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
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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E.)

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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