Express the function below using window and step functions and compute its Laplace transform. 0, 0
Express the function below using window and step functions and compute its Laplace transform. 0, 0
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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![### Express the function below using window and step functions and compute its Laplace transform.
\[
g(t) =
\begin{cases}
0, & 0 < t < 1 \\
5, & 1 \leq t < 2 \\
4, & 2 \leq t < 3 \\
6, & 3 \leq t
\end{cases}
\]
**Resources:**
- [Click here to view the table of Laplace transforms.](#)
- [Click here to view the table of properties of Laplace transforms.](#)
---
### Express \( g(t) \) using window and step functions. Choose the correct answer below.
- A. \( g(t) = 5\Pi_{1,2}(t) + 4\Pi_{2,3}(t) + 6u(t-3) \)
- B. \( g(t) = 5\Pi_{1,2}(t) + 4\Pi_{2,3}(t) + 6I_{0,3}(t) \)
- C. \( g(t) = 5\Pi_{1,2}(t) + 4\Pi_{2,3}(t) - 6u(t-3) \)
- D. \( g(t) = 5u(t-1) + 4u(t-2) + 6u(t-3) \)
**Correct Answer:** A. \( g(t) = 5\Pi_{1,2}(t) + 4\Pi_{2,3}(t) + 6u(t-3) \)
---
### Compute the Laplace transform of \( g(t) \).
\[ \mathcal{L}\{g\} = \_\_\_ \]
*(Type an expression using \( s \) as the variable.)*
---
**Diagram Explanation:**
The problem involves expressing a piecewise function \( g(t) \) using window and step functions. The correct expression then needs to be transformed using the Laplace transform technique. The piecewise intervals are clearly laid out, each associated with a specific function value. The task is made easier with reference materials linked for Laplace tables and properties. The chosen answer option correctly expresses the function based on its piecewise components.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3d7ec503-389e-4b40-b2fe-31c0ac723423%2F3f21fb6b-0155-4640-a94f-ba830a0c2a71%2Fxcs527i_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Express the function below using window and step functions and compute its Laplace transform.
\[
g(t) =
\begin{cases}
0, & 0 < t < 1 \\
5, & 1 \leq t < 2 \\
4, & 2 \leq t < 3 \\
6, & 3 \leq t
\end{cases}
\]
**Resources:**
- [Click here to view the table of Laplace transforms.](#)
- [Click here to view the table of properties of Laplace transforms.](#)
---
### Express \( g(t) \) using window and step functions. Choose the correct answer below.
- A. \( g(t) = 5\Pi_{1,2}(t) + 4\Pi_{2,3}(t) + 6u(t-3) \)
- B. \( g(t) = 5\Pi_{1,2}(t) + 4\Pi_{2,3}(t) + 6I_{0,3}(t) \)
- C. \( g(t) = 5\Pi_{1,2}(t) + 4\Pi_{2,3}(t) - 6u(t-3) \)
- D. \( g(t) = 5u(t-1) + 4u(t-2) + 6u(t-3) \)
**Correct Answer:** A. \( g(t) = 5\Pi_{1,2}(t) + 4\Pi_{2,3}(t) + 6u(t-3) \)
---
### Compute the Laplace transform of \( g(t) \).
\[ \mathcal{L}\{g\} = \_\_\_ \]
*(Type an expression using \( s \) as the variable.)*
---
**Diagram Explanation:**
The problem involves expressing a piecewise function \( g(t) \) using window and step functions. The correct expression then needs to be transformed using the Laplace transform technique. The piecewise intervals are clearly laid out, each associated with a specific function value. The task is made easier with reference materials linked for Laplace tables and properties. The chosen answer option correctly expresses the function based on its piecewise components.
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