -- cycle;
\draw (0,\H) -- (0,0) -- (\W,0);
\draw[mass] (\x-\dx,0) rectangle++ (\w,\h) node[midway] {$m$};
\draw[force] (\x-\dx+0.8*\w,0.8*\h) --++ (\F,0) node[below=0,right=-1] {$\vb{F}$};
\end{tikzpicture}
% VERTICAL spring
\begin{tikzpicture}
\def\H{0.25} % ceiling height
\def\W{1.0} % ceiling width
\def\h{0.7} % mass height
\def\w{0.6} % mass width
\def\y{1.6} % mass width
\draw[spring] (0,0) -- (0,-\y);
\draw[ground] (-\W/2,0) rectangle++ (\W,\H);
\draw (-\W/2,0) --++ (\W,0);
\draw[mass] (-\w/2,-\y) rectangle++ (\w,-\h) node[midway] {$m$};
\end{tikzpicture}
% VERTICAL spring - no mass
\begin{tikzpicture}
\def\H{0.25} % ceiling height
\def\W{1.0} % ceiling width
\def\h{0.7} % mass height
\def\w{0.6} % mass width
\def\y{1.6} % mass width
\draw[spring] (0,0) -- (0,-\y);
\draw[ground] (-\W/2,0) rectangle++ (\W,\H);
\draw (-\W/2,0) --++ (\W,0);
\draw[ell] (-0.4*\W,0) --++ (0,-\y) node[midway,fill=white,inner sep=0] {$\ell_0$};
\end{tikzpicture}
% VERTICAL spring - extension at rest
\begin{tikzpicture}
\def\H{0.25} % ceiling height
\def\W{1.0} % ceiling width
\def\h{0.7} % mass height
\def\w{0.6} % mass width
\def\y{2.1} % mass width
\def\F{0.8} % force magnitude
\draw[spring,segment length=7] (0,0) -- (0,-\y);
\draw[ground] (-\W/2,0) rectangle++ (\W,\H);
\draw (-\W/2,0) --++ (\W,0);
\draw[mass] (-\w/2,-\y) rectangle++ (\w,-\h) node[midway] {$m$};
\draw[force] (0.4*\w,-\y-0.3*\h) --++ (0,\F) node[below right=0] {$\vb{F}$}; %=-k\Delta\ell\vu{y}
\draw[force] (0.3*\w,-\y-0.7*\h) --++ (0,-\F) node[above right=0] {$m\vb{g}$}; %=mg\vu{y}
\draw[ell] (-0.4*\W,0) --++ (0,-0.75*\y) node[midway,fill=white,inner sep=0] {$\ell_0$};
\draw[ell] (-0.4*\W,-0.75*\y) --++ (0,-0.25*\y) node[midway,left=0] {$\Delta\ell$};
\end{tikzpicture}
% VERTICAL spring - extension
\begin{tikzpicture}
\def\H{0.25} % ceiling height
\def\W{2.6} % ceiling width
\def\h{0.7} % mass height
\def\w{0.6} % mass width
\def\l{0.5*\y} % rest length without weight
\def\dl{0.7*\y} % rest length with weight
\def\y{2.4} % mass y position
\def\xy{0.38*\W} % mass y position
\def\F{0.8} % force magnitude
\draw[spring,segment length=7.2] (0,0) -- (0,-\y);
\draw[ground] (-\W/2,0) rectangle++ (\W,\H);
\draw (-\W/2,0) --++ (\W,0);
\draw[axis] (-\xy,0) --++ (0,-\y-0.7*\h) node[left] {$y$};
\draw[axis] ( \xy,0) --++ (0,-\y-0.7*\h) node[right] {$y'$};
\draw[mydashed] (-\xy,-\l) --++ (2.3*\xy,0);
\draw[mydashed] (-\xy,-\dl) --++ (2*\xy,0);
\draw[mydashed] (-0.46*\W,-\y) --++ (0.92*\W,0);
\tick{-\xy,-\l}{0} node[left] {$0$};
\tick{-\xy,-\dl}{0} node[left] {$y_0$};
\tick{ \xy,-\dl}{180} node[right] {$0$};
\draw[mass] (-\w/2,-\y) rectangle++ (\w,-\h) node[midway] {$m$};
\draw[force] (0.4*\w,-\y-0.3*\h) --++ (0,1.6*\F) node[pos=0.9,right=0] {$\vb{F}$};
\draw[force] (0.3*\w,-\y-0.7*\h) --++ (0,-\F) node[above right=0] {$m\vb{g}$};
\draw[ell] (0.45*\W,0) --++ (0,-\l) node[midway,right=-2] {$\ell_0$};
%\draw[ell] (-0.4*\W,-0.75*\y) --++ (0,-0.25*\y) node[midway,left=1] {$y_0$};
\end{tikzpicture}
% HORIZONTAL doubly extended spring (rest position)
\begin{tikzpicture}
\def\H{1.2} % wall height
\def\T{0.3} % wall thickness
\def\W{4.2} % ground length
\def\D{0.25} % ground depth
\def\h{0.6} % mass height
\def\w{0.75} % mass width
\def\x{1.85} % mass x position
\def\lz{1.25} % rest length (ell_0)
\def\ly{0.87*\H} % ell_0 y position
\def\y{1.19*\H} % x axis y position
% AXIS
\draw[mydashed] (\x,0) --++ (0,1.14*\y) (\x+\w,0) --++ (0,1.14*\y);
\draw[axis] (0.15*\W,\y) --++ (0.7*\W,0) node[right=-2] {$x$};
\tick{\x+\w/2,\y}{-90} node[scale=0.8,above=-1] {$0$};
\draw[ell] (0,\ly) --++ (\lz,0) node[midway,fill=white,inner sep=0] {$\ell_0$};
\draw[ell] (\W,\ly) --++ (-\lz,0) node[midway,fill=white,inner sep=0] {$\ell_0$};
\draw[dx] (\lz,1.04*\ly) --++ (\x-\lz,0) node[pos=0.45,above=-2] {$x_1$};
\draw[dx] (\W-\lz,1.04*\ly) --++ (\lz+\x+\w-\W,0) node[pos=0.4,above=-2] {$x_2$};
% SPRINGS & MASS
\draw[spring,segment length=6] (0,\h/2) --++ (\x,0) node[pos=0.3,above=3] {$k_1$};
\draw[spring,segment length=6] (\W,\h/2) --++ (\x+\w-\W,0) node[pos=0.3,above=3] {$k_2$};
\draw[ground] (0,0) |-++ (-\T,\H) |-++ (2*\T+\W,-\H-\D) |-++
(-\T,\H+\D) --++ (0,-\H) -- cycle;
\draw (0,\H) -- (0,0) -- (\W,0) --++ (0,\H);
\draw[mass] (\x,0) rectangle++ (\w,\h) node[midway] {$m$};
\draw[force] (\x+0.1*\w,0.9*\h) --++ (-0.2*\W,0) node[pos=0.65,above=-1] {\contour{white}{$-k_1x_1$}};
\draw[force] (\x+0.9*\w,0.9*\h) --++ ( 0.2*\W,0) node[pos=0.40,above=-1] {\contour{white}{$-k_2x_2$}};
\end{tikzpicture}
% HORIZONTAL doubly compressed spring (rest position)
\begin{tikzpicture}
\def\H{1.2} % wall height
\def\T{0.3} % wall thickness
\def\W{4.2} % ground length
\def\D{0.25} % ground depth
\def\h{0.6} % mass height
\def\w{0.85} % mass width
\def\x{1.62} % mass x position
\def\lz{2.03} % rest length (ell_0)
\def\ly{0.87*\H} % ell_0 y position
\def\y{1.19*\H} % x axis y position
% AXIS
\draw[mydashed] (\x,0) --++ (0,1.14*\y) (\x+\w,0) --++ (0,1.14*\y);
\draw[axis] (0.15*\W,\y) --++ (0.7*\W,0) node[right=-2] {$x$};
\tick{\x+\w/2,\y}{-90} node[scale=0.8,above=-1] {$0$};
\draw[ell] (0,\ly) --++ (\lz,0) node[pos=0.45,fill=white,inner sep=0] {$\ell_0$};
\draw[ell] (\W,\ly) --++ (-\lz,0) node[pos=0.45,fill=white,inner sep=0] {$\ell_0$};
\draw[dx] (\lz,1.06*\ly) --++ (\x-\lz,0) node[pos=0.4,above=-2] {$x_1$};
\draw[dx] (\W-\lz,1.06*\ly) --++ (\lz+\x+\w-\W,0) node[pos=0.7,above=-2] {\contour{white}{$x_2$}};
% SPRINGS & MASS
\draw[spring,segment length=2.9] (0,\h/2) --++ (\x,0) node[pos=0.42,above=3] {$k_1$};
\draw[spring,segment length=2.9] (\W,\h/2) --++ (\x+\w-\W,0) node[pos=0.35,above=3] {$k_2$};
\draw[ground] (0,0) |-++ (-\T,\H) |-++ (2*\T+\W,-\H-\D) |-++
(-\T,\H+\D) --++ (0,-\H) -- cycle;
\draw (0,\H) -- (0,0) -- (\W,0) --++ (0,\H);
\draw[mass] (\x,0) rectangle++ (\w,\h) node[midway] {$m$};
\draw[force] (\x+0.65*\w,0.9*\h) --++ ( 0.2*\W,0) node[pos=0.55,above=-1] {\contour{white}{$-k_1x_1$}};
\draw[force] (\x+0.35*\w,0.9*\h) --++ (-0.2*\W,0) node[pos=0.60,above=-1] {\contour{white}{$-k_2x_2$}};
%\draw[force] (\x+0.7*\w,0.1*\h) --++ (-0.2*\W,0) node[pos=0.5,below=0] {\contour{white}{$-k_2x_2$}};
\end{tikzpicture}
% HORIZONTAL double spring
\begin{tikzpicture}
\def\H{0.8} % wall height
\def\T{0.3} % wall thickness
\def\W{4.2} % ground length
\def\D{0.25} % ground depth
\def\h{0.6} % mass height
\def\w{0.8} % mass width
\def\x{2.2} % mass x position
\draw[spring,segment length=7.0] (0,\h/2) --++ (\x,0) node[midway,above=4] {$k_1$};
\draw[spring,segment length=2.9] (\W,\h/2) --++ (\x+\w-\W,0) node[midway,above=4] {$k_2$};
\draw[ground] (0,0) |-++ (-\T,\H) |-++ (2*\T+\W,-\H-\D) |-++
(-\T,\H+\D) --++ (0,-\H) -- cycle;
\draw (0,\H) -- (0,0) -- (\W,0) --++ (0,\H);
\draw[mass] (\x,0) rectangle++ (\w,\h) node[midway] {$m$};
%\draw[force] (\x+0.1*\w,0.9*\h) --++ (-0.4*\W,0) node[midway,above=0] {$-k_1\vb{x}$};
%\draw[force] (\x+0.9*\w,0.9*\h) --++ ( 0.2*\W,0) node[midway,above=0] {$-k_2\vb{x}$};
\end{tikzpicture}
% HORIZONTAL double spring - lengths
\begin{tikzpicture}
\def\H{1.2} % wall height
\def\T{0.3} % wall thickness
\def\W{4.2} % ground length
\def\D{0.25} % ground depth
\def\h{0.6} % mass height
\def\w{0.8} % mass width
\def\x{2.2} % mass x position
\pgfmathsetmacro\dx{\x+(\w-\W)/2} % extension
\pgfmathsetmacro\lz{\x-\dx} % rest length (ell_0)
\def\ly{0.87*\H} % ell_0 y position
\def\y{1.19*\H} % x axis y position
% AXIS
\draw[mydashed] (\x,0) --++ (0,1.14*\y) (\x+\w,0) --++ (0,1.14*\y);
\draw[axis] (0.15*\W,\y) --++ (0.7*\W,0) node[right=-2] {$x$};
\tick{\lz+\w/2,\y}{-90} node[scale=0.8,above=-1] {$0$};
\draw[ell] (0,\ly) --++ (\lz,0) node[midway,fill=white,inner sep=0] {$\ell_0$};
\draw[ell] (\W,\ly) --++ (\lz+\w-\W,0) node[pos=0.45,fill=white,inner sep=0] {$\ell_0$};
\draw[dx] (\lz,1.06*\ly) --++ (\dx,0) node[pos=0.45,above=-2] {$x$};
\draw[dx] (\lz+\w,1.06*\ly) --++ (\dx,0) node[pos=0.45,above=-2] {$x$};
% SPRINGS & MASS
\draw[spring,segment length=7.0] (0,\h/2) --++ (\x,0) node[pos=0.42,above=3] {$k_1$};
\draw[spring,segment length=2.9] (\W,\h/2) --++ (\x+\w-\W,0) node[pos=0.5,above=3] {$k_2$};
\draw[ground] (0,0) |-++ (-\T,\H) |-++ (2*\T+\W,-\H-\D) |-++
(-\T,\H+\D) --++ (0,-\H) -- cycle;
\draw (0,\H) -- (0,0) -- (\W,0) --++ (0,\H);
\draw[mass] (\x,0) rectangle++ (\w,\h) node[midway] {$m$};
\draw[force] (\x+0.07*\w,0.9*\h) --++ (-0.15*\W,0) node[left=0,above=-1] {\contour{white}{$-k_1x$}};
\draw[force] (\x+0.93*\w,0.9*\h) --++ (-0.15*\W,0) node[pos=0.47,above=-1] {\contour{white}{$-k_2x$}};
\end{tikzpicture}
\end{document}
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