(a) Two of the eigenvectors of a vibrating system are known to be

Prove that these are orthogonal with respect to the mass matrix

\[[m]=\left[\begin{array}{lll}1 & 0 & 0 \\0 & 2 & 0 \\0 & 0 & 3\end{array}\right]\]

Find the remaining \([\mathrm{m}]\)-orthogonal eigenvector.

(b) If the stiffness matrix of the system is given by

\[\left[\begin{array}{rrr}6 & -4 & 0 \\-4 & 10 & 0 \\0 & 0 & 6\end{array}\right]\]

determine all the natural frequencies of the system, using the eigenvectors of part (a).

Transcribed Image Text:

0.2754946 0.6916979 0.3994672 and 0.2974301 0.4490562 -0.3389320