Find the Laplace transform of the given function: So, | t2 – 4t + 8, t> 2 t < 2 f(t) L{f(t)} = s > 0
Find the Laplace transform of the given function: So, | t2 – 4t + 8, t> 2 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:
\[
f(t) =
\begin{cases}
0, & t < 2 \\
t^2 - 4t + 8, & t \geq 2
\end{cases}
\]
\[
\mathcal{L}\{f(t)\} = \, ? , \quad s > 0
\]
**Explanation:**
The problem requires finding the Laplace transform of a piecewise function \( f(t) \), which is defined as follows:
- \( f(t) = 0 \) for \( t < 2 \)
- \( f(t) = t^2 - 4t + 8 \) for \( t \geq 2 \)
The Laplace transform, denoted by \( \mathcal{L} \{ f(t) \} \), is a tool in mathematics and engineering used to transform a function of time \( f(t) \) into a function of a complex variable \( s \).
The solution will involve dealing with the piecewise nature of \( f(t) \) and calculating its Laplace transform for the specified condition \( s > 0 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd5655175-49d2-4db6-a7fd-785d70a02cda%2Fbd000c7d-a973-40e7-8b53-878950fac4af%2Fmpe3lui_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the Laplace transform of the given function:
\[
f(t) =
\begin{cases}
0, & t < 2 \\
t^2 - 4t + 8, & t \geq 2
\end{cases}
\]
\[
\mathcal{L}\{f(t)\} = \, ? , \quad s > 0
\]
**Explanation:**
The problem requires finding the Laplace transform of a piecewise function \( f(t) \), which is defined as follows:
- \( f(t) = 0 \) for \( t < 2 \)
- \( f(t) = t^2 - 4t + 8 \) for \( t \geq 2 \)
The Laplace transform, denoted by \( \mathcal{L} \{ f(t) \} \), is a tool in mathematics and engineering used to transform a function of time \( f(t) \) into a function of a complex variable \( s \).
The solution will involve dealing with the piecewise nature of \( f(t) \) and calculating its Laplace transform for the specified condition \( s > 0 \).
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