f (t) = cos² (πt)
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
Use the laplace transform of derivative to solve for the laplace transform of the following.
![The mathematical expression shown is:
\[ f(t) = \cos^2(\pi |t|) \]
This represents a function \( f \) in terms of the variable \( t \), where:
- \( \cos^2 \) denotes the square of the cosine function.
- \( \pi |t| \) indicates that the input to the cosine function is the absolute value of \( t \) multiplied by \( \pi \).
This function describes how the value of \( f(t) \) changes based on \( t \), considering the periodic nature of the cosine function. The function can be used to model various periodic phenomena, such as waveforms, due to its oscillatory properties.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F42eb3f21-115e-47f2-b59c-753292f0c3d6%2F8fe73e3c-7c84-409c-88dd-c14f27e22e89%2F2g9odbc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The mathematical expression shown is:
\[ f(t) = \cos^2(\pi |t|) \]
This represents a function \( f \) in terms of the variable \( t \), where:
- \( \cos^2 \) denotes the square of the cosine function.
- \( \pi |t| \) indicates that the input to the cosine function is the absolute value of \( t \) multiplied by \( \pi \).
This function describes how the value of \( f(t) \) changes based on \( t \), considering the periodic nature of the cosine function. The function can be used to model various periodic phenomena, such as waveforms, due to its oscillatory properties.
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