A 2 DOF mass-spring system shown below with n = 1, k = 8, and m = 2 with the initial conditions £₁ (0) = 1, ₂(0) = 0, ₁(0) = 0, and ±₂(0) = 1. (a) Find the natural frequencies and normalized modal matr x [X] for the system. (b) Using modal analysis and the Cartesian solution form, find the free vibration re- sponse of the system x₁(t) and r₂(t).

Elements Of Electromagnetics
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Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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A 2 DOF mass-spring system shown below with n = 1, k = 8, and m
initial conditions 2₁ (0) = 1, 2₂(0) = 0, ₁ (0) = 0, and ₂(0) = 1.
(a) Find the natural frequencies and normalized modal matrix [X] for the system.
T
x₁ (1)
(b) Using modal analysis and the Cartesian solution form, find the free vibration re-
sponse of the system x₁(t) and x2(t).
Ţ
x2₂ (1)
www.
00000
= m
m₁ =
00000
k₁ = k
00000
k₂ = nk
m₂ = m
k3= k
=
2 DOF mass-spring system.
2 with the
Transcribed Image Text:A 2 DOF mass-spring system shown below with n = 1, k = 8, and m initial conditions 2₁ (0) = 1, 2₂(0) = 0, ₁ (0) = 0, and ₂(0) = 1. (a) Find the natural frequencies and normalized modal matrix [X] for the system. T x₁ (1) (b) Using modal analysis and the Cartesian solution form, find the free vibration re- sponse of the system x₁(t) and x2(t). Ţ x2₂ (1) www. 00000 = m m₁ = 00000 k₁ = k 00000 k₂ = nk m₂ = m k3= k = 2 DOF mass-spring system. 2 with the
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