Question
Download Solution PDFअवस्था चर द्वारा प्रस्तुत एक द्वितीय कोटि प्रणाली में निम्न है।
\(A = \left[ {\begin{array}{*{20}{c}} -2&-4\\ 1&0 \end{array}} \right]\)
प्राकृतिक आवृत्ति और अवमंदन अनुपात के मान क्रमशः _________ हैं।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDF\(A = \left[ {\begin{array}{*{20}{c}} -2&-4\\ { 1}&0 \end{array}} \right]\)
\(sI - A = \left[ {\begin{array}{*{20}{c}} s&0\\ 0&s \end{array}} \right] - \left[ {\begin{array}{*{20}{c}} -2&-4\\ {1}&0 \end{array}} \right] \)
\(\\ {\left( {sI - A} \right)^{ - 1}} = \frac{1}{s(s+2)+4}\left[ {\begin{array}{*{20}{c}} {s +2}&4\\ {-1}&{s} \end{array}} \right]\)
विशेषता समीकरण है:
s(s + 2) + 4 = 0
s2 + 2s + 4 = 0
के साथ तुलना करके:
s2 + 2ζ ωn + ωn2 = 0
ωn = 2 rad/s
ζ = 0.5
Last updated on Jul 2, 2025
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