BME211HW9 - Homework#9 Solutions Ex 14.6-1 Taking Laplace...

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Homework #9 Solutions Ex. 14.6-1 Taking Laplace Transform of the differential equation: ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 2 ' 10 0 0 5 0 6 3 s F s s f f s F s f F s s - - + - + = + Using the given initial conditions 2 2 10 2 16 40 ( 5 6) ( ) 2 10 3 3 s s s s F s s s s + + + + = + + = + + ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 2 2 2 16 40 3 2 3 3 2 3 s s A B C F s s s s s s s + + = = + + + + + + + + where 10, 14, and 16 A B C = - = - = . Then ( 29 3 3 2 2 10 14 16 ( ) ( ) 10 14 16 for 0 3 2 3 t t t F s f t te e e t s s s - - - - - = + + = - - + + + + P14.2-1 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 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 ϖ ϖ ϖ = L = + = = L + L P14.2-2 ( 29 1 1 1 1 2 1 ! 1! F n n n t s t s s s + + � � �� = = = = � � �� L L
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P14.2-3 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 [ ] ( 29 ( 29 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 L L L L P14.3-1 ( 29 ( 29 ( 29 f t A u t u t T = - - ( 29 ( 29 ( 29 ( 29 1 sT sT e A Ae F s A u t A u t T A s s s - - - = - - = - = L L P14.3-7 2 2 2 0 0 0 3 3(1 ) ( ) ( ) 3 st s st st e e F s f t e dt e dt s s - - - - - = = = = - P14.4-3 ( 29 ( 29 ( 29
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