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Consider a second order system x + 2(wni+w₁₂x = 0 subjected to an initial displacement to and zero initial velocity, i.e., x(0) = xo, * (0) = 0 Assume that the system is underdamped, i.e., § < 1. Show that the response is wat [cos wat + sin wat] VI-C x(t) = e-swnt = roe where wa is the damped natural frequency given by wd = wn√√1-5²

Consider a second order system x + 2(wni+w₁₂x = 0 subjected to an initial displacement to and zero initial velocity, i.e., x(0) = xo, * (0) = 0 Assume that the system is underdamped, i.e., § < 1. Show that the response is wat [cos wat + sin wat] VI-C x(t) = e-swnt = roe where wa is the damped natural frequency given by wd = wn√√1-5²

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