Program Explanation Given information: The function is F ( s ) = 1 s 4 − 8 s 2 + 16 . Explanation: The given function is F ( s ) = 1 s 4 − 8 s 2 + 16 . Apply inverse Laplace transform to the function F ( s ) = 1 s 4 − 8 s 2 + 16 . L − 1 { F ( s ) } = L − 1 { 1 s 4 − 8 s 2 + 16 } = L − 1 { 1 ( s 4 − 4 s − 4 s + 16 ) } = L − 1 { 1 ( s 2 ( s 2 − 4 ) + s 2 ( s − 4 ) ) } = L − 1 { 1 ( ( s − 2 ) ( s + 2 ) ) 2 } Apply partial fraction method to solve the above expression, 1 ( ( s − 2 ) ( s + 2 ) ) 2 = A s + B ( s − 2 ) 2 + C s + D ( s + 2 ) 2 ........... (1) Multiply the equation by denominator as, 1 ( ( ( s − 2 ) ( s + 2 ) ) 2 ) ( ( s − 2 ) ( s + 2 ) ) 2 = ( A s + B ) ( ( ( s − 2 ) ( s + 2 ) ) 2 ) ( s − 2 ) 2 + C s + D ( ( ( s − 2 ) ( s + 2 ) ) 2 ) ( s + 2 ) 2 1 = ( A s + B ) ( s + 2 ) 2 + ( C s + D ) ( s − 2 ) 2 1 = ( A s + B ) ( s 2 + 4 s + 4 ) + ( C s + D ) ( s 2 − 4 s + 4 ) 1 = [ ( A s 3 + C s 3 ) + ( 4 A s 2 + B s 2 − 4 C s 2 + D s 2 ) + ( 4 A s + 4 B s + 4 C s − 4 D s ) + ( 4 B + 4 D ) ] Equating the coefficient of s 3 , s 2 , s and 1 as, A + C = 0 4 A + B − 4 C + D = 0 4 A + 4 B + 4 C − 4 D = 0 4 B + 4 D = 1

Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis

5th Edition

ISBN: 9780321816252

Author: C. Henry Edwards, David E. Penney, David Calvis

Publisher: PEARSON

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Problems on Growing Functions

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Question

Chapter 7.3, Problem 20P

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Program Description: Purpose of problem is to obtain the inverse Laplace transformation of the functions F(s)=1s4−8s2+16 by using partial fraction.

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Chapter 7.3, Problem 19P

Chapter 7.3, Problem 21P

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Chapter 7 Solutions

Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis

Ch. 7.1 - Apply the definition in (1) to find directly tile...Ch. 7.1 - Prob. 2P Ch. 7.1 - Prob. 3P Ch. 7.1 - Prob. 4P Ch. 7.1 - Prob. 5P Ch. 7.1 - Prob. 6P Ch. 7.1 - Prob. 7P Ch. 7.1 - Prob. 8P Ch. 7.1 - Prob. 9P Ch. 7.1 - Prob. 10P

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Program Description: Purpose of problem is to obtain the inverse Laplace transformation of the functions F ( s ) = 1 s 4 − 8 s 2 + 16 by using partial fraction.

Solution Summary: The author explains how to obtain the inverse Laplace transformation of the functions by using partial tion.

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Program Description: Purpose of problem is to obtain the inverse Laplace transformation of the functions F(s)=1s4−8s2+16 by using partial fraction.

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Chapter 7 Solutions