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 of a damped driven oscillator with different damping ratios ζ. The relative driving frequency is plotted in the interval [0, 3]. Additionally the envelope and line of maxima is plotted:
English label version.
Date
Source Own work
Author Geek3
SVG development
Mplwp logo.svg
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
    print 'You need to download mplwp.py from', code_website
    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)

See also

Licensing

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.

Quality images logo.svg
Quality image
This image has been assessed using the Quality image guidelines and is considered a Quality image.

العربية | جازايرية | беларуская | беларуская (тарашкевіца)‎ | български | বাংলা | català | čeština | Cymraeg | Deutsch | Schweizer Hochdeutsch | Zazaki | Ελληνικά | English | Esperanto | español | eesti | euskara | فارسی | suomi | français | galego | עברית | हिन्दी | hrvatski | magyar | հայերեն | Bahasa Indonesia | italiano | 日本語 | ქართული | 한국어 | kurdî | Lëtzebuergesch | lietuvių | македонски | മലയാളം | मराठी | Bahasa Melayu | Nederlands | polski | português | português do Brasil | rumantsch | română | русский | sicilianu | slovenčina | slovenščina | shqip | српски / srpski | svenska | தமிழ் | తెలుగు | ไทย | Tagalog | Türkçe | українська | vèneto | Tiếng Việt | 中文 | 中文(简体)‎ | 中文(繁體)‎ | +/−

Captions

Add a one-line explanation of what this file represents

Items portrayed in this file

depicts

File history

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

Date/TimeThumbnailDimensionsUserComment
current07:20, 9 June 2016Thumbnail for version as of 07:20, 9 June 2016600 × 400 (37 KB)Geek3all labels with one digit
14:23, 11 January 2015Thumbnail for version as of 14:23, 11 January 2015600 × 400 (40 KB)Geek3resonance_zeta_envelope plot by Geek3
The following pages on the English Wikipedia use this file (pages on other projects are not listed):

Metadata