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1) f(t) =t cos(@t) 2) f(t)=tsin(@t) 3) f(t) =t cosh(at)

1) f(t) =t cos(@t) 2) f(t)=tsin(@t) 3) f(t) =t cosh(at)

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 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
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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