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Evaluate the Laplace transform of the following: sta 1. Prove: L{e-at cos kt} = using the integration process. (s+a)²+k2 2. f(t) = e-3t (1+ sin 4t – 2t?) 3. f(t) = (t + 1)sin (t + 2) 4. f(t) = 2(t +3)e-(t+5) 5. f(t) = cos? t 6. L{te2t sin 6t} 7. L{f,t? cos t dt} %3D II 1. 0st< 4 8. G(t) ={0, 4

Evaluate the Laplace transform of the following: sta 1. Prove: L{e-at cos kt} = using the integration process. (s+a)²+k2 2. f(t) = e-3t (1+ sin 4t – 2t?) 3. f(t) = (t + 1)sin (t + 2) 4. f(t) = 2(t +3)e-(t+5) 5. f(t) = cos? t 6. L{te2t sin 6t} 7. L{f,t? cos t dt} %3D II 1. 0st< 4 8. G(t) ={0, 4

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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Evaluate the Laplace transform of the following: sta 1. Prove: L{e-at cos kt} = (s+a)²+k2 using the integration process. 2. f(t) = e-3t (1+ sin 4t – 2t?) 3. f(t) = (t + 1)sin (t + 2) 4. f(t) = 2(t + 3)e-(t+5) 5. f(t) = cos² t 6. L{te2t sin 6t} 7. L{S t2 cos t dt} %3D (1. 0 st< 4 8. G(t) ={0, 4<t <5 (1, t2 5 9. G(t) = e2-t U(t - 2) 10. Given this period function: Sawtooth function f() 26 3b 4b
Transcribed Image Text:Evaluate the Laplace transform of the following: sta 1. Prove: L{e-at cos kt} = (s+a)²+k2 using the integration process. 2. f(t) = e-3t (1+ sin 4t – 2t?) 3. f(t) = (t + 1)sin (t + 2) 4. f(t) = 2(t + 3)e-(t+5) 5. f(t) = cos² t 6. L{te2t sin 6t} 7. L{S t2 cos t dt} %3D (1. 0 st< 4 8. G(t) ={0, 4<t <5 (1, t2 5 9. G(t) = e2-t U(t - 2) 10. Given this period function: Sawtooth function f() 26 3b 4b
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