A 2 DOF mass-spring system shown below with n = 1, k = 8, and minitial 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.Tx₁ (1)(b) Using modal analysis and the Cartesian solution form, find the free vibration re-sponse of the system x₁(t) and x2(t).Ţx2₂ (1)www.00000= mm₁ =00000k₁ = k00000k₂ = nkm₂ = mk3= k=2 DOF mass-spring system.2 with the

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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Concept explainers

Free undamped vibrations

Whenever an object/system displaces in either side of its equilibrium position with the help of an external/internal means, then the object/system moves regularly or randomly on both sides of its equilibrium position. This motion is called vibration. Generally, there are three types of vibration: longitudinal vibration, transverse vibration, and torsional vibration.

Question

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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