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Given the function f(i) = t cos(4 t) Use the Laplace Transform properties table to convert this function into F(S).

Given the function f(i) = t cos(4 t) Use the Laplace Transform properties table to convert this function into F(S).

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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Given the function f(1) = t cos(4t) Use the Laplace Transform properties table to convert this function into F(s). Lif(1) + 8(1)) = L{f(t)} + L{ 8(1)} L{C f(t)} = CL{s(1) } 9{eA'f(1)}(s) = Lis(i)) (s - A) LAf (1))(s) = S L{s()) - f(0) L{f"(1)) (s) = S² L{ f(t)} - Sf (0) - f'(0) L{f"(1)}(s) = s" L{f(1)} - sN - !f(0) - sN - 2f (0) - sN -"(0) - fN - '(0) .... L{"f(1)}(s) = (-1)N ds
Transcribed Image Text:Given the function f(1) = t cos(4t) Use the Laplace Transform properties table to convert this function into F(s). Lif(1) + 8(1)) = L{f(t)} + L{ 8(1)} L{C f(t)} = CL{s(1) } 9{eA'f(1)}(s) = Lis(i)) (s - A) LAf (1))(s) = S L{s()) - f(0) L{f"(1)) (s) = S² L{ f(t)} - Sf (0) - f'(0) L{f"(1)}(s) = s" L{f(1)} - sN - !f(0) - sN - 2f (0) - sN -"(0) - fN - '(0) .... L{"f(1)}(s) = (-1)N ds
S A F(s): s2 16 S - 1 B F(s) = (s - 1)2 + 16 S - 1 F(s) : (s - 1)2 + 4 16 - s2 F(s) = (s2 + 16)2 s2 - 16 E F(s) = (s² + 16)2 -S F(s): s2 + 16 s2 - 25 - 15 G F(s) = [(s - 1)2 + 16]?
Transcribed Image Text:S A F(s): s2 16 S - 1 B F(s) = (s - 1)2 + 16 S - 1 F(s) : (s - 1)2 + 4 16 - s2 F(s) = (s2 + 16)2 s2 - 16 E F(s) = (s² + 16)2 -S F(s): s2 + 16 s2 - 25 - 15 G F(s) = [(s - 1)2 + 16]?
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