File:Pendulum period.svg
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![File:Pendulum period.svg](http://178.128.105.246/content-https-upload.wikimedia.org/wikipedia/commons/thumb/a/a3/Pendulum_period.svg/730px-Pendulum_period.svg.png?20070416195417)
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[edit]DescriptionPendulum period.svg |
A plot of the ratio between the actual period of a pendulum and the approximate value obtained for small angles, as a function of the amplitude. According to Pendulum (mathematics), the oscillation period for small angles is given by: while the actual period for any angle is given by: where: so the ratio is given by: and this is the function plotted in the graph. First, with the following Matlab code I created a file called pendulum_period.dat; then, in order to plot it, I used the Gnuplot code. This code creates a file called pendulum_period.svg. I heavily post-processed it with Inkscape. |
Date | |
Source | Own work using: Matlab, Gnuplot, Inkscape. |
Author | Alessio Damato; thanks to John wayman, he let me notice a mistake in the code. |
SVG development InfoField | |
Source code InfoField |
res=2000; % resolution
sup=pi/2; % max angle to be used in the plot (in radians, less than pi)
phi=pi/2; % integration upper limit
% inizialization
T=zeros(1,res);
for i=1:res
theta0=i*sup/res; % theta0 is the pendulum amplitude
k = sin(theta0/2);
F = @(t) 1./sqrt(1-(k*sin(t)).^2);
T(i)=quad(F,0,phi); % numerical integration
end
T = 2./pi.*T; % normalization
deg = 180/pi*sup*(1:res)./res; % conversion to degrees
% saving in the external file
temp = [deg; T];
temp = temp';
save -ascii 'pendulum_period.dat' temp;
# set the output
set terminal svg
set output "pendulum_period.svg"
# axis properties
set yrange [0.99:1.08]
set xzeroaxis linetype -1 linewidth 0.5
set yzeroaxis linetype -1 linewidth 0.5
set xtics axis
set ytics axis
set key off
plot "pendulum_period.dat" using 1:2 with lines linewidth 2
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Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue |
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This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license. | |
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Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 19:54, 16 April 2007 | ![]() | 730 × 591 (28 KB) | Alejo2083 (talk | contribs) | fixed mistake |
13:48, 29 November 2006 | ![]() | 648 × 480 (24 KB) | Alejo2083 (talk | contribs) | {{Information |Description=The plot represents the ration between the period an oscillator and the approximated value obtained for small angles. According to the relative [http://en.wikipedia.org/wiki/Pendulum_%28mathematics%29 article on wikipedia], the |
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