How to retrieve an unknown value from a matrix
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Point of this task is to retrieve a value of "w" from the matrix "A", where we know that the determinant of this matrix is equal to zero. There will be more than one value of "w" but how do I make the "w" value my output in such a way?
m=9000000;
Ig=1350000000;
D=2.5;
t=0.02;
I=pi()*(D^4-(D-2*t)^4)/64;
l1=16;
l2=14;
l3=17;
l4=13;
k=1000000;
A=[((4*k)-((w^2)*m)) 0 (2*k*(l2-l1)); ...
0 ((4*k)-((w^2)*m)) (2*k*(l4-l3)); ...
(2*k*(l2-l1)) (2*k*(l4-l3)) ((2*k*(l1^2+l2^2-l3^2-l4^2)-(w^2*Ig)))];
det(A)=0;
2 Comments
the cyclist
on 31 Oct 2018
Do you mean that you want to solve for the value of w that will make the determinant of A equal to zero?
Answers (2)
the cyclist
on 31 Oct 2018
Assuming you want to solve for w, as I mentioned in my comment, then this will do it:
m=9000000;
Ig=1350000000;
D=2.5;
t=0.02;
I=pi()*(D^4-(D-2*t)^4)/64;
l1=16;
l2=14;
l3=17;
l4=13;
k=1000000;
detA = @(w) det([((4*k)-((w.^2)*m)) 0 (2*k*(l2-l1));
0 ((4*k)-((w.^2)*m)) (2*k*(l4-l3));
(2*k*(l2-l1)) (2*k*(l4-l3)) ((2*k*(l1^2+l2^2-l3^2-l4^2)-(w.^2*Ig)))]);
w_critical = fzero(detA,0.6);
figure
hold on
for w = 0.66:0.001:0.7
h = plot(w,detA(w),'o');
set(h,'Color','k')
end
A couple things to note:
First, I defined detA as a function of w.
Second, I had to choose a very good initial guess for w_critical, because your function varies over a huge range, so fzero will fail if you are not close. I found a good value by plotting your function, and zooming in on one part near zero. Here is the final plot I used:
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/194208/image.png)
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