"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"%%gnuplot\n",
"# for a clean start, as gnuplot may remember things from previous scripts\n",
"reset\n",
"\n",
"# set parameters controlling the appearance of the graphs\n",
"set xrange [-2.1*pi:2.1*pi]\n",
"set yrange [-1.4:1.4]\n",
"set samples 2001\n",
"set key below\n",
"set zeroaxis\n",
"\n",
"# define the Fourier series' expansion iteratively: sin(x)+sin(3x)/3+sin(5x)/5+...\n",
"f(x,n) = (n==1) ? (4/pi)*sin(x) : f(x,n-1) + (4/pi)*sin((2*n-1)*x)/(2*n-1)\n",
"\n",
"# plot the original square wave, and a couple of interesting approximations\n",
"plot sgn(sin(x)) t 'square wave' lw 2,\\\n",
" f(x,1) t '3-term Fourier series',\\\n",
" f(x,19) t '19-term Fourier series'"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Of course, there are also excellent plotting capabilities within `python`, `matlab/octave` and `maple` environments, all with much more sophisticated computational capabilities. We will learn these as we go along. However, the flexibility and the ability to generate both screen-friendly bitmap (e.g. PNG) plots and publication-quality scalable vector (SVG, Encapsulated PostScript, LaTeX, etc.) plots makes `gnuplot` (and/or `eXtrema`, see Section 4.3 below) useful additions to the scientific toolbox."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 4.2 Homework: analysis of the Cavendish experiment"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Lord Cavendish was the designer of the original experiment that used a pair of lead spheres and a very sensitive torsional balance to measure the universal gravitational constant, $G$. A manual for a modern version of such a torsional balance is here. As described there, in Fig.18 on p.13, the following set of data was obtained. The distance to the board on which the position of the laser dot was recorded was $L=10.31$m.\n",
"\n",
"Produce an eXtrema or a gnuplot macro that would plot and analyze the data, and calculate $G$ from it. It appears that a good fit would result from fitting $S(t)=S_0+Ae^{-(t-t_0)/\\tau}\\cos [\\omega (t-t_0)]$ to each segment of the experiment with $S_0$, $A$, $t_0$, $\\tau$ and $\\omega$ the parameters of the fit. Without knowing the exact geometry of the experiment, $\\Delta S$ between the two equilibrium positions cannot be used, but perhaps the oscillation period can be extracted and used in the analysis. Use the average of the two values obtained for both sections of the data.\n",
"
\n",
"A more careful examination reveals that there might be a small drift in the data. Model it by a small linear-in-time correction term, $\\alpha(t-t_0)$, and see if the precision of the fit improves. "
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"scrolled": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Writing Cavendish.dat\n"
]
}
],
"source": [
"%%file Cavendish.dat\n",
"# Cavendish experiment 2012-02-24\n",
"## minutes, position_of_dot, cm\n",
"\n",
"# set spheres to one side at 11:45:00, 45 mins since the start\n",
"45\t57.5\n",
"45.5\t58\n",
"46\t58.5\n",
"46.5\t60.5\n",
"47\t63\n",
"47.5\t66\n",
"48\t69\n",
"48.5\t72\n",
"49\t74.5\n",
"49.5\t76.7\n",
"50\t78\n",
"50.5\t78.7\n",
"51\t78.7\n",
"51.5\t78\n",
"52\t76.7\n",
"52.5\t75.\n",
"53\t73\n",
"53.5\t70.8\n",
"54\t69.2\n",
"54.5\t67.7\n",
"55\t66.8\n",
"55.5\t66.4\n",
"56\t66.5\n",
"56.5\t67.1\n",
"57\t68.1\n",
"57.5\t69.2\n",
"58\t70.7\n",
"58.75\t73.2\n",
"59\t73.8\n",
"59.5\t74.8\n",
"60\t75.6\n",
"60.5\t76.1\n",
"61\t76.1\n",
"61.5\t75.8\n",
"62\t75.1\n",
"62.5\t74.2\n",
"63\t73.2\n",
"63.5\t72.2\n",
"64\t71.5\n",
"64.5\t70.7\n",
"65\t70.1\n",
"65.5\t69.9\n",
"66\t69.9\n",
"66.5\t70.1\n",
"67\t70.6\n",
"67.5\t71.2\n",
"68\t72\n",
"68.5\t72.7\n",
"69\t73.4\n",
"69.5\t74\n",
"70\t74.2\n",
"70.5\t74.6\n",
"71\t74.7\n",
"72\t74.1\n",
"72.5\t73.8\t\n",
"73\t73.2\n",
"73.5\t72.8\n",
"74\t72.2\n",
"74.75\t71.8\n",
"75\t71.6\n",
"75.5\t71.5\n",
"76\t71.4\n",
"76.5\t71.6\n",
"77\t72\n",
"77.75\t72.6\n",
"78\t72.8\n",
"78.5\t73.1\n",
"79\t73.5\n",
"79.25\t73.7\n",
"79.5\t73.9\n",
"79.75\t74\n",
"80\t74.1\n",
"80.25\t74.1\n",
"80.5\t74.1\n",
"80.75\t74.1\n",
"81\t74.1\n",
"81.25\t74\n",
"81.5\t74\n",
"81.75\t74\n",
"82\t73.8\n",
"82.5\t73.7\n",
"83\t73.4\n",
"83.5\t73.1\n",
"84\t72.9\n",
"84.5\t72.7\n",
"85.25\t72.7\n",
"85.5\t72.7\n",
"86\t72.6\n",
"86.5\t72.6\n",
"87\t72.7\n",
"87.5\t72.8\n",
"88\t73.1\n",
"88.5\t73.3\n",
"89\t73.6\n",
"89.5\t73.7\n",
"90\t73.8\n",
"90.5\t74\n",
"91\t74\n",
"93\t73.8\n",
"93.5\t73.6\n",
"94\t73.5\n",
"98\t73.3\n",
"\n",
"\n",
"# reverse the spheres at 13:25:00, 145 mins since the start\n",
"145\t75.5\n",
"145.5\t73.8\n",
"146\t69.8\n",
"146.5\t61.5\n",
"147\t55\n",
"147.5\t46.5\n",
"148\t36.5\n",
"148.5\t31\n",
"149\t25.8\n",
"149.5\t22.6\n",
"150\t21.6\n",
"150.5\t23\n",
"151\t26\n",
"151.5\t30.8\n",
"152\t36.6\n",
"152.5\t42.5\n",
"153\t48.1\n",
"153.5\t53.2\n",
"154\t57.3\n",
"154.5\t59.5\n",
"155\t60.2\n",
"155.5\t59.7\n",
"155.75\t58.8\n",
"156\t57.7\n",
"156.25\t56.2\n",
"156.5\t54.5\n",
"156.75\t52.8\n",
"157\t50.8\n",
"157.25\t48.7\n",
"157.5\t46.5\n",
"157.75\t44.5\n",
"158\t42.5\n",
"158.25\t40.6\n",
"158.5\t38.8\n",
"158.75\t37.2\n",
"159\t35.9\n",
"159.25\t34.8\n",
"159.5\t34\n",
"159.75\t33.6\n",
"160\t33.2\n",
"160.25\t33.2\n",
"160.5\t33.6\n",
"160.75\t34.1\n",
"161\t35\n",
"161.25\t35.9\n",
"161.5\t37\n",
"161.75\t38.2\n",
"162\t39.5\n",
"162.5\t42.5\n",
"163\t45.3\n",
"163.5\t48\n",
"164\t50.1\n",
"164.5\t51.5\n",
"165\t52.2\n",
"165.5\t52.1\n",
"166\t51.2\n",
"166.5\t49.8\n",
"167\t48\n",
"167.5\t45.9\n",
"168\t43.8\n",
"168.5\t42\n",
"169\t40.5\n",
"169.5\t39.2\n",
"170\t38.9\n",
"170.75\t39.2\n",
"171\t39.7\n",
"171.5\t40.6\n",
"172\t41.9\n",
"172.5\t43.6\n",
"173\t44.9\n",
"173.75\t46.9\n",
"174\t47.5\n",
"174.5\t48.2\n",
"175\t48.7\n",
"175.5\t48.7\n",
"176\t48.4\n",
"176.5\t47.7\n",
"177\t47\n",
"177.5\t46\n",
"178\t45\n",
"178.5\t44\n",
"179\t43.1\n",
"179.5\t42.7\n",
"180\t42.3\n",
"180.5\t42.1\n",
"181\t42.5\n",
"181.5\t42.9\n",
"182\t43.4\n",
"182.5\t44.1\n",
"183\t44.7\n",
"183.5\t45.5\n",
"184\t46\n",
"184.5\t46.4\n",
"185\t46.7\n",
"185.5\t46.7\n",
"186\t46.7\n",
"186.5\t46.4\n",
"187\t46.1\n",
"187.5\t45.6\n",
"188\t45.2\n",
"188.5\t44.7\n",
"189\t44.3\n",
"189.5\t44.1\n",
"190\t43.9\n",
"191\t44\n",
"191.5\t44.2\n",
"192\t44.6\n",
"192.5\t44.7\n",
"193\t45\n",
"193.5\t45.4\n",
"194\t45.7\n",
"194.5\t45.9\n",
"195\t46.1\n",
"195.5\t46.1\n",
"196\t46.1\n",
"196.5\t46\n",
"197\t45.9\n",
"197.5\t45.6\n",
"198\t45.4\n",
"198.5\t45.2\n",
"199\t44.9\n",
"199.5\t44.7\n",
"200\t44.5\n",
"202.5\t44.6\n",
"204\t45.4\n",
"205\t45.7\n",
"217.5\t45.6\n",
"217.75\t45.4\n",
"218\t45.4\n",
"218.5\t45.3\n",
"219\t45.3\n",
"219.5\t45.4\n",
"220\t45.5"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"%gnuplot inline pngcairo size 640,480 font \"Palatino,16\""
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"%%gnuplot\n",
"# for a clean start, as gnuplot may remember things from previous scripts\n",
"reset\n",
"\n",
"#plot \"Cavendish.dat\" with lines\n",
"\n",
"#plot \"Cavendish.dat\" using ($1 < 140 ? $1: NaN ):($2/100) w l title \"forward\",\\\n",
"# \"Cavendish.dat\" using ($1 > 140 ? $1: NaN ):($2/100) w l title \"reversed\"\n",
"\n",
"### requires that TWO blank lines separate data into \"blocks\" in the data file\n",
"plot \\\n",
" \"Cavendish.dat\" index 0 with points title \"forward\",\\\n",
" \"\" index 1 with points title \"reverse\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 4.3 eXtrema\n",
"\n",
"The same, of course, can be done in `eXtrema`:"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Writing Cavendish.pcm\n"
]
}
],
"source": [
"%%file Cavendish.pcm\n",
"read /work/5P10/Cavendish.dat t,x\n",
"x=x/100 ! cm -> m\n",
"m2s=60 ! mins to secs\n",
"\n",
"clear\n",
"defaults\n",
"Pi=2.*acos(0.)\n",
"\n",
"scales 40 220 0 0 0 0\n",
"set\n",
" xlabel `t, min'\n",
" ylabel `x(t), m'\n",
" plotsymbol -15\n",
" %plotsymbolsize 0.75\n",
" plotsymbolcolor purple\n",
"\n",
"graph t,x\n",
"hardcopy\\png Cavendish.png"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Run `eXtrema` and enter `@Cavendish` command to (re-)generate the plot before executing the next cell to include the output in this notebook. Unfortunately, `extrema_kernel` does not exist, so we cannot run `eXtrema` within the noteboolk directly. If you execute a cell like this\n",
"```\n",
"! extrema\n",
"```\n",
"`eXtrema` will launch, but you will need to quit it before you can return to this jupyter notebook, so it's best to launch it separately, outside of this notebook. "
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from IPython.display import display, Image\n",
"display(Image('Cavendish.png'))"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"hide_input": false,
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.8"
},
"toc": {
"nav_menu": {},
"number_sections": false,
"sideBar": true,
"skip_h1_title": false,
"toc_cell": false,
"toc_position": {},
"toc_section_display": "none",
"toc_window_display": true
}
},
"nbformat": 4,
"nbformat_minor": 2
}