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Problem 1: Find the Laplace transform of each of the following functions: a) f(t) = sin(t − 2) U(t − 2) - (2, 0 ≤t<5 b) f(t): (t², 5 ≤t Problem 2: Find the inverse Laplace transform of each of the following functio a) F(s) = es =

Problem 1: Find the Laplace transform of each of the following functions: a) f(t) = sin(t − 2) U(t − 2) - (2, 0 ≤t<5 b) f(t): (t², 5 ≤t Problem 2: Find the inverse Laplace transform of each of the following functio a) F(s) = es =

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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Problem 1: Find the Laplace transform of each of the following functions: a) f(t) = sin(t − 2) U(t − 2) - (2, 0 ≤t<5 b) f(t): (t², 5 ≤t Problem 2: Find the inverse Laplace transform of each of the following functions: a) F(s) === S b) F(s) e3s 52444 s² +4 1 c) F(s) = e-5s (₁-2) \s+1 s+2, Problem 3: Consider the IVP y² + y = -1, 0≤t<1 1, y(0) = 0, ) 1<t a) Apply the Laplace transform to both sides of the differential equation. b) Solve the result of Part a) for the Laplace transform of y. c) Use the inverse Laplace transform to find the solution y(t). =
Transcribed Image Text:Problem 1: Find the Laplace transform of each of the following functions: a) f(t) = sin(t − 2) U(t − 2) - (2, 0 ≤t<5 b) f(t): (t², 5 ≤t Problem 2: Find the inverse Laplace transform of each of the following functions: a) F(s) === S b) F(s) e3s 52444 s² +4 1 c) F(s) = e-5s (₁-2) \s+1 s+2, Problem 3: Consider the IVP y² + y = -1, 0≤t<1 1, y(0) = 0, ) 1<t a) Apply the Laplace transform to both sides of the differential equation. b) Solve the result of Part a) for the Laplace transform of y. c) Use the inverse Laplace transform to find the solution y(t). =
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