% pluck & visulaize a guitar string

% parameters
Nx = 101; % elements in a unit-length string
dx = 1/(Nx-1);
c = 1; % convenient
dt = c*dx; % since we require r = 1
f = 0.35; % fraction of length at which string is plucked
Nt = 500;  % # of time steps

% preallocate results
Y = zeros(Nx,Nt+2);

% establish initial conditions
pluckPoint = round(f*Nx);

% various types of plucks
type = 2;
if type == 1
    Y(:,1) = [
        ((1:pluckPoint)-1)'/(pluckPoint-1)
        (Nx-(pluckPoint+1:Nx))'/(Nx-pluckPoint)
        ];
elseif type == 2
    Y(:,1) = exp(-0.02*((1:Nx)-pluckPoint).^2);
end

% copy IC in two places
Y(:,2) = Y(:,1);

% loop through time for solutions
for n = 3:Nt+2
    Y(:,n-2:n) = stringFixed(Y(:,n-2:n),c,dt,dx);
end

% image results
clf
plot(Y(:,1))
set(gca,'ylim',1.05*[-1 1])
pause
for n = 2:size(Y,2)
    plot(Y(:,n))
    set(gca,'ylim',1.05*[-1 1])
    pause(0.001)
end

return