Find the Laplace transform of the given function. [1, 0≤ t <2 10, t> 2 f(t) L{f(t)} = = S> 0.
Find the Laplace transform of the given function. [1, 0≤ t <2 10, t> 2 f(t) L{f(t)} = = S> 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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![**Problem Statement:**
Find the Laplace transform of the given function.
\[
f(t) =
\begin{cases}
1, & 0 \leq t < 2 \\
0, & t \geq 2
\end{cases}
\]
\[
\mathcal{L}\{f(t)\} = \, \underline{\phantom{answer}} \, , \, s > 0.
\]
**Explanation:**
We are asked to find the Laplace transform of a piecewise function \( f(t) \). The function \( f(t) \) is defined as 1 for the interval \( 0 \leq t < 2 \), and 0 for \( t \geq 2 \).
**Note:** The box is meant to be filled in with the solution once the Laplace transform is calculated.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff6ed396a-58be-4ac0-9d00-206a35697371%2Fdd242f55-90bd-40ab-85a2-11413d308fe2%2F3cri0z_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the Laplace transform of the given function.
\[
f(t) =
\begin{cases}
1, & 0 \leq t < 2 \\
0, & t \geq 2
\end{cases}
\]
\[
\mathcal{L}\{f(t)\} = \, \underline{\phantom{answer}} \, , \, s > 0.
\]
**Explanation:**
We are asked to find the Laplace transform of a piecewise function \( f(t) \). The function \( f(t) \) is defined as 1 for the interval \( 0 \leq t < 2 \), and 0 for \( t \geq 2 \).
**Note:** The box is meant to be filled in with the solution once the Laplace transform is calculated.
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