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Determine the Laplace transforms of the follow- ing functions: 1. (a) 2re2 (b) re (a) (s- 2)2 2. (b) (s-1) 2.

Determine the Laplace transforms of the follow- ing functions: 1. (a) 2re2 (b) re (a) (s- 2)2 2. (b) (s-1) 2.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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634 LAPLACE TRANSFORMS Now try the following exercise. Exercise 232 Further problems on Laplace transforms of the form e f(1) Determine the Laplace transforms of the follow- ing functions: 1. (a) 2re" (b) re' (b) (s - 2)2 (s 1)3 [ 24 12 (b) (s +3)5 (s+ 2)4 3. (a) e' cos 1 (b) 3e2 sin 21 S- 1 52-2s+2 (b) 52 - 4s + 8 4. (a) Se-2 cos 31 (b) 4e-S1 sin r 4 5(s+ 2) |(a) 2+ 4s + 13 (b) s2 + 10s + 26 5. (a) 2e' sin? (b) e3 cos? 1 s - 1 (a) S - 1 52 2s +5 s- 3 s2 - 6s + 13 6. (a) e' sinh t (b) 3e2' cosh 41 3(s-2) (b) 52 - 4s - 12 s(s - 2) 7. (a) 2e sinh 31 (b) -31 cosh 21 s+ 3 (a) s2 + 2s - 8 (b) 4(s2+6s+ 5). 8. (a) 2e'(cos 31 - 3 sin 3t) (b) 3e-2( sinh 21 - 2 cosh 21) -6(s+ 1) (b) s(s +4) 2(s-10) 52 - 2s + 10
Transcribed Image Text:634 LAPLACE TRANSFORMS Now try the following exercise. Exercise 232 Further problems on Laplace transforms of the form e f(1) Determine the Laplace transforms of the follow- ing functions: 1. (a) 2re" (b) re' (b) (s - 2)2 (s 1)3 [ 24 12 (b) (s +3)5 (s+ 2)4 3. (a) e' cos 1 (b) 3e2 sin 21 S- 1 52-2s+2 (b) 52 - 4s + 8 4. (a) Se-2 cos 31 (b) 4e-S1 sin r 4 5(s+ 2) |(a) 2+ 4s + 13 (b) s2 + 10s + 26 5. (a) 2e' sin? (b) e3 cos? 1 s - 1 (a) S - 1 52 2s +5 s- 3 s2 - 6s + 13 6. (a) e' sinh t (b) 3e2' cosh 41 3(s-2) (b) 52 - 4s - 12 s(s - 2) 7. (a) 2e sinh 31 (b) -31 cosh 21 s+ 3 (a) s2 + 2s - 8 (b) 4(s2+6s+ 5). 8. (a) 2e'(cos 31 - 3 sin 3t) (b) 3e-2( sinh 21 - 2 cosh 21) -6(s+ 1) (b) s(s +4) 2(s-10) 52 - 2s + 10
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