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(s) = 20 (s+3)(s² +8s+25) f(t)=2e-3t2e-4t cos3t- -

(s) = 20 (s+3)(s² +8s+25) f(t)=2e-3t2e-4t cos3t- -

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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Show the solution of finding the inverse laplace of each functions. The answer/s is already given.

20 (s+3)(s² +8s +25) f(t) = 2e-³t - 2e-4t cos3t 1) F₁(s) = 2) F₁(s) = 10 (s + 1)(s² + 4s +13) 3) F₂(s) = - f(t) = e-t-e-21 cos3t - 12e-21: 3 4) F₂(s) = 2-4t ₂-4t sin3t 3 s² +5s +6 (s + 1)²(s+4) 7 2 f(t) (10) = ²e²¹² +²e=¹ + ²/1-² te-1 9 9 -e-2¹ sin3t s²2s+4 (s + 1)(s + 2)² f(t) = 7e-¹-6-2t - 12te-2t
Transcribed Image Text:20 (s+3)(s² +8s +25) f(t) = 2e-³t - 2e-4t cos3t 1) F₁(s) = 2) F₁(s) = 10 (s + 1)(s² + 4s +13) 3) F₂(s) = - f(t) = e-t-e-21 cos3t - 12e-21: 3 4) F₂(s) = 2-4t ₂-4t sin3t 3 s² +5s +6 (s + 1)²(s+4) 7 2 f(t) (10) = ²e²¹² +²e=¹ + ²/1-² te-1 9 9 -e-2¹ sin3t s²2s+4 (s + 1)(s + 2)² f(t) = 7e-¹-6-2t - 12te-2t
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