Determine £¹{F}. F(s) = 3s² +32s + 77 (s-3) (s² +2s+10) Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms L-¹{F} =[
Determine £¹{F}. F(s) = 3s² +32s + 77 (s-3) (s² +2s+10) Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms L-¹{F} =[
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
![**Topic: Inverse Laplace Transform**
**Objective:**
Determine \(\mathcal{L}^{-1}\{F(s)\}\).
**Given:**
\[
F(s) = \frac{3s^2 + 32s + 77}{(s - 3)(s^2 + 2s + 10)}
\]
**Instructions:**
Click here to view the table of Laplace transforms.
Click here to view the table of properties of Laplace transforms.
**Solution:**
\[
\mathcal{L}^{-1}\{F(s)\} = \boxed{}
\]
---
**Diagram Explanation:**
The given expression is a rational function \(F(s)\) in the Laplace domain. To find its inverse Laplace transform and determine the corresponding time-domain function, we typically factor the denominator and use partial fraction decomposition.
The denominator \(P(s) = (s - 3)(s^2 + 2s + 10)\) can be decomposed to identify its simpler components. From this decomposition, the inverse Laplace transform \(\mathcal{L}^{-1}\) can be performed by applying known inverse transforms to each term.
Details on the partial fractions and subsequent inverses can be extracted using tables of Laplace transforms and their properties linked above.
**Graph/Diagram Representation:**
There are no specific graphs or visual diagrams in the given image. The key elements are mathematical expressions and hyperlinks to useful resources (tables for Laplace transforms and properties).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F45088ba1-a1a3-4a96-b462-54f2c0a5a29e%2F1a9d770f-4a39-4118-a5ee-f01cc7c6ab91%2Fcsgufip_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Topic: Inverse Laplace Transform**
**Objective:**
Determine \(\mathcal{L}^{-1}\{F(s)\}\).
**Given:**
\[
F(s) = \frac{3s^2 + 32s + 77}{(s - 3)(s^2 + 2s + 10)}
\]
**Instructions:**
Click here to view the table of Laplace transforms.
Click here to view the table of properties of Laplace transforms.
**Solution:**
\[
\mathcal{L}^{-1}\{F(s)\} = \boxed{}
\]
---
**Diagram Explanation:**
The given expression is a rational function \(F(s)\) in the Laplace domain. To find its inverse Laplace transform and determine the corresponding time-domain function, we typically factor the denominator and use partial fraction decomposition.
The denominator \(P(s) = (s - 3)(s^2 + 2s + 10)\) can be decomposed to identify its simpler components. From this decomposition, the inverse Laplace transform \(\mathcal{L}^{-1}\) can be performed by applying known inverse transforms to each term.
Details on the partial fractions and subsequent inverses can be extracted using tables of Laplace transforms and their properties linked above.
**Graph/Diagram Representation:**
There are no specific graphs or visual diagrams in the given image. The key elements are mathematical expressions and hyperlinks to useful resources (tables for Laplace transforms and properties).
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 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,
