3. Consider a second order system*+2(wni+w²x = 0subjected to an initial displacement to and zero initial velocity, i.e.,x(0) = xo, ż (0) = 0Assume that the system is underdamped, i.e., ¢ < 1. Show that the response isiune [cs wist te sin wast]x(t) = xoe Sunt cos wat +where wa is the damped natural frequency given byWd = =W₁ √√1-5²

Answered: Image /qna-images/answer/9ecd6c42-0e80-438c-a41a-7d347e5cfec3.jpg

Answered: Consider a second order system x +…

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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Question 3 a) Consider the system shown in Figure Q3a, consisting of a spring connected to the free end of a clamped bar. Estimate the first two natural frequencies using finite element approach. The element matrices are given by [M]=P\[1 PA2 1] 1 2 and [K] spring k E, P Figure Q3a. b) Describe the convergence studies that are carried out during a finite element based modal analysis. c) Describe mode shape orthogonality. Use mode shape vector, mass and stiffness matrices in the discussion.
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