Consider the double mass/double spring system shown below.- click to expand.Both springs have spring constants k, and both masses have mass m; each spring is subject to a damping force of F frictionWe can write the resulting system of second-order DEs as a first-order system, w'(t) = Aw(t), with w = (x₁, x₁, x₂, x₂) TFor values of k = 4, m = 1 and c=21,2 = 0.5±3.2i, V₁23,4= - 0.5 ± 1.13i, V31, the resulting eigenvalues and eigenvectors of A are-0.039 0.248i0.8130.024 +0.153i-0.502-0.134-0.302i'0.409-0.216 - 0.489i0.661and(a) Find a set of initial displacements x₁(0), x₂(0) that will lead to the fast mode of oscillation for this sytem. Assume that the initial velocities wil be zero.(x₁(0), x₂(0))Enter your answer using angle braces, (and ).cx (friction proportional to velocity).(b) At what frequency will the masses be oscillating in this mode?Frequency =rad/s

Given:To find:Initial displacementsFrequency

Consider the double mass/double spring system shown below. - click to expand. Both springs have spring constants k, and both masses have mass m; each spring is subject to a damping force of F friction We can write the resulting system of second-order DEs as a first-order system, w ´(1) = Aw(1), with w = (x₁, x₁, x₂, x₂) ™ For values of k = 4, m = 1 and c = 1, the resulting eigenvalues and eigenvectors of A are 21.2 -0.5±3.2i, V₁ = -0.039-0.248i 0.813 0.024 +0.153i -0.502 -0.134-0.302i 0.409 23.4 = -0.5 ± 1.13i, V3 = -0.216 - 0.489i 0.661 and - cx (friction proportional to velocity). (a) Find a set of initial displacements x₁ (0), x₂(0) that will lead to the fast mode of oscillation for this sytem. Assume that the initial velocities wil be zero. (0), x₂(0)) = Enter your answer using angle braces, (and). (b) At what frequency will the masses be oscillating in this mode? Frequency = rad/s

Consider the double mass/double spring system shown below. - click to expand. Both springs have spring constants k, and both masses have mass m; each spring is subject to a damping force of F friction We can write the resulting system of second-order DEs as a first-order system, w ´(1) = Aw(1), with w = (x₁, x₁, x₂, x₂) ™ For values of k = 4, m = 1 and c = 1, the resulting eigenvalues and eigenvectors of A are 21.2 -0.5±3.2i, V₁ = -0.039-0.248i 0.813 0.024 +0.153i -0.502 -0.134-0.302i 0.409 23.4 = -0.5 ± 1.13i, V3 = -0.216 - 0.489i 0.661 and - cx (friction proportional to velocity). (a) Find a set of initial displacements x₁ (0), x₂(0) that will lead to the fast mode of oscillation for this sytem. Assume that the initial velocities wil be zero. (0), x₂(0)) = Enter your answer using angle braces, (and). (b) At what frequency will the masses be oscillating in this mode? Frequency = rad/s

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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