2. (CV-1) Evaluate the following inverse Laplace transforms as convolution integrals, and then evaluate the integrals. Do not just reference the table of Laplace transforms. + 1 s(s+3)² (a) L-1 {** S (b) 2-1 (s²+4)² (Hint: you may want to use the trig identity sin(a) cos(b) = sin(a+b)+sin(a-b))
2. (CV-1) Evaluate the following inverse Laplace transforms as convolution integrals, and then evaluate the integrals. Do not just reference the table of Laplace transforms. + 1 s(s+3)² (a) L-1 {** S (b) 2-1 (s²+4)² (Hint: you may want to use the trig identity sin(a) cos(b) = sin(a+b)+sin(a-b))
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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Question
![Certainly! Here is the transcription for the educational website:
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### Problem 2 (CV-1)
**Objective:**
Evaluate the following inverse Laplace transforms as convolution integrals, and then evaluate the integrals. Do not just reference the table of Laplace transforms.
---
**(a)** \(\mathcal{L}^{-1} \left\{ \frac{1}{s(s + 3)^2} \right\}\)
---
**(b)** \(\mathcal{L}^{-1} \left\{ \frac{s}{(s^2 + 4)^2} \right\}\)
*Hint:* You may want to use the trigonometric identity \(\sin(a) \cos(b) = \frac{1}{2} \sin(a + b) + \frac{1}{2} \sin(a - b)\)
---
**Grading Criteria:**
- [ ] Exemplary
- [ ] Satisfactory
- [ ] Unsatisfactory
---
**Note:** This exercise involves finding the inverse Laplace transform using the method of convolution integrals, without simply referencing pre-existing tables of transforms. Start by expressing each given function in a suitable form for evaluating the convolution and apply relevant integration techniques to obtain the solution. Use any given hints or identities as needed.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F74a50780-bdf2-45e2-b018-f4cc84bd693f%2Fabcfe9f3-9ad1-4482-9aa7-cc67e670f437%2Flte10ki_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Certainly! Here is the transcription for the educational website:
---
### Problem 2 (CV-1)
**Objective:**
Evaluate the following inverse Laplace transforms as convolution integrals, and then evaluate the integrals. Do not just reference the table of Laplace transforms.
---
**(a)** \(\mathcal{L}^{-1} \left\{ \frac{1}{s(s + 3)^2} \right\}\)
---
**(b)** \(\mathcal{L}^{-1} \left\{ \frac{s}{(s^2 + 4)^2} \right\}\)
*Hint:* You may want to use the trigonometric identity \(\sin(a) \cos(b) = \frac{1}{2} \sin(a + b) + \frac{1}{2} \sin(a - b)\)
---
**Grading Criteria:**
- [ ] Exemplary
- [ ] Satisfactory
- [ ] Unsatisfactory
---
**Note:** This exercise involves finding the inverse Laplace transform using the method of convolution integrals, without simply referencing pre-existing tables of transforms. Start by expressing each given function in a suitable form for evaluating the convolution and apply relevant integration techniques to obtain the solution. Use any given hints or identities as needed.
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