File:Driven harmonic oscillators.gif
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Driven_harmonic_oscillators.gif (480 × 297 pixels, file size: 6.25 MB, MIME type: image/gif, looped, 1,081 frames, 1 min 48 s)
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Captions
Captions
Dumped harmonic oscillators of different masses driven by a pulse.
Summary
[edit]
| Description |
English: A set of harmonic oscillators with the same elastic coefficient k, and the same friction b, but different masses.
The lightest and heaviest ones are out of resonance and don't move much, but the intermediate mass ones keep oscillating for a while. |
| Date | |
| Source | https://twitter.com/j_bertolotti/status/1246115268729978880 |
| Author | Jacopo Bertolotti |
| Permission (Reusing this file) |
https://twitter.com/j_bertolotti/status/1030470604418428929 |
Mathematica 12.0 code
[edit]
pulse[t_, t0_] := E^(-((t - t0)^2/(2 1^2))) Cos[10*t];
Plot[pulse[t], {t, 0, 20}, PlotRange -> All]
sol3 = Table[
NDSolveValue[{m x''[t] + 0.05 x'[t] + 20 x[t] == pulse[t, 10], x[0] == 0, x'[0] == 0}, x, {t, 0, 100}]
, {m, 0.05, 0.4, 0.025}];
dim = Dimensions[sol3][[1]];
p0 = Table[
Show[
Plot[5 pulse[t, -10 + \[Tau]], {t, -50, 50}, PlotRange -> All, PlotPoints -> 100, Axes -> False, PlotStyle -> {Orange}]
,
Graphics[{
Gray, Table[
Line[{{j, 0}, {j, 15*sol3[[j]][Max[0, \[Tau] + 1 - j] ]}}]
, {j, 1, dim, 1}]
, Black, Table[
Disk[{j, 15*sol3[[j]][Max[0, \[Tau] + 1 - j] ]}, 0.1 (0.5 + 0.25 j) {1, 1 36/(dim + 2)}]
, {j, 1, dim, 1}]
,
Text[Style["m y''(t) + b y'(t) + k y(t) = \!\(\*SubscriptBox[\(F\), \(ext\)]\)(t)", Black, Bold, FontSize -> 14], {dim/2, 9}]
}]
, PlotRange -> {{0, dim + 2}, {-10, 10}}
]
, {\[Tau], 6, 60, 0.05}];
ListAnimate[p0]
Licensing
[edit]
I, the copyright holder of this work, hereby publish it under the following license:
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International 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.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 10:19, 4 April 2020 | | 480 × 297 (6.25 MB) | Berto (talk | contribs) | Uploaded own work with UploadWizard |
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