how to find eigenvalues using the determinant ?
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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 ?
Christine Tobler on 14 Nov 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)).