Find the solutions of the systems d2x dt2 = Ax(t) in Exercise 2 by converting them to

Chapter 7, Problem 12

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QUESTION:

Find the solutions of the systems d2x dt2 = Ax(t) in Exercise 2 by converting them to first-order systems, as in Exercise 11.

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QUESTION:

Find the solutions of the systems d2x dt2 = Ax(t) in Exercise 2 by converting them to first-order systems, as in Exercise 11.

ANSWER:

Step 1 of 7

a. A= ,

Thus the characteristic polynomial of A is  , and so its eigenvalues are  with corresponding eigenvectors

Now,  , where

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