= Problem 1 (Problem 7.2-4 from the textbook) 7.2-4. Consider a sampled-data system with T = 05 s and the characteristic

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Problem 1 Problem 7 2 4 From The Textbook 7 2 4 Consider A Sampled Data System With T 05 S And The Characteristic 1 (54.65 KiB) Viewed 44 times

= Problem 1 (Problem 7.2-4 from the textbook) 7.2-4. Consider a sampled-data system with T = 05 s and the characteristic equation given by (2–0.9)(= – 0.8)(– 1.92 +1.0) = 0 (a) Find the terms in the system natural response. (b) A discrete LTI system is stable, unstable, or marginally stable. Identify the type of stability for this system (c) The natural response of this system contains an undamped sinusoidal response term of the form A cos(wkT +) - Find the frequency w of this term. Solution: T=0.5, char.eq.: (=-0.9): -0.8):2 -1.9z+1) = 0) Complex roots: :=0.95 j0.3122 =12+18.19° =12+0.3175 rad (a) k(0.9)", k2(0.8)", A cos (0.3175k+0) (b) marginally stable 0.3175 (c) root = 12+oT,.. OT = 0.3175 = 0= 0.5 0.635 rad/s