Problem 1: (Laplace Transforms of Unit Step Functions) Obtain the Laplace transforms of the ff. functions. 1. {[2(t – 1) – sin3(t – 1)]u(t – 1)} 2. A[t² + 1]u(t – 3)} 3. S{u(t – 1) + 2u(t – 2) + 3u(t – 4)} 4. S[[4t – 1]u(t - n)} 5. L{F(t)}where F(t) = 3,0st< 4 l2t – 5, t24
Problem 1: (Laplace Transforms of Unit Step Functions) Obtain the Laplace transforms of the ff. functions. 1. {[2(t – 1) – sin3(t – 1)]u(t – 1)} 2. A[t² + 1]u(t – 3)} 3. S{u(t – 1) + 2u(t – 2) + 3u(t – 4)} 4. S[[4t – 1]u(t - n)} 5. L{F(t)}where F(t) = 3,0st< 4 l2t – 5, t24
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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Laplace and Inverse Laplace Transforms
![Problem 1: (Laplace Transforms of Unit Step Functions)
Obtain the Laplace transforms of the ff. functions.
1. A[2(t – 1) – sin3(t – 1)]u(t – 1)}
2. {[t? + 1]u(t – 3)}
3. S{u(t – 1) + 2u(t – 2) + 3u(t – 4)}
4. S{[4t – 1]u(t - 1)}
5. S{F(t)}where F(t)
( 3,0<t< 4
l2t – 5, t24
Problem 2: (Inverse Laplace Transforms)
Obtain the following inverse Laplace transforms.
15
1. L -1.
(
s2+4s+13.
2. S -1.
s2-4s+8)
3. L -1
s2+6s+13.
4. L -1
(s2+4s)
s2-6
s3+4s2+3s)
5. I -1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6548d0cf-0ed4-445b-9276-94ab0cf815ab%2F28cef01d-137a-4b42-a2e9-9ed709f73705%2Fbx3f2aq_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 1: (Laplace Transforms of Unit Step Functions)
Obtain the Laplace transforms of the ff. functions.
1. A[2(t – 1) – sin3(t – 1)]u(t – 1)}
2. {[t? + 1]u(t – 3)}
3. S{u(t – 1) + 2u(t – 2) + 3u(t – 4)}
4. S{[4t – 1]u(t - 1)}
5. S{F(t)}where F(t)
( 3,0<t< 4
l2t – 5, t24
Problem 2: (Inverse Laplace Transforms)
Obtain the following inverse Laplace transforms.
15
1. L -1.
(
s2+4s+13.
2. S -1.
s2-4s+8)
3. L -1
s2+6s+13.
4. L -1
(s2+4s)
s2-6
s3+4s2+3s)
5. I -1.
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