numerical approximation of complex number
I am attempting to evaluate a matrix multiplication, then extract 4 specific cells from the resultant matrix and create a new 2x2 matrix with these 4 specific cells. I then need to calculate the points at which the determinant of the 2x2 matrix equals zero. This is to solve the resonant frequency of transverse vibration of a beam. My attempt at doing this:
e,f,g,h,i,j,k,l,m,n,o,p,g,r,s,t=var('e,f,g,h,i,j,k,l,m,n,o,p,g,r,s,t');
var("w", domain="complex");
a=4;
b=8;
c=32/3;
d=4;
m1=1;
m2=m1/2;
x=m1*(w);
y=m2*(w);
F=matrix([[1,a,b,c],[0,1,d,b],[0,0,1,a],[0,0,0,1]]);
M1=matrix([[1,0,0,0],[0,1,0,0],[0,0,1,0],[x,0,0,1]]);
M2=matrix([[1,0,0,0],[0,1,0,0],[0,0,1,0],[y,0,0,1]]);
([[e,f,g,h],[i,j,k,l],[m,n,o,p],[q,r,s,t]])=F*M1*F*M1*F*M1*F*M2;
A=matrix([[o,p],[s,t]]);
B=A.determinant();
C=solve(B==0,w);
numerical_approx(C)
Sagemath returns an error since there are complex numbers.
I require numerical solutions.
apologies if the question is unclear, I have zero programming background, this is for my engineering dissertation.
Any help is appreciated.
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