(2) Apply inverse Laplace transform and find f(t) of the following: 6(5+3) S (5+1) (5+2) a) F(s) = b) F(S) = c) FIS) = 55²-25-3 (5²+1) (5² 25+5) 53+5² + 25+ 3 (5+1)² (5+2)²
(2) Apply inverse Laplace transform and find f(t) of the following: 6(5+3) S (5+1) (5+2) a) F(s) = b) F(S) = c) FIS) = 55²-25-3 (5²+1) (5² 25+5) 53+5² + 25+ 3 (5+1)² (5+2)²
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
How does one apply inverse laplace transform and find f(t) ?
![**Problem 2: Inverse Laplace Transform**
Apply the inverse Laplace transform and find \( f(t) \) of the following expressions:
a) \[
F(s) = \frac{6(s + 3)}{5(s + 1)(s + 2)}
\]
b) \[
F(s) = \frac{5s^2 - 2s - 3}{(s^2 + 1)(s^2 - 2s + 5)}
\]
c) \[
F(s) = \frac{s^3 + s^2 + 2s + 3}{(s + 1)^2(s + 2)^2}
\]
d) \[
F(s) = \frac{2 - 2e^{-2s} - 4se^{-2s} + 2s^2e^{-2s}}{s^3}
\]
e) \[
F(s) = \frac{s}{(s + 2)^2 + 4}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0e02c446-9367-41d9-9f9b-9aac6cb957ab%2F07f10feb-447e-4ae7-818c-4a6cd8779f1a%2Fhulthm9_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 2: Inverse Laplace Transform**
Apply the inverse Laplace transform and find \( f(t) \) of the following expressions:
a) \[
F(s) = \frac{6(s + 3)}{5(s + 1)(s + 2)}
\]
b) \[
F(s) = \frac{5s^2 - 2s - 3}{(s^2 + 1)(s^2 - 2s + 5)}
\]
c) \[
F(s) = \frac{s^3 + s^2 + 2s + 3}{(s + 1)^2(s + 2)^2}
\]
d) \[
F(s) = \frac{2 - 2e^{-2s} - 4se^{-2s} + 2s^2e^{-2s}}{s^3}
\]
e) \[
F(s) = \frac{s}{(s + 2)^2 + 4}
\]
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 5 steps with 4 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,
