Homework Problems with Solutions for Fundamental Electric Circuits | ECE 2260, Assignments of Electrical and Electronics Engineering

Download Homework Problems with Solutions for Fundamental Electric Circuits | ECE 2260 and more Assignments Electrical and Electronics Engineering in PDF only on Docsity! 2260 F 08 HW #6 prob 1 solution 1. a) Find € L e−6τ cos(7τ)dτ 0 t∫      . b) Find v(t) if € V (s) = 18s+148 s2 +12s+11 . c) Find € lim t→∞ v(t) if € V (s) = s 2 + 4 (s+ 3)3 . d) Plot the poles and zeros of V(s) in the s plane. € V (s) = s 2 + 5s+ 6 (s+1) (s+ 4)2 + 52[ ] Re Im SOL'N: a) We use the identity for integration and the transform pair for the decaying cosine: € L e−6τ cos(7τ)dτ 0 t∫      = 1 s L e−6t cos(7t){ } = s+ 6 s[(s+ 6)2 + 72] b) We have two real roots: € L-1 18s+148 s2 +12s+11       = L-1 18s+148 (s+1)(s+11)       = L-1 A s+1 + B s+11       We fine A and B by the usual method of removing the pole and evaluating at the pole value: € A = (s+1)V (s) s=−1 = 18s+148 s+11 s=−1 = 130 10 =13