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Homework#2 (2/1) Answers ME 3600 Control Systems 1. E2.2: T . R Δ = Δ 3 135 2. E2.11: a) ( ) 50 0.015 3333 , so 3333 (N/m) f x x k Δ = Δ = Δ = b) ( ) 40 0.02 2000 , so 2000 (N/m) f x x k Δ = Δ = Δ = c) ( ) 14 0.04 350 , so 350 (N/m) f x x k Δ = Δ = Δ = 3. E2.17: a) ( ) ( ) 0 0 0 0 1, 2.4 , 2, 13.2 x y x y = = = = b) { } { } 0 0 1, 5.2 , 2, 17.8 x y x x y x = Δ = Δ = Δ = Δ 4. P2.5: a) Define 2 1 P P R = ; Operating point = R o = ( P 1 -P 2 ) o R P P K Q R R Δ = Δ = o 2 1 2 b) When R o = ( P 1 -P 2 ) o = 0, no linear model exists. 5. E2.25: 1 1 1 2 ( ) m x kx kx F t + = ±± 2 2 2 1 0 m x kx kx + = ±± ( 1 x and 2 x are measured from the equilibrium positions.) 6. P2.2: ) ( ) ( 2 12 1 12 1 1 1 1 t F y k y k k y b y M = + + + ± ± ± 0 2 12 1 12 2 2 = + y k y k y M ± ± ( 1 y and 2 y are measured from the equilibrium positions.) 7. P2.3:
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