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EL611 DiffEq Soln

# EL611 DiffEq Soln - EL611 Differential Eq Fall 2008 1 Find...

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EL611 Differential Eq Fall 2008 1. Find the System functions (transfer functions) of the systems described by the following differential equations. Also, assuming the systems are causal, state whether or not they are BIBO stable. a) ) ( ) ( ) ( 6 ) ( 8 ) ( 2 t x t x t y t y t y Taking laplace transform of both sides using the derivative theorem yields ) ( ) ( ) ( 6 ) ( 8 ) ( 2 2 2 3 s X s X s s sY s Y s s Y s ) ( 1 ) ( 6 8 2 2 2 3 s X s s Y s s s So, ) 3 ( 2 ) 1 ( ) 3 )( 1 ( 2 ) 1 )( 1 ( 6 8 2 1 ) ( ) ( ) ( 2 3 2 s s s s s s s s s s s s s X s Y s H The system is not BIBO stable because there is a pole ( 0 s ) on the j - axis. b) ) ( ) ( ) ( 2 ) ( ) ( t x t x t y t y t y ) 2 ( 1 ) 2 )( 1 ( 1 2 1 ) ( 2 s s s s s s s s H The system is BIBO stable because all poles are in the left half-plane, 0 } Re{ s . 2. Find the differential equation of a system with the transfer function below.

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