Evaluate the Laplace transform of the following: 1. Prove: L{e-at cos kt} = sta (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) cos? t %3D II 5. f(t) = cos² t 6. L{te2t sin 6t} non t da)
Evaluate the Laplace transform of the following: 1. Prove: L{e-at cos kt} = sta (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) cos? t %3D II 5. f(t) = cos² t 6. L{te2t sin 6t} non t da)
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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2 and 3
![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F01678e5f-48f5-4d64-aa90-28bc7b500125%2F7a947d26-2bc8-41cf-b3bf-2f3e39b59d90%2F8bvzda_processed.jpeg&w=3840&q=75)
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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