I need answer ASAP The equations of motion of three equal massesconnected by springs of equal stiffness are*=-2x+yÿ = x-2y+zž=y - 2zShow that for normal modes of oscillationx = X cos@ot,y = Y cos cot,z = Zcos cotto exist then the condition on λ = @o² is2-2011= 001 1 2-2Find the three values of λ that satisfy thiscondition, and find the ratios X: Y: Z ineach case.Fλ-2

Problem is solved using concept of eigenvalue and eigen vector.

The equations of motion of three equal masses connected by springs of equal stiffness are i = -2x+y ÿ=x-2y+z ž=y-2z Show that for normal modes of oscillation x = Xcos cot, y = Y cos cot, z = Z cos cot to exist then the condition on λ = ² is 2-2 1 0 1 2-2 1 = 0 0 1 1 2-2 Find the three values of that satisfy this condition, and find the ratios X: Y: Z in each case.

The equations of motion of three equal masses connected by springs of equal stiffness are i = -2x+y ÿ=x-2y+z ž=y-2z Show that for normal modes of oscillation x = Xcos cot, y = Y cos cot, z = Z cos cot to exist then the condition on λ = ² is 2-2 1 0 1 2-2 1 = 0 0 1 1 2-2 Find the three values of that satisfy this condition, and find the ratios X: Y: Z in each case.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.4: Values Of The Trigonometric Functions

Problem 24E

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