# 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 $A/A_{\mathrm {stat} }$ of a damped driven oscillator with different damping ratios ζ. The relative driving frequency $\eta =\omega /\omega _{0}$ is plotted in the interval [0, 3]. Additionally the envelope and line of maxima is plotted:
$A/A_{stat}={\frac {1}{\sqrt {(1-\eta ^{2})^{2}+(2\eta \zeta )^{2}}}}$ $\zeta \in [0.1,0.2,0.3,0.5,1]$ $A_{env}/A_{stat}={\frac {1}{|1-\eta ^{2}|}}$ $A_{max}/A_{stat}={\frac {1}{\sqrt {1-\eta ^{4}}}}$ 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, 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, xlim, 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.  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. Quality image This image has been assessed using the Quality image guidelines and is considered a Quality image.

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## File history

The following pages on the English Wikipedia use this file (pages on other projects are not listed):