File:Mplwp resonance D envelope.svg

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Original file ‎(SVG file, nominally 600 × 400 pixels, file size: 40 KB)

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Description
English: Plot of the steady-state amplitude of a damped driven oscillator with different damping ratios D. The relative driving frequency is plotted in the interval [0, 3]. Additionally the envelope and line of maxima is plotted:
German label version.
Date
Source Own work
Author Geek3
SVG development
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This plot was created with mplwp, the Matplotlib extension for Wikipedia plots.
Source code
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mplwp source code

The plot was generated with mplwp 1.0 
#!/usr/bin/python
# -*- coding: utf8 -*-

import matplotlib.pyplot as plt
import matplotlib as mpl
import numpy as np
from math import *

code_website = 'http://commons.wikimedia.org/wiki/User:Geek3/mplwp'
try:
    import mplwp
except ImportError, er:
    print 'ImportError:', er
    print 'You need to download mplwp.py from', code_website
    exit(1)

name = 'mplwp_resonance_D_envelope.svg'
fig = mplwp.fig_standard(mpl)
xlim = 0,3; fig.gca().set_xlim(xlim)
ylim = 0,6; fig.gca().set_ylim(ylim)
mplwp.mark_axeszero(fig.gca())

envelope = lambda x: 1.0 / abs(1 - x**2)
x = np.linspace(xlim[0], xlim[1], 6001)
y_env = [envelope(xx) for xx in x]
plt.plot(x, y_env, color='grey', dashes=[10,5], label=u'Einhüllende')

maxima = lambda x: 1.0 / sqrt(1 - x**4)
x_max = np.linspace(xlim[0], 1, 1001)[:-1]
y_max = [maxima(xx) for xx in x_max]
plt.plot(x_max, y_max, color='grey', dashes=[3,3], label='Maxima')

for D in [0.1, 0.2, 0.3, 0.5, 1]:
    f = lambda x: 1.0 / sqrt((x**2 - 1.0)**2 + (2*x*D)**2)
    y = [f(xx) for xx in x]
    plt.plot(x, y, label='D={:g}'.format(D))
    
plt.legend(loc='upper right').get_frame().set_alpha(0.9)

plt.savefig(name)
mplwp.postprocess(name)

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Licensing[edit]

I, the copyright holder of this work, hereby publish it under the following licenses:
GNU head 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.
w:en:Creative Commons
attribution
This file is licensed under the Creative Commons Attribution 3.0 Unported license.
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.
You may select the license of your choice.

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Date/TimeThumbnailDimensionsUserComment
current14:10, 11 January 2015Thumbnail for version as of 14:10, 11 January 2015600 × 400 (40 KB)Geek3 (talk | contribs)resonance_D_envelope plot by Geek3

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