# Damped plucked string wave equation Fourier series assignment/ matrix dimensions problem

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Michael on 24 Jan 2013
Hi there.
I'm having a little trouble implementing the solution to the damped 1-dimensional wave equation for a damped, plucked string. I would like to plot the position of a large number of points along the string (to represent the string itself), at discrete time instants.
My commented code is:
MATLAB code
L_s = 0.33; % length of string (m)
m = 0.000125; % mass of string (kg)
T = 68; % stretched tension of string (N)
R = 100; % linear resistance for string (Ns/m)
rho_L = m/L_s; % mass per unit length of string (kg/m)
c = sqrt(T/rho_L); % wave speed in string (m/s)
t = 1.3; % current time value (s)
d_0 = 0.2; % initial displacement value (m)
% range variables
x = linspace(0,L_s,1000); % position points on string (m)
n = linspace(1,length(x),length(x)); % integers for Fourier series
Omega_n = sqrt((c.*n.*pi./L_s).^2 - R^2); % argument coefficient for Fourier sine series
alpha_n = 8*d_0./(n.^2*pi^2).*sin(n.*pi./2); % first Fourier series coefficient
beta_n = R.*alpha_n./Omega_n; % second Fourier series coefficient
w = zeros(1,length(n),length(x)); % displacement function for string
for i = 1:length(n)
for j = 1:length(x)
w(i,j) = w + sin(n(i).*pi.*x(j)./L_s).*exp(-R./t).*(alpha_n(i).*cos(Omega_n(i).*t) ...
+ beta_n(i).*sin(Omega_n(i).*t));
end
end
hold on
figure(1)
plot(x,w)
xlabel('Position on string (m)')
ylabel('Displacement (m)')
xlim([0 0.33])
The error message is: "Assignment has more non-singleton rhs dimensions than non-singleton subscripts
Error in ass_assignment2 (line 39) w(i,j) = w + sin(n(i).*pi.*x(j)./L_s).*exp(-R./t).*(alpha_n(i).*cos(Omega_n(i).*t) ..."
Could anyone offer some advice? I understand the error message is telling me that the RHS comprises more dimensions than the LHS, but I cannot see why this would be.
Any help is much appreciated. Any general comments on more efficient and clearer coding techniques are also most welcome.
Regards,
Mike

Jonathan Epperl on 24 Jan 2013
In here
w(i,j) = w + sin(n(i).*pi.*x(j)./L_s).*exp(-R./t).*alpha_n(i).*cos(Omega_n(i).*t) ...
+ beta_n(i).*sin(Omega_n(i).*t));
the term w is a vector, as you defined it, the rest is all scalars, so what you will get is a vector with size size(w) with the scalars added to each element.
I'm also not sure why you initialize w as a 1 x length(n) x length(x) 3-D array, wouldn't a matrix be sufficient?
Jonathan Epperl on 27 Jan 2013
Glad I could help. Vectorization is probably the most speed-gaining technique in Matlab, you should definitely get familiar with it. Functions that I find often helpful:
ones(), diag(), blkdiag(), repmat(), meshgrid(), ndgrid()