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
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F514923f2-e704-4cb3-8e16-d4c01e5e97ad%2F9ecd6c42-0e80-438c-a41a-7d347e5cfec3%2F3s9acoe_processed.png&w=3840&q=75)
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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