Laplace Transformations

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Section 8.2 Solutions 1a) 7t 1c) -e -2t sin(4t) 4 ) - sin(3t) 1f) -e2 sinh(2t) 17 2a ). tell + -pelt 6 2c) e-3t cos(3t) + -e-3t sin(3t) 2d) 2 cos(3t) + - sin(3t) 2i) 1 - cos(t) 2j) 2 - OR 3 cosh(t) + 4 sinh(t) You can solve using the Heaviside's method or regular partial fraction decomposition 3a) -2t - -18.2 Exercises 1. Use the table of Laplace transforms to find the inverse Laplace transform. 3 1 2 1 (a) ( 5 - 7 ) 4 (c) (d) (f) $2 + 4s + 20 $2 + 9 (s - 2)2 - 4 2. Use Theorem 8.2.1 and the table of Laplace transforms to find the inverse Laplace transform. 2s + 3 S +5 (a) ( 5 - 7) 4 (c) $2 + 6s + 18 (d) 2s + 1 S 3s + 4 (i) $2 + 9 (j) S + 1 $2 - 1 3. Use Heaviside's method to find the inverse Laplace transform. 3 - (s+1)(s - 2) (a) (s + 1 ) ( s + 2)( s - 2)