A system of differential equations can be created for two masses connected by springs between one another, and connected to opposing walls. The dependent variables form a 4 × 1 vector y consisting of the displacement and velocity of each of the two masses. For the system y' = Ay, the matrix A is given by: 0 0 0 0 0 1 -37 15 -8 0 15 -37 0 -8 Because the system oscillates, there will be complex eigenvalues. Find the eigenvalue associated with the following eigenvector. -6i 6i 36 + 24i -36 - 24i
A system of differential equations can be created for two masses connected by springs between one another, and connected to opposing walls. The dependent variables form a 4 × 1 vector y consisting of the displacement and velocity of each of the two masses. For the system y' = Ay, the matrix A is given by: 0 0 0 0 0 1 -37 15 -8 0 15 -37 0 -8 Because the system oscillates, there will be complex eigenvalues. Find the eigenvalue associated with the following eigenvector. -6i 6i 36 + 24i -36 - 24i
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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
Transcribed Image Text:A system of differential equations can be created for two masses connected by springs between one another, and
connected to opposing walls. The dependent variables form a 4 × 1 vector y consisting of the displacement and
velocity of each of the two masses. For the system y' = Ay, the matrix A is given by:
0
0
1
0
0
0
0
1
-37
15 -8 0
15 -37 0 -8
Because the system oscillates, there will be complex eigenvalues. Find the eigenvalue associated with the
following eigenvector.
-6i
6i
36 + 24i
-36 - 24i
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