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20081ee110_1_hw4

# 20081ee110_1_hw4 - EE 110 Homework 4 Problem 1 5points 2 j...

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EE 110 Homework 4 Problem 1. 5points If a complex time-varying voltage is given as v s ( t ) = (20 j 30) e t j ) 50 2 ( + V, find ( a ) v s (0.1) in polar form; ( b ) Re { v s ( t )}; ( c ) Re [ v s (0.1)] ; ( d ) s ; ( e ) s *. Problem 2. 8points Find the Laplace transform from first principles of the following: ( a ) 2 + 3 u ( t ) ; ( b ) 3 e t 8 ; ( c ) u ( t ); ( d ) K , where K is an unknown real constant. Problem 3. 8points Determine the one-sided Laplace transform of each of the following: ( a ) L { } 1 1 s ; ( b ) 1 + u ( t ) + [ u (t)] 2 ; ( c ) tu ( t ) 3; ( d ) 1 – δ ( t ) + δ ( t 1) δ ( t 2). Problem 4. 4points Find L 1 { F ( s )} if F ( s ) = 2 s 1 + ) 2 5 4 ( 2 3 + + + s s s π . Problem 5. 6points Find L 1 { H ( s )} if H ( s ) is ( a ) ) 2 )( 1 ( ) 1 ( 2 + + + s s s ; (b) ) 2 )( 1 ( 3 + + + s s s ; (c) 3 s ) 3 )( 1 2 ( 2 4 + + + s s s s +1. Problem 6. 10points Find V ( s ) if v ( t ) = ( a ) 4 cos(100 t ) V; ( b ) 2 sin(10 3 t ) 3 cos(100 t ) V; ( c ) 14 cos(8 t ) 2sin( ) 8 ringoperator V; ( d ) δ ( t ) + sin(6 t ) u (6 t ); ( e ) cos(5 t ) sin(3 t ) V. Problem 7. 8points Find both the initial and final values (or show that they do not exist) of the time functions corresponding to ( a ) 10 6 2 8 2 + + s s s ; ( b ) s s s s s s 10 6

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20081ee110_1_hw4 - EE 110 Homework 4 Problem 1 5points 2 j...

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