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Solution z3+z² + 1.5Kz - (K + 0.5) = 0 Let N = ω Or 3 + w+1 @-1 .The characteristic equation becomes. 2 +1.5K (+1)-(K + 0.5) = 0 ELECTRIC (1.5 + 0.5K) w³ + (5.5 + 1.5K)w² + (0.5 - 4.5K)w + (2.5K + 0.5) = 0 0.5)=0

Solution z3+z² + 1.5Kz - (K + 0.5) = 0 Let N = ω Or 3 + w+1 @-1 .The characteristic equation becomes. 2 +1.5K (+1)-(K + 0.5) = 0 ELECTRIC (1.5 + 0.5K) w³ + (5.5 + 1.5K)w² + (0.5 - 4.5K)w + (2.5K + 0.5) = 0 0.5)=0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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z3+z2+ 1.5Kz - (K + 0.5) = 0 Solution Let z= 3 w+1 @-1 . The characteristic equation becomes. 2 (+1)² + (+1)² + 15K (+1)-(K+0.5) = 0 Or + (0.5 4.5K)w + (2.5K + 0.5) = 0 (1.5 + 0.5K) w³ + (5.5+ 1.5K) w² + (0.5 - 4.5 How was it simplified to get to this part?
Transcribed Image Text:z3+z2+ 1.5Kz - (K + 0.5) = 0 Solution Let z= 3 w+1 @-1 . The characteristic equation becomes. 2 (+1)² + (+1)² + 15K (+1)-(K+0.5) = 0 Or + (0.5 4.5K)w + (2.5K + 0.5) = 0 (1.5 + 0.5K) w³ + (5.5+ 1.5K) w² + (0.5 - 4.5 How was it simplified to get to this part?
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