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 Ffrictionca' (friction proportional to velocity). We can write the resulting system of second-order DEs as a first-order system, t'(t) = Au(t), with = (₁, ₁, ₂, For values of k= 4, m= 1 and c= 1, the resulting eigenvalues and eigenvectors of A are -0.039-0.248 0.813 A₁,2 -0.53.21, ₁- 0.024 +0.153 -0.502 -0.134-0.3021 0.409 -0.2160.4891 0.661 (a) Find a set of initial displacements (0), 2(0) that will lead to the fast mode of oscillation for this sytem. Assume that the initial velocities will be zero. ((0), ₂(0)) Enter your answer using angle braces, (and). A3,4 -0.5 1.134. = 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 Ffrictionca' (friction proportional to velocity). We can write the resulting system of second-order DEs as a first-order system, t'(t) = Au(t), with = (₁, ₁, ₂, For values of k= 4, m= 1 and c= 1, the resulting eigenvalues and eigenvectors of A are -0.039-0.248 0.813 A₁,2 -0.53.21, ₁- 0.024 +0.153 -0.502 -0.134-0.3021 0.409 -0.2160.4891 0.661 (a) Find a set of initial displacements (0), 2(0) that will lead to the fast mode of oscillation for this sytem. Assume that the initial velocities will be zero. ((0), ₂(0)) Enter your answer using angle braces, (and). A3,4 -0.5 1.134. = 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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