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).
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
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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![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F38b56bf0-a460-4322-b159-175f7d47f441%2F82f242ee-1bd2-4cb0-b16c-7d151e834f33%2F263p50u_processed.png&w=3840&q=75)
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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