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# hw11 - γv i t Problem 1.3(a Apply the deﬁnition of the...

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ECE360 HOMEWORK #1 DUE: FRIDAY, SEPTEMBER 7, 2007 Problem 1.1 o 1 R 2 v 1 v 2 C 1 C 2 + - R i + - v (t) v (t) Derive a state-space model for the above electric circuit in the form: " ˙ v 1 ˙ v 2 # = " a 11 a 12 a 21 a 22 #" v 1 v 2 # + " b 1 b 2 # v i ( t ) v o = h c 1 c 2 i " v 1 v 2 # + [ d ] v i ( t ) Problem 1.2 Using the results of Problem 1.1, derive the input-output diﬀerential equation of the circuit in the form: d 2 v o dt 2 + α dv o dt + βv o =
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Unformatted text preview: γv i ( t ) Problem 1.3 (a) Apply the deﬁnition of the Laplace transform and show that: L n e-at o = 1 s + a (b) Use the linearity property of the Laplace transform and show that: L{ cosh at } = s s 2-a 2 L{ sinh at } = a s 2-a 2 Problem 1.4 (Problem B-2-4)...
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