23000064940 *} } [ < € ] {* } + [ ^** + m₂ + m₂ m₂ m₂ m₁ =1kg m₂ = 2kg k₁ = k₁= k₂ = 1¾ 2₁ Determine (analytically do not use Matlab): 1) The characteristic equation 2) The natural frequencies 3) The mode shapes normalized to the largest value = 1.0 4) Sketch the mode shapes 6) Determine the solutions [10] X₂0 Wis using the modal method. 7) Plot your results using MatLab. 5) Show the mode shapes are orthogonal with respect to the mass matrix x₂ (1) and x₂ (1) for -.7207 rad/s ₁₂ Wn₂ = .1.7552 rad/s 1.0 -0.1754) 11 = 1 [(k₂ + 4k₂ + k₂) −4k₂ 11 -4k₂ 2 = nm 30-4 [0.701 1.0 x₁ (t) = 7.1664 sin(.7207t-.00719)+8.7643 sin 1.1552t+2.9678) x₂ (t)=10.2149 sin(.7207t-.00719)-1.5372 sin 1.1552t +2.9678) {*}={100mm/sec M(t) M(t) R
23000064940 *} } [ < € ] {* } + [ ^** + m₂ + m₂ m₂ m₂ m₁ =1kg m₂ = 2kg k₁ = k₁= k₂ = 1¾ 2₁ Determine (analytically do not use Matlab): 1) The characteristic equation 2) The natural frequencies 3) The mode shapes normalized to the largest value = 1.0 4) Sketch the mode shapes 6) Determine the solutions [10] X₂0 Wis using the modal method. 7) Plot your results using MatLab. 5) Show the mode shapes are orthogonal with respect to the mass matrix x₂ (1) and x₂ (1) for -.7207 rad/s ₁₂ Wn₂ = .1.7552 rad/s 1.0 -0.1754) 11 = 1 [(k₂ + 4k₂ + k₂) −4k₂ 11 -4k₂ 2 = nm 30-4 [0.701 1.0 x₁ (t) = 7.1664 sin(.7207t-.00719)+8.7643 sin 1.1552t+2.9678) x₂ (t)=10.2149 sin(.7207t-.00719)-1.5372 sin 1.1552t +2.9678) {*}={100mm/sec M(t) M(t) R
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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