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3. Determine the inverse Laplace transform of the given function. a) F(s) = =- c) F(s) = 7 e) F(s) = = S 2 S² +9 4-2s 2 S² +25 6 g) F(s) =²-2s +1 b) F(s) = nslation s²-25 +1 -1 4 S+2 3ssta 5s² +20 d) F(s)=- 4 f) F(s) = 3²-3 h) F(s) = 3+ s 5s²

3. Determine the inverse Laplace transform of the given function. a) F(s) = =- c) F(s) = 7 e) F(s) = = S 2 S² +9 4-2s 2 S² +25 6 g) F(s) =²-2s +1 b) F(s) = nslation s²-25 +1 -1 4 S+2 3ssta 5s² +20 d) F(s)=- 4 f) F(s) = 3²-3 h) F(s) = 3+ s 5s²

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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### Determine the Inverse Laplace Transform Given the following Laplace-transformed functions, find their inverse Laplace transforms: 1. \(a) \quad F(s) = \frac{7}{s}\) 2. \(b) \quad F(s) = \frac{4}{s+2}\) 3. \(c) \quad F(s) = \frac{2}{s^2+9}\) 4. \(d) \quad F(s) = \frac{3s}{5s^2+20}\) 5. \(e) \quad F(s) = \frac{4-2s}{s^2+25}\) 6. \(f) \quad F(s) = \frac{4}{s^2-3}\) 7. \(g) \quad F(s) = \frac{6}{s^2-2s+1}\) 8. \(h) \quad F(s) = \frac{3+s}{5s^2}\) These functions are represented in the s-domain and require transformation back to the time-domain. You will employ methods such as partial fraction decomposition, shifting theorems, or standard Laplace transform pairs to execute this task effectively.
Transcribed Image Text:### Determine the Inverse Laplace Transform Given the following Laplace-transformed functions, find their inverse Laplace transforms: 1. \(a) \quad F(s) = \frac{7}{s}\) 2. \(b) \quad F(s) = \frac{4}{s+2}\) 3. \(c) \quad F(s) = \frac{2}{s^2+9}\) 4. \(d) \quad F(s) = \frac{3s}{5s^2+20}\) 5. \(e) \quad F(s) = \frac{4-2s}{s^2+25}\) 6. \(f) \quad F(s) = \frac{4}{s^2-3}\) 7. \(g) \quad F(s) = \frac{6}{s^2-2s+1}\) 8. \(h) \quad F(s) = \frac{3+s}{5s^2}\) These functions are represented in the s-domain and require transformation back to the time-domain. You will employ methods such as partial fraction decomposition, shifting theorems, or standard Laplace transform pairs to execute this task effectively.
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