3_1_HW 5 Solutions

3_1_HW 5 Solutions - By KVL: −v t Ri t L L di t =0 dt di...

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Unformatted text preview: By KVL: −v t Ri t L L di t =0 dt di t Ri t = v t dt By Laplace Transform: da t ℒ = sA s − a 0 dt di t ∴ℒ = sI s , i 0 =0 dt and ℒ{ i t } = I s So LsI s RI s = V s I s [ Ls R ] = V s I s 1 = V s Ls R {} {} We know from Pblm 1 that 2 Y s s 2 2 2 = = = X s 1 s 21 s 3 1 s 2 So now we have a new block diagram: Y s G s = X s 1 0.5G s X 2 s 3 Y To get the time constant, we need to apply a unit step input u t . 2 1 2 Since Y s = [ ℒ{ u t } ] = , s 3 s s 3 and from the Laplace Transform tables, ℒ−1 2 −1 1 3 we have y t = ℒ 3 s s 3 ∴= ⅓ 1 s s [ ] { } { } = ⅔ 1 −e − 3t = 1− e− t , − t ⅓ = ⅔ 1 −e ...
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This note was uploaded on 04/04/2010 for the course EE 3 taught by Professor Staff during the Winter '08 term at UCLA.

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