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t is the minimum dampening ratio for an underdamped system such that its overshoot is limited to 10%? This image is my scratch work based of an in-class problem. I'

t is the minimum dampening ratio for an underdamped system such that its overshoot is limited to 10%? This image is my scratch work based of an in-class problem. I'

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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What is the minimum dampening ratio for an underdamped system such that its overshoot is limited to 10%? This image is my scratch work based of an in-class problem. I'm unsure of the steps and the final equation for Zeta. It also puts out a different number that my professor wrote…
Qushtimit 10% AAF -overshoot x ( 7 ) = f(0.5.) X(T) =-.05A 7(+) = A= Paint tre identity 7(0) = A= Asin D₂ _*(+) - A₂²¹² ( x ( )= - Asin D₂ e + sin(w₁t+ (₂) ^^ ( ²² ) = -A=²² - Pun (%) O.S. (A) = -A₂ ACT) for an under damped sys -7w. (7/2) sin (w + (₁₂²30₂) Pw7% unded without G=\ In (O.S.) In (Q.S.)+² In(.1) Tal·1)3² +TT ².
Transcribed Image Text:Qushtimit 10% AAF -overshoot x ( 7 ) = f(0.5.) X(T) =-.05A 7(+) = A= Paint tre identity 7(0) = A= Asin D₂ _*(+) - A₂²¹² ( x ( )= - Asin D₂ e + sin(w₁t+ (₂) ^^ ( ²² ) = -A=²² - Pun (%) O.S. (A) = -A₂ ACT) for an under damped sys -7w. (7/2) sin (w + (₁₂²30₂) Pw7% unded without G=\ In (O.S.) In (Q.S.)+² In(.1) Tal·1)3² +TT ².
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