File:Simple harmonic oscillator.gif
From WikiLectures
Simple_harmonic_oscillator.gif (116 × 359 pixels, file size: 52 KB, MIME type: image/gif, looped, 15 frames, 1.1 s)
Note: Due to technical limitations, thumbnails of high resolution GIF images such as this one will not be animated.
This file is from Wikimedia Commons and may be used by other projects. The description on its file description page there is shown below.
DescriptionSimple harmonic oscillator.gif | Illustration of a en:Simple harmonic oscillator |
Date | |
Source | self-made with en:Matlab. Converted to gif animation with the en:ImageMagick convert tool (see the specific command later in the code). |
Author | Oleg Alexandrov |
Other versions | Damped spring.gif: Damped version |
GIF development InfoField | This diagram was created with MATLAB. |
Source code InfoField | MATLAB codefunction main()
% colors
red = [0.867 0.06 0.14];
blue = [0 129 205]/256;
green = [0 200 70]/256;
black = [0 0 0];
white = [1 1 1]*0.99;
cardinal = [196 30 58]/256;
cerulean = [0 123 167]/256;
denim = [21 96 189]/256;
cobalt = [0 71 171]/256;
pblue = [0 49 83]/256;
teracotta= [226 114 91]/256;
tene = [205 87 0]/256;
wall_color = pblue;
spring_color = cobalt;
mass_color = tene;
a=0.65; bmass_color = a*mass_color+(1-a)*black;
% linewidth and fontsize
lw=2;
fs=20;
ww = 0.5; % wall width
ms = 0.25; % the size of the mass
sw=0.1; % spring width
curls = 8;
A = 0.2; % the amplitude of spring oscillations
B = -1; % the y coordinate of the base state (the origin is higher, at the wall)
% Each of the small lines has length l
l = 0.05;
N = 15; % times per oscillation
No = 1; % number of oscillations
for i = 1:N*No
% set up the plotting window
figure(1); clf; hold on; axis equal; axis off;
t = 2*pi*(i-1)/(N-0)+pi/2; % current time
H= A*sin(t) + B; % position of the mass
% plot the spring from Start to End
Start = [0, 0]; End = [0, H];
[X, Y]=do_plot_spring(Start, End, curls, sw);
plot(X, Y, 'linewidth', lw, 'color', spring_color);
% Here we cheat. We modify the point B so that the mass is attached exactly at the end of the
% spring. This should not be necessary. I am too lazy to to the exact calculation.
K = length(X); End(1) = X(K); End(2) = Y(K);
% plot the wall from which the spring is hanging
plot_wall(-ww/2, ww/2, l, lw, wall_color);
% plot the mass at the end of the spring
X=[-ms/2 ms/2 ms/2 -ms/2 -ms/2 ms/2]+End(1); Y=[0 0 -ms -ms 0 0]+End(2);
H=fill(X, Y, mass_color, 'EdgeColor', bmass_color, 'linewidth', lw);
% the bounding box
Sx = -0.4*ww; Sy = B-A-ms+0.05;
Lx = 0.4*ww+l; Ly=l;
axis([Sx, Lx, Sy, Ly]);
plot(Sx, Sy, '*', 'color', white); % a hack to avoid a saveas to eps bug
saveas(gcf, sprintf('Spring_frame%d.eps', 1000+i), 'psc2') %save the current frame
disp(sprintf('Spring_frame%d', 1000+i)); %show the frame number we are at
pause(0.1);
end
% The following command was used to create the animated figure.
% convert -antialias -loop 10000 -delay 7 -compress LZW Spring_frame10* Simple_harmonic_oscillator.gif
function [X, Y]=do_plot_spring(A, B, curls, sw);
% plot a 3D spring, then project it onto 2D. theta controls the angle of projection.
% The string starts at A and ends at B
% will rotate by theta when projecting from 1D to 2D
theta=pi/6;
Npoints = 500;
% spring length
D = sqrt((A(1)-B(1))^2+(A(2)-B(2))^2);
X=linspace(0, 1, Npoints);
XX = linspace(-pi/2, 2*pi*curls+pi/2, Npoints);
Y=-sw*cos(XX);
Z=sw*sin(XX);
% b gives the length of the small straight segments at the ends
% of the spring (to which the wall and the mass are attached)
b= 0.05;
% stretch the spring in X to make it of length D - 2*b
N = length(X);
X = (D-2*b)*(X-X(1))/(X(N)-X(1));
% shift by b to the right and add the two small segments of length b
X=[0, X+b X(N)+2*b]; Y=[Y(1) Y Y(N)]; Z=[Z(1) Z Z(N)];
% project the 3D spring to 2D
M=[cos(theta) sin(theta); -sin(theta) cos(theta)];
N=length(X);
for i=1:N;
V=M*[X(i), Z(i)]';
X(i)=V(1); Z(i)=V(2);
end
% shift the spring to start from 0
X = X-X(1);
% now that we have the horisontal spring (X, Y) of length D,
% rotate and translate it to go from A to B
Theta = atan2(B(2)-A(2), B(1)-A(1));
M=[cos(Theta) -sin(Theta); sin(Theta) cos(Theta)];
N=length(X);
for i=1:N;
V=M*[X(i), Y(i)]'+A';
X(i)=V(1); Y(i)=V(2);
end
function plot_wall(S, E, l, lw, wall_color)
% Plot a wall from S to E.
no=20; spacing=(E-S)/(no-1);
plot([S, E], [0, 0], 'linewidth', 1.8*lw, 'color', wall_color);
V=l*(0:0.1:1);
for i=0:(no-1)
plot(S+ i*spacing + V, V, 'color', wall_color)
end
|
Public domainPublic domainfalsefalse |
I, the copyright holder of this work, release this work into the public domain. This applies worldwide. In some countries this may not be legally possible; if so: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law. |
Annotations InfoField | This image is annotated: View the annotations at Commons |
84
321
8
8
116
359
- γυςδοθς
Items portrayed in this file
depicts
some value
24 June 2007
image/gif
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 05:12, 24 June 2007 | 116 × 359 (52 KB) | wikimediacommons>Oleg Alexandrov | tweak |
File usage
The following page uses this file:
Retrieved from "https://www.wikilectures.eu/w/File:Simple_harmonic_oscillator.gif"