File:Anharmonic oscillators solutions.png

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Anharmonic_oscillators_solutions.png ‎(623 × 567 pixels, file size: 13 KB, MIME type: image/png)

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Description
English: solution to several anharmonic oscillator problems
Date
Source Own work
Author Jkrieger
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PNG development
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This diagram was created with MATLAB.
Source code
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MATLAB code

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





m=1;
k=1;
l=0.2;
c=0;

x0=1;
x01=2.4;
x02=3;
p0=0;



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]);

PSRange=[-10 10];

subplot(3,2,1);
[T,Y] = ode45(dy,[0 40],[x0, p0],options);
[Th,Yh] = ode45(dyh,[0 40],[x0, p0],options);
[TB,YB] = ode45(dyB,[0 40],[x0, p0],options);
plot(Th,Yh(:,1), 'b-', T,Y(:,1),'r-', TB,YB(:,1),'g-');
ylim([-1.5 1.5]*x0);
xlabel('time t');
ylabel('position x(t)');
title(['solution for x_0=' num2str(x0) ', p_0=0']);

subplot(3,2,2);
for x0=-5:0.5:10
    [Th,Yh] = ode45(dyh,[0 100],[x0, p0],options);
    plot(Yh(:,1),Yh(:,2), 'b-');
    if x0==0.5
        hold on
    end
end
hold off
xlim(PSRange);
ylim(PSRange);
title(['phase space plot, harmonic oscillator']);


subplot(3,2,3);
[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('time t');
ylabel('position x(t)');
title(['solution for x_0=' num2str(x01) ', p_0=0']);
ylim([-2 2]*x01);
subplot(3,2,4);
for x0=-5:0.5:10
    [T,Y] = ode45(dy,[0 100],[x0, p0],options);
    plot(Y(:,1),Y(:,2), 'r-');
    if x0==0.5
        hold on
    end
end
hold off
xlim(PSRange);
ylim(PSRange);
title(['phase space plot, asymmetric force law']);


subplot(3,2,5);
[T,Y] = ode45(dy,[0 40],[x02, p0],options);
[Th,Yh] = ode45(dyh,[0 40],[x02, p0],options);
[TB,YB] = ode45(dyB,[0 40],[x02, p0],options);
plot(Th,Yh(:,1), 'b-', T,Y(:,1),'r-', TB,YB(:,1),'g-');
xlabel('time t');
ylabel('position x(t)');
title(['solution for x_0=' num2str(x02) ', p_0=0']);
ylim([-3 3]*abs(x02));
subplot(3,2,6);
for x0=-5:0.5:10
    [TB,YB] = ode45(dyB,[0 100],[x0, p0],options);
    plot(YB(:,1),YB(:,2), 'g-');
    if x0==0.5
        hold on
    end
end
hold off
xlim(PSRange);
ylim(PSRange);
xlabel('position x');
ylabel('impulse p');
title(['phase space plot, symmetric force law']);

Licensing

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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.

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Date/TimeThumbnailDimensionsUserComment
current13:58, 31 May 2013Thumbnail for version as of 13:58, 31 May 2013623 × 567 (13 KB)AnonMoos (talk | contribs)adjust margins
12:43, 31 May 2013Thumbnail for version as of 12:43, 31 May 2013710 × 614 (23 KB)Jkrieger (talk | contribs){{Information |Description ={{en|1=solution to several anharmonic oscillator problems}} |Source ={{own}} |Author =Jkrieger |Date =2013-05-31 |Permission = |other_versions = }} [[Category:Theoretical p...

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