Show that A has the eigenpairs 1 1 1 i2, -1 -1 -i2, i4, -i4, i2 -i2 i4 -i4 i2 i2 -i4 i4
Show that A has the eigenpairs 1 1 1 i2, -1 -1 -i2, i4, -i4, i2 -i2 i4 -i4 i2 i2 -i4 i4
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.2: Systems Of Linear Equations In Two Variables
Problem 20E
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Question
Two masses are connected by springs and slide along a frictionless horizontal track.
Their motion is governed by the second-order system
h1'' = -4h1 - 6(h1 - h2), h1'' = -6(h2 - h1) - 4h2
where h1 and h2 are the horizontal displacements of the masses from their respective equilibrium positions.
(a)Recast this system as a first-order system in the form x' = Ax where
(b)Show that A has the eigenpairs
(c)Give a fundamental set of real solutions for the system x'= Ax.
(Images are attached for part a and b)
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