The following mass-and-spring system has stiffness matrix K. For the mks values, find the two natural frequencies of the system and describe its two natural modes of oscillation. m1m2k1k2k3x1x2K=−k1+k2k2k2−k2+k3 m1=m2=4; k1=8, k2=12, k3=8 Let ω1<ω2 be the two natural frequencies. ω1=ω2=(Type exact answers, using radicals as needed.)

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Answered: The following mass-and-spring system…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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The following mass-and-spring system has stiffness matrix K. For the mks values, find the two natural frequencies of the system and describe its two natural modes of oscillation.

−k1+k2	k2
k2	−k2+k3

m1=m2=4; k1=8, k2=12, k3=8

Let ω1<ω2 be the two natural frequencies.

ω1=

ω2=

(Type exact answers, using radicals as needed.)

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