Question: Consider the eigenvalue problem: a. Find the natural frequencies and mode shapes of the system. b. Change the coordinates in Eq. (E.1) as (X_{1}=Y_{1}) and

Consider the eigenvalue problem:

1 0 6-2 X (E.1) * 98-[4]} = 2

a. Find the natural frequencies and mode shapes of the system.

b. Change the coordinates in Eq. (E.1) as $X_{1}=Y_{1}$ and $X_{2}=3 Y_{2}$ and express the eigenvalue problem in terms of the eigenvector $\vec{Y}=\left\{\begin{array}{l}Y_{1} \\ Y_{2}\end{array}\right\}$, solve it, and find the natural frequencies and mode shapes.

c. Compare the results found in parts

(a) and

(b) and give your observations.

1 0 6-2 X (E.1) * 98-[4]} = 2

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