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Find the Laplace transforms of the following functions using the transform of derivatives. 1) f(t) = t Ans. s2 s2 + 8 %3D 2) f(t) = cos²2t Ans. %3D s(s2 + 16) 1 (s + 7)2 3) f(t) = te-7t Ans. %3D

Find the Laplace transforms of the following functions using the transform of derivatives. 1) f(t) = t Ans. s2 s2 + 8 %3D 2) f(t) = cos²2t Ans. %3D s(s2 + 16) 1 (s + 7)2 3) f(t) = te-7t Ans. %3D

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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Е. LAPLACE TRANSFORMS OF DERIVATIVES Find the Laplace transforms of the following functions using the transform of derivatives. 1) f(t) = t Ans. 1 %3D s2 s2 + 8 s(s? + 16) 2) f(t) = cos?2t Ans. 3) f(t) te-7t %3D Ans. 1. (s + 7)2 4) f(t) = e2t cos 5t S- 2 (s – 2)2 + 25 s² – 2s + 4_ s(s? + 4) Ans. 5) f(t) = (sint - cos t)? Ans. |
Transcribed Image Text:Е. LAPLACE TRANSFORMS OF DERIVATIVES Find the Laplace transforms of the following functions using the transform of derivatives. 1) f(t) = t Ans. 1 %3D s2 s2 + 8 s(s? + 16) 2) f(t) = cos?2t Ans. 3) f(t) te-7t %3D Ans. 1. (s + 7)2 4) f(t) = e2t cos 5t S- 2 (s – 2)2 + 25 s² – 2s + 4_ s(s? + 4) Ans. 5) f(t) = (sint - cos t)? Ans. |
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