Question 64

The system described by the following governing equation of motion, will have how many natural frequencies?
$$\begin{bmatrix}m & 0 \\0 & m \end{bmatrix}\begin{bmatrix}\ddot{x1} \\\ddot{x2} \end{bmatrix} + \begin{bmatrix}2k & -k \\-k & 3k \end{bmatrix}\begin{bmatrix}x1 \\x2 \end{bmatrix} = \begin{bmatrix}0 \\0 \end{bmatrix}$$


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