 #1
happyparticle
 372
 19
 Homework Statement:
 Find the eigenvalues of a 3x3 matrix
 Relevant Equations:

##\begin{pmatrix}  \omega^2 +\frac{k}{m} &\frac{k}{m} &0\\ \frac{k}{M}&  \omega^2 + 2 \frac{k}{M} &\frac{k}{M} \\
0& \frac{k}{m} & \omega^2 + \frac{k}{m}
\end{pmatrix} \begin{pmatrix}A_1\\A_2\\A_3 \end{pmatrix} =0##
Hi,
I have a 3 mass system. ##M \neq m##
I found the forces and I get the following matrix.
I have to find ##\omega_1 , \omega_2, \omega_3## I know I have to find the values of ##\omega## where det(A) = 0, but with a 3x3 matrix it is a nightmare. I can't find the values.
I'm wondering if there's another way to have the eigenvalues.
##\begin{pmatrix}  \omega^2 +\frac{k}{m} &\frac{k}{m} &0\\ \frac{k}{M}&  \omega^2 + 2 \frac{k}{M} &\frac{k}{M} \\
0& \frac{k}{m} & \omega^2 + \frac{k}{m}
\end{pmatrix} \begin{pmatrix}A_1\\A_2\\A_3 \end{pmatrix} =0
##
I have a 3 mass system. ##M \neq m##
I found the forces and I get the following matrix.
I have to find ##\omega_1 , \omega_2, \omega_3## I know I have to find the values of ##\omega## where det(A) = 0, but with a 3x3 matrix it is a nightmare. I can't find the values.
I'm wondering if there's another way to have the eigenvalues.
##\begin{pmatrix}  \omega^2 +\frac{k}{m} &\frac{k}{m} &0\\ \frac{k}{M}&  \omega^2 + 2 \frac{k}{M} &\frac{k}{M} \\
0& \frac{k}{m} & \omega^2 + \frac{k}{m}
\end{pmatrix} \begin{pmatrix}A_1\\A_2\\A_3 \end{pmatrix} =0
##