# HW2 - 1 s 2 2 determine the values of f(0 and ˙ f(0(Use...

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AAE 364 Control Systems Analysis Problem Set 2 Professor Inseok Hwang School of Aeronautics and Astronautics, Purdue University Fall 2011 Issued 9/2; Due 9/9 Reading Assignment: Chapter 1 and the class material for the Laplace Transform. Problems 1. Obtain the Laplace transforms of the following functions: (a) f 1 ( t ) = 0 for t < 0 = e - 0 . 4 t cos 12 t for t 0 (b) f ( t ) = 0 for t < 0 = sin(4 t + π 3 ) for t 0 2. Obtain the Laplace transform of the function deﬁned by f ( t ) = 0 for t < 0 = t 2 e - at for t 0 3. Obtain the Laplace transform of the function deﬁned by f ( t ) = 0 for t < 0 = cos 2 ωt · cos 3 ωt for t 0 4. Given F ( s ) =

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Unformatted text preview: 1 ( s + 2) 2 determine the values of f (0+) and ˙ f (0+). (Use the initial-value theorem.) 1 5. By applying the ﬁnal-value theorem, ﬁnd the ﬁnal value of f ( t ) whose Laplace transform is given by F ( s ) = 10 s ( s + 1) Verify this result by taking the inverse Laplace transform of F ( s ) and letting t → ∞ . 6. Obtained the Laplace transform of the function f ( t ) shown in Figure 1. f(t) t a a + b b Figure 1: Function f ( t ) 2...
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HW2 - 1 s 2 2 determine the values of f(0 and ˙ f(0(Use...

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