Table of Laplace Transforms This table summarizes the general properties of Laplace transforms and the Laplace transforms of particular functions derived in Chapter 10. Function Transform Transform Function 1 F(s) s-a n! aF(s) + bG(s) (s-a)n+1 S SF(s)-f(0) 32+42 k s2 F(s)-sf (0) - ƒ'(0) s²+k² S s" F(s)-5-1 f(0)-... -f(n-1) (0) s2-k2 k F(s) 52-k2 S s-a F(s-a) (s-a)²+k2 k e-as F(s) (s-a)²+k2 F(s)G(s) - F'(s) (-1)" F(n) (s) 1.º, F(a) do 1 1-e-ps 1 52 n! gn+1 • f(t) af(t) + bg(1) f'(1) for f(t) dr eat f(t) u(t-a) f(t-a) S tf(1) 1" f(1) f(1) 1 f(t), period p f(t)g(1-1)dt fe e-st f(t) dt n=positive eat Otheat cos kt sinkt cosh kt S>KO sinh kt eat cos kt eat sinkt - - 1 2k3 -(sinkt - kt cos kt) sinkt 2k 1 -(sinkt + kt cos kt) 2k u(t - a) 8(1-a) (-1)[/a] (square wave) [1] (staircase) IN (5²+k2)2 (5² + k²)² (52+k2)2 e-as S e-as 1 as tanh 2 S e-as s(1-e-as)
Table of Laplace Transforms This table summarizes the general properties of Laplace transforms and the Laplace transforms of particular functions derived in Chapter 10. Function Transform Transform Function 1 F(s) s-a n! aF(s) + bG(s) (s-a)n+1 S SF(s)-f(0) 32+42 k s2 F(s)-sf (0) - ƒ'(0) s²+k² S s" F(s)-5-1 f(0)-... -f(n-1) (0) s2-k2 k F(s) 52-k2 S s-a F(s-a) (s-a)²+k2 k e-as F(s) (s-a)²+k2 F(s)G(s) - F'(s) (-1)" F(n) (s) 1.º, F(a) do 1 1-e-ps 1 52 n! gn+1 • f(t) af(t) + bg(1) f'(1) for f(t) dr eat f(t) u(t-a) f(t-a) S tf(1) 1" f(1) f(1) 1 f(t), period p f(t)g(1-1)dt fe e-st f(t) dt n=positive eat Otheat cos kt sinkt cosh kt S>KO sinh kt eat cos kt eat sinkt - - 1 2k3 -(sinkt - kt cos kt) sinkt 2k 1 -(sinkt + kt cos kt) 2k u(t - a) 8(1-a) (-1)[/a] (square wave) [1] (staircase) IN (5²+k2)2 (5² + k²)² (52+k2)2 e-as S e-as 1 as tanh 2 S e-as s(1-e-as)
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
Question 1: Find the Laplace transform of the given functions by using the table of Laplace transforms.
f(t) = 2e−5t
![Table of Laplace Transforms
This table summarizes the general properties of Laplace transforms and the Laplace transforms of particular functions
derived in Chapter 10.
Transform
Function
Transform
Function
1
F(s)
s-a
n!
a F(s) + bG(s)
(s-a)n+1
S
sF(s)-f(0)
s²+k²
k
s2 F(s)-sf (0) - f'(0)
s²+k²
S
sn F(s)-s-1 f(0) --
52-k2
F(s)
k
s2k2
S
s-a
F(s-a)
(s-a)²+k²
k
e-as F(s)
(s-a)²+k²
1
(52+k²)2
F(s)G(s)
S
-F'(s)
(s²+k²)2
$2
(52+k²)2
(-1)" F(n) (s)
1.80
e-as
S
F(o) do
♥ ƒ(1)
af(t) + bg(t)
f'(1)
ƒ" (1)
f(n) (1)
So
f(t) dr
eat f(1)
u(t-a) f(t-a)
[ f(t)g(1 – t) dr
tf(t)
t" f(1)
ƒ(1)
1
f(t), period p
1
- f(n-1) (0)
1
1-e-ps
= 1² e
So e-st f(t) dt
1
n!
sn+1
n=positive
1
r(a + ¹) d =R> -1
sa+1
eat
theat
cos kt
sink 1
cosh kt 5>x>0
sinh kt
eat cos kt
eat sinkt
1
(sin ktkt cos kt)
2k3
1
sinkt
2k
1
2k
(sinkt+kt cos kt)
u(ta)
8(1 - a)
(-1) [t/a] (square wave)
[a]
(staircase)
e-as
1
S
-as
s(1-e-as)
tanh
as](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcc808094-e396-40c0-88ba-511e056f9017%2Fdac7079b-d0b6-4bc8-9e2b-5febad82ef27%2Frddkvyk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Table of Laplace Transforms
This table summarizes the general properties of Laplace transforms and the Laplace transforms of particular functions
derived in Chapter 10.
Transform
Function
Transform
Function
1
F(s)
s-a
n!
a F(s) + bG(s)
(s-a)n+1
S
sF(s)-f(0)
s²+k²
k
s2 F(s)-sf (0) - f'(0)
s²+k²
S
sn F(s)-s-1 f(0) --
52-k2
F(s)
k
s2k2
S
s-a
F(s-a)
(s-a)²+k²
k
e-as F(s)
(s-a)²+k²
1
(52+k²)2
F(s)G(s)
S
-F'(s)
(s²+k²)2
$2
(52+k²)2
(-1)" F(n) (s)
1.80
e-as
S
F(o) do
♥ ƒ(1)
af(t) + bg(t)
f'(1)
ƒ" (1)
f(n) (1)
So
f(t) dr
eat f(1)
u(t-a) f(t-a)
[ f(t)g(1 – t) dr
tf(t)
t" f(1)
ƒ(1)
1
f(t), period p
1
- f(n-1) (0)
1
1-e-ps
= 1² e
So e-st f(t) dt
1
n!
sn+1
n=positive
1
r(a + ¹) d =R> -1
sa+1
eat
theat
cos kt
sink 1
cosh kt 5>x>0
sinh kt
eat cos kt
eat sinkt
1
(sin ktkt cos kt)
2k3
1
sinkt
2k
1
2k
(sinkt+kt cos kt)
u(ta)
8(1 - a)
(-1) [t/a] (square wave)
[a]
(staircase)
e-as
1
S
-as
s(1-e-as)
tanh
as
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
