10) = {*": f (t) 12, 0 1. ||
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
Determine the LaPlace transform of the
![The image shows a piecewise function \( f(t) \), defined as follows:
\[
f(t) =
\begin{cases}
t^2, & 0 \leq t \leq 1, \\
1, & t > 1.
\end{cases}
\]
This function has two parts:
- For values of \( t \) between 0 and 1 (inclusive), \( f(t) \) is equal to \( t^2 \).
- For values of \( t \) greater than 1, \( f(t) \) is equal to 1.
This piecewise function represents a quadratic relationship within the interval from 0 to 1 and becomes a constant function with a value of 1 for any \( t \) greater than 1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc2abac25-b303-4f3c-8d4b-bdabf692fa6e%2F6f2c2ba0-933e-4b12-9b90-d2cc1eff824c%2Ff3u2ai9_processed.png&w=3840&q=75)
Transcribed Image Text:The image shows a piecewise function \( f(t) \), defined as follows:
\[
f(t) =
\begin{cases}
t^2, & 0 \leq t \leq 1, \\
1, & t > 1.
\end{cases}
\]
This function has two parts:
- For values of \( t \) between 0 and 1 (inclusive), \( f(t) \) is equal to \( t^2 \).
- For values of \( t \) greater than 1, \( f(t) \) is equal to 1.
This piecewise function represents a quadratic relationship within the interval from 0 to 1 and becomes a constant function with a value of 1 for any \( t \) greater than 1.
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