% String driven at the left end with known sinusoidal displacement 
% with amplitude Y0 and fixed at the right end. Input is the ratio of the 
% forcing frequency to the first natural frequency.
% This m-file was written at the University of Wyoming in the Electrical
% and Computer Engineering Department and is to be distributed without
% cost.
clear all
set(0,'DefaultAxesFontSize',12);
set(0,'DefaultTextFontSize',12);
string1='The ratio of excitation freq. to first natl freq. = ';
fratio=input(string1);
xoverL=linspace(0,1,201);
sw=cos(fratio*pi*xoverL)-(sin(fratio*pi*xoverL)/tan(fratio*pi));
lim=max(abs(sw));

figure(1);clf;
plot(xoverL,abs(sw))
hold on
plot([0 1],[0 0]);
axis([0 1 -.2*lim 1.2*lim]);
text(.8,1.1*lim,['f/f_1 = ',num2str(fratio)])
xlabel('Dimensionless distance from the fixed end, x/L')
ylabel('Dimensionless Amplitude, y(x)/Y_0')
text(.1,1.1*lim,'Press Enter to Continue')
xp1=.5+.5*[1 1 1.1 1.3 1.2 1.32 1.2 1 1];
yp1=1.5*lim*[0 .4 .3 .2 .1 0 -.2 -.4 0];
pause

figure(2);clf;
set(gca,'Box','on')
axis([-.3 1.3 -2*lim 2*lim]);
patch(xp1,yp1,'r')
xlabel('Distance, x/L')
ylabel('Displacement, y(x,t)/Y_0')
hold on
x1=[-.3 1];y1=[0 0];
plot(x1,y1)
hold on
texthandle2=text(-.1,-1.6*lim,['f/f_1 = ',num2str(fratio)]);
ys=sw*0;
plot(xoverL,ys,'k','LineWidth',[1.5]);
hold on
ydata=[ys];
texthandle2=text(0,1.5*lim,'Press Enter to Animate one Frame at a Time');
xlabel('Distance , x/L');
ylabel('Displacement, y(x,t)/Y_0');
pause
t=linspace(0,8*pi,257);
sine=sin(t);
for k=1:2:65
    ys=sw*sine(1,k);
    plot(xoverL, ys,'k','LineWidth',[1.5]);
    hold on
    set(texthandle2,'String', 'Press Enter to Animate One Frame at a Time');
    pause
end
set(texthandle2,'String','Press Enter to Continue');
pause

figure(3);clf;
set(gca,'Box','on')
axis([-.3 1.3 -2*lim 2*lim]);
patch(xp1,yp1,'r')
xlabel('Distance, x/L')
ylabel('Displacement, y(x,t)/Y_0')
hold on
x1=[-.3 1];y1=[0 0];
plot(x1,y1)
hold on
texthandle2=text(-.1,-1.6*lim,['f/f_1 = ',num2str(fratio)]);
ys=sw*0;
L=plot(xoverL,ys,'k','EraseMode','xor','LineWidth',[2.5]);
ydata=[ys];
texthandl=text(0,1.5*lim,'Press Enter to Animate');
xlabel('Distance , x/L')
ylabel('Displacement, y(x,t)/Y_0')
pause
set(texthandl,'String','   ');
t=linspace(0,8*pi,257);
sine=sin(t);
for k=2:257
    ys=sw*sine(1,k);;
    set(L,'Ydata',ys)
    pause(.05)
    ydata=[ydata ;ys];
end
set(texthandl,'String','Press Enter to Continue');
pause

figure(4);clf;
[X,T]=meshgrid(xoverL,t);
mesh(X,T,ydata)
axis([0 1 0 8*pi -1.2*lim 1.2*lim]);
text(1,5,-lim,'Dimensionless Time, \omegat','Rotation',-10)
text(1,25,-lim,'Dimensionless Distance, x/L','Rotation',32)
zlabel('Displacement, y(x,t)/Y_0')
text(0,4,1.1*lim,'Press Enter to Continue','Rotation',-10)
view(120,30)
pause