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how to find eigenvalues using the determinant ?

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aiman
aiman el 13 de Nov. de 2022
Respondida: Christine Tobler el 14 de Nov. de 2022
Hello,
I have mass and stiffness matrices and i want to find the eigenfrequency using det(K-w^2*M)=0 while K and M are the matrices and w is the eigenvfrequencies.How can i change this equation into mode and getting w ?

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Christine Tobler
Christine Tobler el 14 de Nov. de 2022
The determinant should only be used explicitly to solve an eigenvalue problem for symbolic calculation (for example, when you solve a 2-by-2 problem by hand). In numeric computations, the determinant is not robust and not advised to use.
You can compute the eigenvalues and eigenvectors using the EIG function, [V, D] = eig(K, M). This gives you eigenvalues (diagonal of D) and eigenvectors (columns of V) of this problem. The matrices satisfy
norm(K*V-M*V*D) % == 0 up to round-off error
To get the w value you want, you simply take the square root of the eigenvalues, sqrt(diag(D)).

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John D'Errico
John D'Errico el 13 de Nov. de 2022
Editada: John D'Errico el 13 de Nov. de 2022
This is a generalized eigenvalue problem. READ THE HELP FOR EIG. If you pass in both matrices, it still computes the eigenvalues.
Do you want to use the determinant? NO! Learn to use eig.

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