Compute the inverse Laplace transform of 5s – 12 - F(s) = s3 – 7s2 + 12s
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
using partial fraction decomposition
![**Problem Statement:**
Compute the inverse Laplace transform of
\[ F(s) = \frac{5s - 12}{s^3 - 7s^2 + 12s} \]
**Explanation:**
This problem involves finding the inverse Laplace transform of the function \( F(s) \), which is given by the rational expression:
- **Numerator:** \( 5s - 12 \)
- **Denominator:** \( s^3 - 7s^2 + 12s \)
To solve this, you would typically:
1. Factor the denominator to find the roots.
2. Use partial fraction decomposition to express the function as a sum of simpler fractions.
3. Apply inverse Laplace transform techniques to each term separately.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1d1201ee-b82e-4716-ad1c-c8a4e9fac5cd%2F49d5d66e-8255-4550-8cdf-05272eb2f6cc%2Fimcp35_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Compute the inverse Laplace transform of
\[ F(s) = \frac{5s - 12}{s^3 - 7s^2 + 12s} \]
**Explanation:**
This problem involves finding the inverse Laplace transform of the function \( F(s) \), which is given by the rational expression:
- **Numerator:** \( 5s - 12 \)
- **Denominator:** \( s^3 - 7s^2 + 12s \)
To solve this, you would typically:
1. Factor the denominator to find the roots.
2. Use partial fraction decomposition to express the function as a sum of simpler fractions.
3. Apply inverse Laplace transform techniques to each term separately.
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
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.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,
