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Consider the following piecewise-defined function: 2, tIn4 (a) Sketch the graph of f(t) and clearly mark all points where the character of the function changes. (b) Express f(t) as a linear combination of shifted Heaviside functions. The coefficients of this linear combination may be functions of t. (c) Calculate the Laplace transform £{f}.

Consider the following piecewise-defined function: 2, tIn4 (a) Sketch the graph of f(t) and clearly mark all points where the character of the function changes. (b) Express f(t) as a linear combination of shifted Heaviside functions. The coefficients of this linear combination may be functions of t. (c) Calculate the Laplace transform £{f}.

Advanced Engineering Mathematics
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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Consider the following piecewise-defined function: 2, t<ln 2 f(t)= = et In 2<t<ln 4 +2, t>In4 (a) Sketch the graph of f(t) and clearly mark all points where the character of the function changes. (b) Express f(t) as a linear combination of shifted Heaviside functions. The coefficients of this linear combination may be functions of t. (c) Calculate the Laplace transform £{f}.
Transcribed Image Text:Consider the following piecewise-defined function: 2, t<ln 2 f(t)= = et In 2<t<ln 4 +2, t>In4 (a) Sketch the graph of f(t) and clearly mark all points where the character of the function changes. (b) Express f(t) as a linear combination of shifted Heaviside functions. The coefficients of this linear combination may be functions of t. (c) Calculate the Laplace transform £{f}.
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