LaplaceTransformsExercisesSolutions162.pdf

LaplaceTransformsExercisesSolutions162.pdf - Laplace...

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Laplace Transforms Exercises STUDY Smarter Question 1 Find the Laplace transform of each of the following functions. (a) f ( t ) = 7 (b) f ( t ) = 4 t (c) f ( t ) = t 2 (d) f ( t ) = 3 t 2 + 5 t + 2 (e) f ( t ) = sin(5 t ) (f) f ( t ) = cos( - 3 t ) (g) f ( t ) = 4 sin(3 t ) + 2 cos(9 t ) (h) f ( t ) = 3 e - 4 t Question 2 Find the inverse Laplace transform of each of the following functions. (a) F ( s ) = 4 s (b) F ( s ) = 7 s 2 + 49 (c) F ( s ) = 24 s 5 (d) F ( s ) = s s 2 - 25 + 3 s 2 - 9 (e) F ( s ) = 2 s + 4 - 3 s 2 - 4 (f) F ( s ) = 32 s 3 - 5 s s 2 + 2 (g) F ( s ) = 4 s ( s + 2)( s + 3) (h) ? F ( s ) = s + 1 ( s 2 + s + 1)( s + 2) ? This one is quite challenging Question 3 Use Laplace transforms to solve each of the following ODE’s. (a) y 00 ( t ) + 2 y 0 ( t ) + y ( t ) = 3, y 0 (0) = y (0) = 0 (b) 4 y 00 ( t ) - 2 y ( t ) = 7, y 0 (0) = y (0) = 0 (c) 3 y 00 ( t ) + 2 y 0 ( t ) + 5 y ( t ) = 3, y 0 (0) = 1 , y (0) = 0 (d) y 00 ( t ) + 3 y 0 ( t ) = - 2, y 0 (0) = 1 , y (0) = 2 A Dudek 1 July 2016
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Laplace Transforms Exercises STUDY Smarter Question 4 Use a table of Laplace transforms to find each of the following. (a) L - 1 s + 2 s 2 + 1 (b) L - 1 4 s 2 ( s - 2) (c) L - 1 e - s s ( s 2 + 1) (d) L - 1 se - 3 s s 2 + 4 A Dudek 2 July 2016
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Laplace Transforms Exercises STUDY Smarter Question 1 Find the Laplace transform of each of the following functions.
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