4. Find the Laplace transform of the following function. if 0 < t < 4, if t> 4. f(t) = t, 4e-t+4,
4. Find the Laplace transform of the following function. if 0 < t < 4, if t> 4. f(t) = t, 4e-t+4,
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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Transcribed Image Text:4. Find the Laplace transform of the following function.
t,
f(t) = { ½ e
if 0 < t < 4,
4e-t+4, if t> 4.
Bs. Find the inverse Laplace transform of F(s) = In
(³²)
s² - 4s+
s²+1
![f(1)
1. f(a)
2.6²(1)
3.500
4. (1)
5. 1900)
</100
6.
7.) do
& (g)(1)
9. f(+7)-f(t)
10. f(-a)(-a), azo
11. githat-a) [[20]
12 ut-a) 420
13. 8(1-0) 420
14. "
15. r.
16. P. N=1,2,...
17.-
1,2,...
18. a-be
F(x)=f(/}()
F(x-a)
3F(1)-f(0)
F)-0(0)
-(0)(0)
(-1)
F(x) du
F(x)
FU)G()
1-6
"F(1)
de
e(t + a)(s)
U-CHIE
(t-ope
(a-b)
(s-a)(s-b)
(a-b)
(s-a)(s-b)
1(0)
19.
1
20. √
21.) -1,2,...
22. r>-1
23. sin be
24. cos br
25. sin de
26. con be
27. br
28. cosh be
29. sin be--becon be
30. t sin br
31. sin be+br com be
32. rcos br
33. sin be cosh be-cos be sinh be
31. sủi bt sinh bộ
35, tỉnh bt . sin be
36. cosh be-cos be
37. JJb),v>-1
F(x)= {f}(0)
SIS
21/12
1.3.5 (21)√
2+3)
T(+1)
1-a+b
3-0
-a)³+²
ਰਾਜਨਾ
(+8¹)
G+8)
26²
(8³ +6¹)
2-8
(s³ +6²)
48³
3+ 48*
26³
+48
26³
3-4
26²
3¹-84
(√²+8¹-8)"](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F81e03d6c-c953-47c6-a5f9-daf0571ac32a%2F30ef154b-ca1a-4a7b-b389-6d57a5ed3dd7%2Fmcsgafn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:f(1)
1. f(a)
2.6²(1)
3.500
4. (1)
5. 1900)
</100
6.
7.) do
& (g)(1)
9. f(+7)-f(t)
10. f(-a)(-a), azo
11. githat-a) [[20]
12 ut-a) 420
13. 8(1-0) 420
14. "
15. r.
16. P. N=1,2,...
17.-
1,2,...
18. a-be
F(x)=f(/}()
F(x-a)
3F(1)-f(0)
F)-0(0)
-(0)(0)
(-1)
F(x) du
F(x)
FU)G()
1-6
"F(1)
de
e(t + a)(s)
U-CHIE
(t-ope
(a-b)
(s-a)(s-b)
(a-b)
(s-a)(s-b)
1(0)
19.
1
20. √
21.) -1,2,...
22. r>-1
23. sin be
24. cos br
25. sin de
26. con be
27. br
28. cosh be
29. sin be--becon be
30. t sin br
31. sin be+br com be
32. rcos br
33. sin be cosh be-cos be sinh be
31. sủi bt sinh bộ
35, tỉnh bt . sin be
36. cosh be-cos be
37. JJb),v>-1
F(x)= {f}(0)
SIS
21/12
1.3.5 (21)√
2+3)
T(+1)
1-a+b
3-0
-a)³+²
ਰਾਜਨਾ
(+8¹)
G+8)
26²
(8³ +6¹)
2-8
(s³ +6²)
48³
3+ 48*
26³
+48
26³
3-4
26²
3¹-84
(√²+8¹-8)"
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