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Unformatted text preview: The force or input u is applied to mass m 2 . The distance from the ±oor to m 2 is x 2 , while the distance from the ±oor to m 1 is x 1 . Moreover, m 1 = m 2 = 1 ; k 1 = k 2 = 1 and c = 1 : Find the transfer function from u to the output y = x 1 . Y ( s ) U ( s ) = G ( s ) = 9 i u y Z 1 Z 2 Figure Problem 9 Problem 9. Find the transfer function with the input u and output voltage y for the circuit given in the Figure for Problem 9 where Z 1 is a resistor R 1 = 1 and a capacitor C = 1 in parallel, while Z 2 consists of a single resistor R 2 = 1. 10 Laplace transform pairs g ( t ) G ( s ) = R 1 e ¡ st g ( t ) dt – ( t ) 1 1 1 =s t n n ! =s n +1 e at 1 = ( s ¡ a ) cos( !t ) s= ( s 2 + ! 2 ) sin( !t ) != ( s 2 + ! 2 ) e at t n n ! = ( s ¡ a ) n +1 e at cos( !t ) ( s ¡ a ) = (( s ¡ a ) 2 + ! 2 ) e at sin( !t ) != (( s ¡ a ) 2 + ! 2 ) 11...
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 Fall '09

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