File:Damping 1.svg

Original file(SVG file, nominally 650 × 356 pixels, file size: 69 KB)

Summary

Description
English: Damping. Refer Ingard, 1988 for more information on the equations.
Date (original upload date)
Source

Transferred from en.wikipedia; transferred to Commons by Kropotkine 113 using CommonsHelper.

(Original text : Self-made using Matlab. Source code provided below.)
Author

Nuno Nogueira. Original uploader was Nmnogueira at en.wikipedia.

Later version(s) were uploaded by Dicklyon at en.wikipedia.
Other versions Second order transfer function.svg Second order transfer function.svg
SVG development
Matlab Logo.png
This diagram was created with MATLAB.

Matlab

%Uses the files from Matlab Central File Exchange "plot2svg"
clear all
t = 0:0.01:11;
damping = [0.5, 1, 1.5, 0];  % damping values
colors = {'b', [0, 0.7, 0], 'r', 'm'};
h_fig = figure;
set(h_fig, 'Position',[360 673 354 249])
h_axes = axes;
axis([0, t(end), -1.05, 1.05]);
xlabel('time(s)')
ylabel('x/x0')
hold on
omega_0 = 1;  % natural frequency
for k = 1:length(damping)
  gamma = damping(k) * omega_0;
  if damping(k) > 1  % over-damped
    gamma1 = gamma - sqrt(gamma^2 - omega_0^2);
    gamma2 = gamma + sqrt(gamma^2 - omega_0^2);
    x = (gamma2 * exp(-gamma1 * t) - gamma1 * exp(-gamma2 * t)) / (gamma2 - gamma1);
  else
    if damping(k) == 1  % critically damped
      x = (1 + gamma * t) .* exp(-gamma * t);
    else  % under-damped
      omega_prime = sqrt(omega_0^2 - gamma^2);
      alpha = atan(gamma / omega_prime);
      x = exp(-gamma*t) .* cos(omega_prime * t - alpha) / cos(alpha);
    end
  end
  plot(t, x, 'Color', colors{k}, 'LineWidth', 1)
end
plot([0; t(end)], [0; 0], 'k')
legend('\zeta < 1', '\zeta = 1', '\zeta > 1', '\zeta = 0')
hold off
plot2svg('damping.svg',h_fig)

Licensing

Nmnogueira at en.wikipedia, the copyright holder of this work, hereby publishes it under the following license:
w:en:Creative Commons

attribution share alike

This file is licensed under the Creative Commons Attribution-Share Alike 2.5 Generic license.
Attribution: Nmnogueira at en.wikipedia
You are free:
  • to share – to copy, distribute and transmit the work
  • to remix – to adapt the work
Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
  • share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.

Original upload log

The original description page was here. All following user names refer to en.wikipedia.
  • 2009-08-05 00:30 [[[:en:User:Dicklyon|Dicklyon]] 512×360× (87765 bytes) Hacked the axis labels to be better
  • 2009-08-02 08:52 Dicklyon 512×360× (86099 bytes) Updated equations, using a book source, to match accelerations at t = 0. New code.
  • 2007-09-20 16:08 Nmnogueira 200×200 (58385 bytes)
  • 2007-09-20 15:59 Nmnogueira 200×200 (63244 bytes)
  • 2007-09-20 15:49 Nmnogueira 200×200 (63017 bytes)
  • 2007-09-20 15:43 Nmnogueira 200×200 (63865 bytes)
  • 2007-09-20 15:41 Nmnogueira 200×200 (63986 bytes)
  • 2007-09-20 15:40 Nmnogueira 200×200 (58391 bytes)
  • 2007-09-20 15:37 Nmnogueira 200×200 (58391 bytes) {{Information| |Description = [[Damping]] |Source = Self-made using Matlab. Source code provided below. |Date = 2007-09-20 |Author = Nuno Nogueira (~~~) |Permission = {{self|cc-by-sa-2.5}} }} ==Source Code== Uses the files from Matlab Central File Exchan

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current06:37, 6 June 2011Thumbnail for version as of 06:37, 6 June 2011650 × 356 (69 KB)Krishnavedalaaxis labels
06:31, 6 June 2011Thumbnail for version as of 06:31, 6 June 2011656 × 354 (68 KB)Krishnavedalakept the original 'y' axis label
06:29, 6 June 2011Thumbnail for version as of 06:29, 6 June 2011644 × 354 (70 KB)Krishnavedalaupdated the fonts, picture quality ,etc..
20:32, 5 May 2010Thumbnail for version as of 20:32, 5 May 2010512 × 360 (86 KB)Kropotkine 113{{Information |Description={{en|en:Damping<br/> ==Source Code== Uses the files from Matlab Central File Exchange "plot2svg" <source lang="matlab"> clear all t = 0:0.01:11; damping = [0.5, 1, 1.5, 0]; % damping values colors = {'b', [0, 0.7, 0], 'r'
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