File:Anharmonic oscillators solutions fft de.svg

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Description
English: solution to an anharmonic oscillator problem, with fourier-decomposition of the resulting trajectories (blue=harmonic oscillator)
Date
Source Own work
Author Jkrieger

Sourcecode[edit]

Note: This script need the plot2svg() function package by Juerg Schwizer!

 
The SVG code is valid.
 
This diagram was created with MATLAB.

Source code

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MATLAB code

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% three function files 
function [ dy ] = harmonic( t,y,m,k,l,c )
%UNTITLED3 Summary of this function goes here
%   Detailed explanation goes here
dy=zeros(2,1);
dy(1)=y(2);
dy(2)=-(c*y(2)+k*y(1))/m;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function [ dy ] = anharmonicA( t,y,m,k,l,c )
%UNTITLED3 Summary of this function goes here
%   Detailed explanation goes here
dy=zeros(2,1);
dy(1)=y(2);
dy(2)=-(c*y(2)+k*y(1)+l*y(1)^2)/m;
end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function [ dy ] = anharmonicB( t,y,m,k,l,c )
%UNTITLED3 Summary of this function goes here
%   Detailed explanation goes here
dy=zeros(2,1);
dy(1)=y(2);
dy(2)=-(c*y(2)+k*y(1)+l*y(1)^3)/m;
end



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% main script
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
clear all
addpath('plot2svg');

m=1;
k=1;
l=0.2;
c=0;
x0=0.2;
x01=2.4;
x02=0;
p02=2;
p0=0;

PSX0range=0:(0.4):(2.4);

PSRange=[-4.5 4.5];
 
 
 
dy=@(t,y) anharmonicA(t,y,m,k,l,c);
dyB=@(t,y) anharmonicB(t,y,m,k,l,c);
dyh=@(t,y) harmonic(t,y,m,k,l,c);
options = odeset('RelTol',1e-4,'AbsTol',[1e-4 1e-4]);
 
 
h=figure(1);
subplot(3,2,[1 2]);

[T,Y] = ode45(dy,[0 40],[x01, p0],options);
[Th,Yh] = ode45(dyh,[0 40],[x01, p0],options);
[TB,YB] = ode45(dyB,[0 40],[x01, p0],options);
plot(Th,Yh(:,1), 'b-', T,Y(:,1),'r--', TB,YB(:,1),'g:');
xlabel('Zeit t');
ylabel('Ort x(t)');
title(['\bf Trajektorie (x(0)=' num2str(x01) ', p(0)=0)']);
ylim([-2 2]*x01);

 

subplot(3,2,[3 4 5 6]);


FFTST=0.02;
FFTSF=1/FFTST;
FFTT=FFTST:FFTST:2000;
NFFT = 2^nextpow2(length(FFTT));
FFTF = FFTSF/2*linspace(0,1,NFFT/2+1);
[T,Y] = ode45(dy,FFTT,[x01, p0],options);
[Th,Yh] = ode45(dyh,FFTT,[x01, p0],options);
[TB,YB] = ode45(dyB,FFTT,[x01, p0],options);
FFTY=fft(Y,NFFT)/length(FFTT);
FFTYh=fft(Yh,NFFT)/length(FFTT);
FFTYB=fft(YB,NFFT)/length(FFTT);

windowSize = 5;

xdata=FFTF(1:windowSize:end);
ydata1=2*abs(FFTYh(1:NFFT/2+1));
ydata2=2*abs(FFTY(1:NFFT/2+1));
ydata3=2*abs(FFTYB(1:NFFT/2+1));

ydata1=filter(ones(1,windowSize)/windowSize,1,ydata1);
ydata1=ydata1(1:windowSize:end);
ydata2=filter(ones(1,windowSize)/windowSize,1,ydata2);
ydata2=ydata2(1:windowSize:end);
ydata3=filter(ones(1,windowSize)/windowSize,1,ydata3);
ydata3=ydata3(1:windowSize:end);


plot(xdata, ydata1, 'b-', xdata, ydata2, 'r-', xdata, ydata3, 'g-')
xlim([0 0.3])
xlabel('Schwingungsfrequenz f');
ylabel('Fourier-Anteil der Frequenz');
title('\bf Fourier-Spektrum der Schwingung')
plot2svg('anharmonic_oscillators_solutions_fft.svg', h)

Licensing[edit]

I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
attribution share alike
This file is licensed under the Creative Commons Attribution-Share Alike 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.
  • 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/TimeThumbnailDimensionsUserComment
current06:30, 14 August 2013Thumbnail for version as of 06:30, 14 August 2013512 × 645 (715 KB)Jkrieger (talk | contribs)-phase space plot
06:17, 14 August 2013Thumbnail for version as of 06:17, 14 August 2013512 × 384 (728 KB)Jkrieger (talk | contribs){{Information |Description ={{en|1=solution to an anharmonic oscillator problem, with fourier-decomposition of the resulting trajectories (blue=harmonic oscillator)}} |Source ={{own}} |Author =Jkrieger |Date ...

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