Using only the Laplace transform table given to obtain the Laplace transform of the following functions: (a) t³ + t sin(2t) + t² cos(3t). (b) te²t sin(3t), The results must be written as a single rational function and be simplified whenever possible. Showing result only without reasoning or argumentation will be insufficient.
Using only the Laplace transform table given to obtain the Laplace transform of the following functions: (a) t³ + t sin(2t) + t² cos(3t). (b) te²t sin(3t), The results must be written as a single rational function and be simplified whenever possible. Showing result only without reasoning or argumentation will be insufficient.
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
Transcribed Image Text:(a) Table of Laplace
transform pairs;
(b) some properties of
the Laplace transform.
(a)
(b)
The Laplace transform table
f(t)
c, c a constant
t
t", n a positive integer
ekt, k a constant
sin at, a a real constant
cos at, a a real constant
e-kr
kt sin at, k and a real constants
e-kt cos at, k and a real constants
Linearity:
First shift theorem:
L{f(t)} = F(s)
Derivative of transform:
C
12-13
n!
S
2+1
2
-k
a
2
+ a
S
s² + a²
2
(s+k)² + a²
s+k
2
(s+k)² +a
Region of convergence
Re(s) > 0
Re(s) > 0
Re(s) > 0
Re(s) > Re(k)
Re(s) > 0
Re(s) > 0
Re(s) > -k
L{f(t)} = F(s), Re(s) >₁ and L{g(t)} = G(s), Re(s) > 0₂
L{ af(t) + Bg(t)} = aF(s) + BG(s), Re(s) > max(σ₁,0₂)
Leat f(t)} = F(sa), Re(s) > σ₁ + Re(a)
Re(s) > -k
L{t" f(t)} = (-1)d"F(s), (n=1,2,...), Re(s) > 0₁
ds"
Transcribed Image Text:Using only the Laplace transform table given to obtain the Laplace transform of the following functions:
(a) t³ + tsin(2t) + t² cos(3t).
(b) te2t sin(3t),
The results must be written as a single rational function and be simplified whenever possible.
Showing result only without reasoning or argumentation will be insufficient.
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