HW_5_sol[1] - HW 5 ECE 2704 Due 10-16-06 A system is given...

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DKL:10/18/06 HW 5 solutiions 1/3 HW 5 ECE 2704 Due 10-16-06 A system is given by its pole-zero diagram 1. (5) What is the transfer function of this system? (gain = 1) Solution Y ( s ) X ( s ) = H ( s ) = 1 s + 1 ( ) 2 + 6 2 = 1 s 2 + 2 s + 37 2. (5) Find ! , " n ( ) for these poles. Solution ! n 2 = 37 "! n = 6.08 rad/sec , 2 !" n s = 2 s # ! = 1 " n # ! = 0.164 Other approach to obtain this solution is to use damp command in Matlab. h = tf ([1], [1 2 37]) Transfer function: 1 ----------------- s^2 + 2 s + 37 >> damp (h) Eigenvalue Damping Freq. (rad/s) -1.00e+000 + 6.00e+000i 1.64e-001 6.08e+000 -1.00e+000 - 6.00e+000i 1.64e-001 6.08e+000
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DKL:10/18/06 HW 5 solutiions 2/3 3. (10) Find y ( t ) by Laplace transforms. Solution Y ( s ) = H ( s ) X ( s ) = 1 s 2 + 2 s + 37 1 s y ( t ) = 1 ! n 2 1 " 1 1 " # 2 e "#! n
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HW_5_sol[1] - HW 5 ECE 2704 Due 10-16-06 A system is given...

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