File:Spring beforeresonance.gif
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Spring_beforeresonance.gif (435 × 290 pixels, file size: 230 KB, MIME type: image/gif, looped, 100 frames, 5.0 s)
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Summary[edit]
DescriptionSpring beforeresonance.gif |
Deutsch: getriebener Oszillator, omega_drive=omega0*0.15 |
Date | |
Source | Own work |
Author | Jkrieger |
base upon work by Oleg Alexandrov: [Simple harmonic oscillator.gif]
This diagram was created with MATLAB.
Source code[edit]
function 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;
exc_color=cardinal;
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 = 5;
exc_size=0.05;
plot_width=1.5; % width of plots
K_osz = 0.05; % excitation amplitude
omega =0.15; % excitation frequency
omega0=1; % eigen frequency
gamma=0.02; % damping factor
filename='spring_beforeresonance.gif';
frames=100;
options = odeset('RelTol',1e-4,'AbsTol',1e-4);
[T,YODE] = ode45(@(t,y) dampedoszi(t,y,K_osz, omega, omega0, gamma),[0 20*pi],[0 0],options);
figure(2)
plot(T,YODE(:,1));
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 = length(T); % times per oscillation
No = 1; % number of oscillations
for f = 1:frames
i=floor(length(T)/frames*f);
% set up the plotting window
figure(1); clf; hold on; axis equal; axis off;
t = T(i); % current time
POSW=K_osz*sin(omega*t); % position of exciter with cos-excitation is a sine!
H= B+YODE(i); % position of the mass
%H=K/sqrt((1-omega).^2+(2*gamma*omega).^2)*cos(
% plot the spring from Start to End
Start = [0, POSW]; End = [0, POSW+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);
% plot exciter
rectangle('Position',[0-exc_size/2,POSW-exc_size/2,exc_size,exc_size], 'FaceColor',exc_color)
% the bounding box
Sx = -0.4*ww; Sy = B-max(abs(YODE(:,1)))-ms-0.05;
Lx = ww+l+plot_width; Ly=l+K_osz;
axis([Sx, Lx, Sy, Ly]);
% plot amplitude time course
plot(ww+T(1:i)./max(T).*plot_width, B+YODE(1:i,1), 'b-');
line([ww ww+plot_width], [B B], 'Color', black);
plot(ww+(T(1:i)-1)./(max(T)+1).*plot_width, K_osz*cos(omega*T(1:i)), 'r-');
line([ww ww+plot_width], [0 0], 'Color', black);
% plot resonance curve
omeg=0.05:0.01:2;
phase=atan2(-2.*gamma.*omeg, (omega0.^2-omeg.^2));
amplitude=K./sqrt((omega0^2-omeg.^2).^2+(2*gamma*omeg).^2);
plot(ww+omeg./max(omeg).*plot_width, B/2+B/3*phase/abs(max(phase)-min(phase)), 'g-')
plot(ww+omeg./max(omeg).*plot_width, B/2-B/3*amplitude/abs(max(amplitude)-min(amplitude)), 'r-')
line([ww ww+plot_width], [B/2 B/2], 'Color', black);
rx=ww+omega/max(omeg).*plot_width;
line([rx rx], [B/2 B/2-B/3], 'Color', cardinal)
frame=getframe;
[im,map1] = rgb2ind(frame.cdata,32,'nodither');
if f==1
map=map1;
imwrite(im, map, filename, 'gif', 'WriteMode', 'overwrite', 'DelayTime', 0.05, 'LoopCount', Inf);
else
im= rgb2ind(frame.cdata,map);
imwrite(im, map, filename, 'gif', 'WriteMode', 'append', 'DelayTime', 0.05);
end
disp(sprintf('Spring_frame%d', 1000+f)); %show the frame number we are at
pause(0.1);
end
function dy = dampedoszi(t,y, K, omega, omega0, gamma);
dy = zeros(2,1); % a column vector
dy(1) = y(2);
dy(2) = K*cos(omega*t)-2*gamma*y(2)-omega0^2*y(1);
function dy = damper(t,y, K, omega, omega0, gamma);
dy = zeros(2,1); % a column vector
dy(1) = y(2);
dy(2) = K*cos(omega*t);
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);
Licensing[edit]
I, the copyright holder of this work, hereby publish it under the following license:
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- You are free:
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- Under the following conditions:
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Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 16:19, 29 January 2012 | 435 × 290 (230 KB) | Jkrieger (talk | contribs) |
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