LHS.m

function [ W ] = LHS ( w,EIpa,n,omega,t )
%LHS rewrites the coefficient matrix w to the form denoted in
%equation 12 in the derivation, after the e^iwt coefficient was expanded to
%cos(wt)-isin(wt)

% Rewrite coefficient matrix in to follow form of equation 4 in derivation
wp = w./EIpa;

% Preallocate W for speed
W = wp;

% Precalculate coefficient to w term in equation 4
A = ((omega)^2)/EIpa;

% Rewrite eigenvalue problem such that the w matrix becomes (Aw - lambda w)
% which is the same as the terms in paranthesis in equation 4 (see issue in
% our project)
for i = 1:n+1
    W(i,i) = wp(i,i) - A;
end

% Element by element multiplication of term in paranthesis by cos(omega*t)
W = W.*cos(omega*t);

end