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2. f(t) = sin(wt - ) where w, are constant

2. f(t) = sin(wt - ) where w, are constant

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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Find the Laplace transform F(s) = L[f(t)] for each of the following functions. For full credit, show all of your work by expanding each Laplace transform into one or more Laplace transforms of the common functions listed in the provided Laplace Transform Table. Indicate which rows of the table you used to obtain your solution and fully simplify the result to a single term. 1. f(t) = eat+b where a, b are constant 2. f(t) = sin(wt - p) where w, p are constant 3. f(t) = ³-1/2 4. f(t) = (e-¹/4) [2+t² + cos (3)]. (Note: For this problem there is no need to simplify to a common denominator.) 5. f(t) = (t − 2)H(t – 2), where H(-) is the unit step or Heaviside function
Transcribed Image Text:Find the Laplace transform F(s) = L[f(t)] for each of the following functions. For full credit, show all of your work by expanding each Laplace transform into one or more Laplace transforms of the common functions listed in the provided Laplace Transform Table. Indicate which rows of the table you used to obtain your solution and fully simplify the result to a single term. 1. f(t) = eat+b where a, b are constant 2. f(t) = sin(wt - p) where w, p are constant 3. f(t) = ³-1/2 4. f(t) = (e-¹/4) [2+t² + cos (3)]. (Note: For this problem there is no need to simplify to a common denominator.) 5. f(t) = (t − 2)H(t – 2), where H(-) is the unit step or Heaviside function
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