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# prc 7 - ECSE-210 Winter 2011 Electric Circuits 2 Practice...

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ECSE-210 Winter 2011 Electric Circuits 2 7-1 Practice Set #7 P14.2-1 ( ) ( ) ( ) ( ) ( ) ( ) 1 1 2 2 1 1 2 2 cos A f t A F s As F s s s f t t F s s ! ! ! " = # \$ % & ' ( = ) + = ( = ' + * L P14.2-2 ( ) 1 1 1 1 2 1 ! 1! F n n n t s t s s s + + ! " ! " = = = = # \$ # \$ LL P14.2-3 ( ) ( ) ( ) ( ) ( ) ( ) ( ) [ ] ( ) ( ) 1 1 2 2 1 1 2 2 1 2 3 1 1 2 2 2 2 Linearity: a a Here 1 1 3 1 1 1 so 3 t f t a f t F s a F s a a f t e F s s f t t F s s F s s s ! + = + " # \$ % = = " # = = = " # \$ % \$ % + = = = " # \$ % = + + L LL LL P14.2-4 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 1 2 3 2 3 1 2 3 1 ( ) 1 1 1 1 , 1 1 bt bt bt f t A e u t A f t f t e u t u t e u t f t f t F s F s s s b Ab F s AF s A F s F s A s s b s s b ! ! ! = ! = = ! = ! = + ! = = + " # \$ = = + = ! = " # % & ' ( + + % & P14.3-8 ( ) 5 2 0 2 0 otherwise t t f t < < ! = " # ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 2 2 2 2 5 5 5 5 2 2 2 2 2 ( 2) 2 2 2 2 5 1 2 5 1 1 2 2 2 s s s s f t t u t u t t u t t u t t u t t u t u t e e F s f t e se s s s s ! ! ! ! = ! ! = ! ! = ! ! ! ! ! " # " # \$ % \$ % " # " # & = = ! ! = ! ! " # ' ( \$ % \$ % \$ % L

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ECSE-210 Winter 2011 Electric Circuits 2 7-2 P14.4-1 ( ) ( ) 3 2 2 2 3 3 ( ) 3 6 4 1 2 4 1 1 3 s s A Bs C F s s s s s s s s s + + + = = = + + + + + + + ! " + + + # \$ where ( ) 2 1 3 2 3 1 3 s s A s = ! + = = + + Then ( ) ( ) ( ) ( ) 2 2 2 2 3 2 4 8 3 3 ( ) 1 2 4 3 3 3 1 2 4 s Bs C s B s B C s C s s s s s s + + ! " = + # + = + + + + + + \$ % + + + + + + & ' Equating coefficient yields 2 2 2 s : 0 3 3 4 2 1 s : 1 3 3 3 B B C C = + ! = " = " + ! = Then ( ) ( ) ( ) ( ) ( ) 2 2 2 1 2 2 1 2 2 3 1 3 3 3 3 3 3 1 1 1 3 1 3 1 3 s s F s s s s s s ! + ! + = + = + + + + + + + + + + Taking the inverse Laplace transform yields ( )
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prc 7 - ECSE-210 Winter 2011 Electric Circuits 2 Practice...

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