1) f(t) =t cos(@t) 2) f(t)=tsin(@t) 3) f(t) =t cosh(at)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![Find the Laplace Transform of the following functions
s? - o?
1) f(t)=t cos(@t)
Ans. F(s)=
(s² + w* }
20s
2) f(t) =t sin(@t)
Ans. F(s)=
(s² + w° }
s? +a?
3) f(t) =t cosh(at)
Ans. F(s) =
(s² – a*}
2as
Ans. F(s) =
(s² – a²)}
4) f(t) =tsinh(at)
2
Ans. F(s) =
(s–1)
5) f(t)= 2te'
s+2
6) f(t) =e" cos(1)
Ans. F(s)=-
(s+2) +1
7) f(t)=e"(Acos(ßt)+ B sin(ßt)) Ans. F(s)=-
A(s+a)+Bß
(s +a)² + ß²
-at
Ans. F(s)=
e
8) f(t)=(t – x)u¸(t)
-2s
9) f(t) = tu,(t)
Ans. F(s)=
2
S
ets
10) f(t) =u,(t)sin(t)
Ans. F(s) =
s? +1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F55f6ada0-2dca-4d2d-a940-9fb76e1c634b%2F9e6554f8-aa59-4516-ba52-4578f3bfe9e3%2Fkj0yzhm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Find the Laplace Transform of the following functions
s? - o?
1) f(t)=t cos(@t)
Ans. F(s)=
(s² + w* }
20s
2) f(t) =t sin(@t)
Ans. F(s)=
(s² + w° }
s? +a?
3) f(t) =t cosh(at)
Ans. F(s) =
(s² – a*}
2as
Ans. F(s) =
(s² – a²)}
4) f(t) =tsinh(at)
2
Ans. F(s) =
(s–1)
5) f(t)= 2te'
s+2
6) f(t) =e" cos(1)
Ans. F(s)=-
(s+2) +1
7) f(t)=e"(Acos(ßt)+ B sin(ßt)) Ans. F(s)=-
A(s+a)+Bß
(s +a)² + ß²
-at
Ans. F(s)=
e
8) f(t)=(t – x)u¸(t)
-2s
9) f(t) = tu,(t)
Ans. F(s)=
2
S
ets
10) f(t) =u,(t)sin(t)
Ans. F(s) =
s? +1
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