Explanation Given: The function is f ( t ) = { sin t , 0 ≤ t < π 0 , t ≥ π . Definition used: If f ( t ) is a piecewise continuous function and of exponential of order t > 0 such that f ( t ) is defined in two pieces; then Laplace transform of f ( t ) is expressed as the sum of two integrals. L { f ( t ) } = ∫ 0 ∞ e − s t f ( t ) d t = ∫ 0 a e − s t f ( t ) d t + ∫ a ∞ e − s t f ( t ) d t Calculation: Note that, the domain of f ( t ) is split into two parts, 0 to π and π to ∞ . Use the above definition to write the Laplace transform of the given function. L { f ( t ) } = ∫ 0 π e − s t ( sin t ) d t + ∫ π ∞ e − s t ( 0 ) d t = [ e − s t s 2 + 1 { ( − s ) sin t − 1 cos t } ] 0 π + 0 ( ∵ ∫ ( f ⋅ g ) d x = g

6th Edition

ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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Chapter 4.1, Problem 5E

To determine

To find: The expression for the Laplace transform of the given function

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Chapter 4.1, Problem 4E

Chapter 4.1, Problem 6E

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Chapter 4 Solutions

Advanced Engineering Mathematics

Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E Ch. 4.1 - Prob. 7E Ch. 4.1 - Prob. 8E Ch. 4.1 - Prob. 9E Ch. 4.1 - Prob. 10E

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