Answered: Show that A has the eigenpairs 1 1 1…

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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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)

Show that A has the eigenpairs
1
() (-0) (E) (-E)
1
-i4,
1
i2,
1
-i2,
i4 ,
-i4
i4
i2
-i2
i4
-i2
-i4
i2

Recast this system as a first-order system in the form x = Ax where
1 0
0 1
0 0
A =
-10
6
6.
-10 0 0

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