Program Explanation Given information: The Laplace transform of piecewise continuous function f ( t ) for t ≥ 0 is written as, L { f ( t ) } = F ( s ) = 1 1 − e − p s ∫ 0 p e − s t f ( t ) d t s > 0 Here, function f ( t ) is a periodic function of period p . Calculation: Consider the function f ( t ) as cos k t and therefore, the period p is equivalent to 2 π k . f ( t ) = cos k t = cos k ( 2 π n k + t ) n ∈ ℤ Take Laplace transform of the periodic function f ( t ) and evaluate as shown below. L { f ( t ) } = L { cos k t } = 1 1 − e − ( 2 π k ) s ∫ 0 ( 2 π k ) e − s t ( cos k t ) d t = 1 1 − e − ( 2 π k ) s [ e ( − s ) t ( ( − s ) cos ( k ) t + ( k ) sin ( k ) t ( − s ) 2 + ( k ) 2 ) ] 0 2 π k = 1 1 − e − ( 2 π k ) s [ e − s t ( − s cos k t + k sin k t s 2 + k 2 ) ] 0 2 π k Further, solve the equation as shown below

5th Edition

ISBN: 9780321974235

Author: Calvis

Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)

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A naïve solution for the above-stated problem is to evaluate all of the possible combinations of different pieces of varying size to find the maximum revenue-generating combination. Although this method seems the easiest and quick to practice, it has exp…

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Chapter 7.5, Problem 24P

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Program Description: Purpose of the problem is to verify L{coskt}=ss2+k2 from the theorem of periodic functions with period of f(t) is 1.

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Chapter 7.5, Problem 23P

Chapter 7.5, Problem 25P

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Chapter 7 Solutions

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Program Description: Purpose of the problem is to verify L { cos k t } = s s 2 + k 2 from the theorem of periodic functions with period of f ( t ) is 1.

Solution Summary: The author analyzes the Laplace transform of the periodic function f(t).

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Program Description: Purpose of the problem is to verify L{coskt}=ss2+k2 from the theorem of periodic functions with period of f(t) is 1.

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Chapter 7 Solutions