Matlab 20. For a tightly stretched string with 5 evenly spaced masses andUse MatLab to determine:a) the natural frequenciesb) the mode shapes - plot them as in the example in the notesc) Show that the 1st and 3rd mode shapes are orthogonal with respectto the mass matrixd) Determine the responses for :0-1 mm1-.3626-.6280d) {x(t)}=-.7251.6280.3626and.40820(0)e) Plot your resultsf) Show that system vibrates in the 4th mode shape if the initialdisplacements are the 4th mode shapeAnswer:x₁, x₂ and x, for1 mm/00nm/secsin(.5176t+2.6639)+f) All C₁=C₂ = C₂ = C₁=0 C₁=0000 sin(t-1.0420)+004082 sin(1.4142t+2.1863) + 1 sin(1.7321t-1.5708)+0.4082.1877-.32513753 sin(1.9319t-1.0931).3251.1877

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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. m1 m2 k1 k2 k3 x1 x2 K= −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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