File:Phaseshift across resonance (forced harmonic oscillator).gif

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Phaseshift_across_resonance_(forced_harmonic_oscillator).gif ‎(360 × 223 pixels, file size: 7.66 MB, MIME type: image/gif, looped, 801 frames)

Captions

Captions

Time evolution of a damped harmonic oscillator while changing the driving frequency

Summary[edit]

Description
English: If you drive a (damped) harmonic oscillator at low frequency, the oscillations will follow the forcing. If the frequency increases the oscillations will start lagging behind, and (after the resonance) they will be exactly out of phase with the forcing.
Date
Source https://twitter.com/j_bertolotti/status/1113773016025042944
Author Jacopo Bertolotti
Permission
(Reusing this file)		 https://twitter.com/j_bertolotti/status/1030470604418428929

Mathematica 11.0 code[edit]

sol = NDSolve[{f''[t] + 2/10 f'[t] + 1* f[t] == 0.2*Sin[(1/1000 t) t], f'[0] == 0, f[0] == 1}, f[t], {t, 0, 1000}];
p1 = Table[
   Show[
    Plot[Sin[(1/1000 t) t], {t, \[Tau] - 20, \[Tau] + 20}, PlotStyle -> Blue]
    ,
    Plot[Evaluate[f[t] /. sol], {t, \[Tau] - 20, \[Tau]}, PlotStyle -> Orange]
    ,
    Graphics[{Black, Disk[{\[Tau], (Evaluate[f[t] /. sol] /. {t -> \[Tau]})[[1]]}, Scaled[{0.02, 0.02 GoldenRatio}]]}]
    , PlotRange -> {{\[Tau] - 20, \[Tau] + 20}, {-1.1, 1.1}}, Axes -> False]
   , {\[Tau], 100, 1000 - 100, 1}];
ListAnimate[p1, 10]

Licensing[edit]

I, the copyright holder of this work, hereby publish it under the following license:
Creative Commons CC-Zero This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication.
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.

This file, which was originally posted to https://twitter.com/j_bertolotti/status/1113773016025042944, was reviewed on 5 April 2019 by reviewer Ronhjones, who confirmed that it was available there under the stated license on that date.

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Date/TimeThumbnailDimensionsUserComment
current08:15, 5 April 2019Thumbnail for version as of 08:15, 5 April 2019360 × 223 (7.66 MB)Berto (talk | contribs)User created page with UploadWizard

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