hw#3

# Hw#3 - Y s X s = 10 s 1 s 5 5 Find the inverse Laplace transform for Y 1 s = 10 s 1 s s 2 s 5 Y 2 s = 2 s 2 s 1 s 2 4 s 8 Y 3 s = 20 s 4 s 1 s 2 16

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EE3530 Homework # 3 Due on Friday, February 22, 2008. Midterm 1 will be on Friday, February 29. 1. Find the Laplace transform of the following functions f 1 ( t ) = 1 + t 2 + te - 2 t f 2 ( t ) = te t + t sin t f 3 ( t ) = 2 t cos(5 t + 45 o ) f 4 ( t ) = 10 e - 2 t sin(5 t + 30 o ) 2. A system is described by ¨ y + 5 ˙ y + 6 y = 10 ˙ u + 5 u Find the transfer function Y ( s ) U ( s ) . Find y ( t ) if y (0) = 0, ˙ y (0) = 1, and u = 1( t ). 3. Solve the following diﬀerential equation using Laplace transform ¨ y ( t ) - 8 ˙ y ( t ) + 15 y ( t ) = sin t, y (0) = 1 , ˙ y (0) = 2 4. Write the diﬀerential equation corresponding to the following transfer function

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Unformatted text preview: Y ( s ) X ( s ) = 10 ( s + 1)( s + 5) 5. Find the inverse Laplace transform for Y 1 ( s ) = 10( s + 1) s ( s + 2)( s + 5) Y 2 ( s ) = 2( s + 2) ( s + 1)( s 2 + 4 s + 8) Y 3 ( s ) = 20( s + 4) ( s + 1)( s 2 + 16) Y 4 ( s ) = e-2 s s 3 6. Find the transfer functions of the following diagrams 1 G 1 H h G 2 H Y R (a) G 1 H G 7 H Y R (b) G 3 G 2 G 4 H G 6 G 5 G 1 H ± G 6 H Y R G 7 G 2 G 3 H G 4 G 5 (c) 2...
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## This note was uploaded on 02/03/2012 for the course EE 3530 taught by Professor Chen during the Fall '07 term at LSU.

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Hw#3 - Y s X s = 10 s 1 s 5 5 Find the inverse Laplace transform for Y 1 s = 10 s 1 s s 2 s 5 Y 2 s = 2 s 2 s 1 s 2 4 s 8 Y 3 s = 20 s 4 s 1 s 2 16

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