Answer: Consider the two-mass, three-spring system of Example 3 in the text. Instead of

Chapter 7, Problem 29

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Consider the two-mass, three-spring system of Example 3 in the text. Instead of converting the problem into a system of four first order equations, we indicate here how to proceed directly from Eqs. (22). (a) Show that Eqs. (22) can be written in the form x = 2 3/2 4/3 3 x = Ax. (i) (b) Assume that x = ert and show that (A r2 I) = 0. Note that r2 (rather than r) is an eigenvalue of A corresponding to an eigenvector .(c) Find the eigenvalues and eigenvectors of A.(d) Write down expressions for x1 and x2. There should be four arbitrary constants inthese expressions.(e) By differentiating the results from part (d), write down expressions for x1 and x2. Yourresults from parts (d) and (e) should agree with Eq. (31) in the text.

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