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# HW3 - s 1 s 3 2 3 Solve the diﬀerential equation 2¨ x 7...

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AAE 364 Control Systems Analysis Problem Set 3 Professor Inseok Hwang School of Aeronautics and Astronautics, Purdue University Fall 2011 Issued 9/9; Due 9/16 Reading Assignment: Class material for the Laplace Transform; Sections 1,2,3, and 7 in Chapter 2 and Sections 1 and 2 in Chapter 3. Problem 1 1. Obtain the inverse Laplace transform of the following function: F ( s ) = 10 e - 2 s s + 3 2. Find the inverse Laplace transforms of the following function: F ( s ) = 5
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Unformatted text preview: ( s + 1)( s + 3) 2 3. Solve the diﬀerential equation 2¨ x + 7 ˙ x + 3 x = 0 , x (0) = 2 , ˙ x (0) = 0 4. Solve the diﬀerential equation ˙ x + 5 x = δ ( t ) , x (0-) = 0 5. Solve the following diﬀerential equation: ¨ x + 2 ζω n ˙ x + ω n 2 x = 0 , x (0) = a, ˙ x (0) = b where a and b are constants. 6. Solve the following diﬀerential equation: ¨ x + 3 ˙ x + 6 x = 0 , x (0) = 0 , ˙ x (0) = 3 1...
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