# File:Mplwp resonance zeta envelope.svg

Original file(SVG file, nominally 600 × 400 pixels, file size: 37 KB)

## Summary

Description
English: Plot of the steady-state amplitude ${\displaystyle A/A_{\mathrm {stat} }}$ of a damped driven oscillator with different damping ratios ζ. The relative driving frequency ${\displaystyle \eta =\omega /\omega _{0}}$ is plotted in the interval [0, 3]. Additionally the envelope and line of maxima is plotted:
${\displaystyle A/A_{stat}={\frac {1}{\sqrt {(1-\eta ^{2})^{2}+(2\eta \zeta )^{2}}}}}$
${\displaystyle \zeta \in [0.1,0.2,0.3,0.5,1]}$
${\displaystyle A_{env}/A_{stat}={\frac {1}{|1-\eta ^{2}|}}}$
${\displaystyle A_{max}/A_{stat}={\frac {1}{\sqrt {1-\eta ^{4}}}}}$
English label version.
Date
Source Own work
Author Geek3
SVG development
 This plot was created with mplwp, the Matplotlib extension for Wikipedia plots.

## mplwp source code

The plot was generated with mplwp 1.6.3
#!/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
exit(1)

name = 'mplwp_resonance_zeta_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())

maxima = lambda x: 1.0 / sqrt(1 - x**4)
x_max = np.linspace(xlim[0], 1, 2001)[:-1]
y_max = [maxima(xx) for xx in x_max]
plt.plot(x_max, y_max, color='grey', dashes=[3,3], label='maxima', zorder=-2)

x = np.linspace(xlim[0], xlim[1], 6001)
def resonance(x, zeta):
den = sqrt((x**2 - 1.0)**2 + (2*x*zeta)**2)
if den == 0:
return float('nan')
return 1.0 / den

for zeta in [0.0, 0.1, 0.2, 0.3, 0.5, 1.0]:
y = [resonance(xx, zeta) for xx in x]
l = label='$\zeta={:.1f}$'.format(zeta)
if zeta == 0.0:
plt.plot(x, y, color='grey', dashes=[10,5], label=l, zorder=0)
else:
plt.plot(x, y, label=l, zorder=1.1-zeta)

plt.legend(loc='upper right').get_frame().set_alpha(0.9)

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


## Licensing

I, the copyright holder of this work, hereby publish it under the following licenses:
 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.

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## File history

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

Date/TimeThumbnailDimensionsUserComment
current07:20, 9 June 2016600 × 400 (37 KB)Geek3all labels with one digit
14:23, 11 January 2015600 × 400 (40 KB)Geek3resonance_zeta_envelope plot by Geek3
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