MATLAB: Eigenvector problem with complex conjugate eigenvalues

complexdampingeigenvalueeigenvectorviscous

Hello, im solving here a viscous damping problem. As you can see det(A) is the equation that must be solved in order to obtain the eigenvalues of the problem. My issue is after having all 10 eigenvalues (20 with their conjugates) i do not know exactly how to make MATLAB calculate me the eigenvectors of the problem, given that im not using the 'eig' command.
M=[1 0 0 0 0 0 0 0 0 0;           
   0 1 0 0 0 0 0 0 0 0;
   0 0 1 0 0 0 0 0 0 0;
   0 0 0 1 0 0 0 0 0 0;
   0 0 0 0 1 0 0 0 0 0;
   0 0 0 0 0 2 0 0 0 0;
   0 0 0 0 0 0 3 0 0 0;
   0 0 0 0 0 0 0 3 0 0;
   0 0 0 0 0 0 0 0 4 0;
   0 0 0 0 0 0 0 0 0 1];
K=[1 -1 0 0 0 0 0 0 0 0;           
  -1 3 0 0 0 0 -2 0 0 0;
   0 0 3 -1 0 0 0 -2 0 0;
   0 0 -1 1 0 0 0 0 0 0;
   0 0 0 0 1 -1 0 0 0 0;
   0 0 0 0 -1 3 -2 0 0 0;
   0 -2 0 0 0 -2 8 -4 0 0;
   0 0 -2 0 0 0 -4 11 -5 0;
   0 0 0 0 0 0 0 -5 10 -5;
   0 0 0 0 0 0 0 0 -5 5];
F=[1 -1 0 0 0 0 0 0 0 0;
   -1 2 0 0 0 0 -1 0 0 0;
   0 0 0 0 0 0 0 0 0 0;
   0 0 0 0 0 0 0 0 0 0;
   0 0 0 0 0 0 0 0 0 0;
   0 0 0 0 0 0 0 0 0 0;
   0 -1 0 0 0 0 2 -1 0 0;
   0 0 0 0 0 0 -1 1 0 0;
   0 0 0 0 0 0 0 0 0 0;
   0 0 0 0 0 0 0 0 0 0];
f=2/50;
m=8;
k=2000; 
Mv=m*M;
Fv=f*F;
Kv=K*k;
syms s phi
A=s^2*Mv +s*Fv+ Kv;
r=det(A);
s=double(subs(solve(r)));
for i=1:20
   A=s(i)^2*Mv +s(i)*Fv+ Kv;
   eqn= A*phi==0;
   Mod(i)=double(subs(solve(eqn,phi)));
   end

Best Answer

null(A) might help:
https://de.mathworks.com/help/matlab/ref/null.html
Best wishes
Torsten.
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