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Unformatted text preview: the eigenvalues of the symmetric matrix A.
c. Find an orthonormal basis for R 3 consisting of eigenvectors of A.
d. Find an orthogonal matrix B such that B −1 AB is diagonal.
e. Find the general solution to the matrix diﬀerential equation
f. Find the solution to the initial value problem 1
x(0) = 2 ,
(0) = 0.
dt 2.4.3.a. Find the eigenvalues of the symmetric matrix −2 1
0 1 −2 1
1 −2 1 0
b. What are the frequencies of oscillation of a mechanical system which is
governed by the matrix diﬀerential equation
dt2 2.5 Mechanical systems with many degrees of
freedom* Using an approach similar to the one used in the preceding section, we can
consider more complicated systems consisting of many masses and springs. For
53 Figure 2.7: A circular array of carts and springs.
example, we could consider the box spring underlying the mattress in a bed.
Although such a box spring contains hundreds of individual springs, and hence
the matrix A in the corresponding dyn...
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- Winter '14