Program Explanation Given information: Transforms of derivatives theorem states that L { f ′ ( t ) } = s L { f ( t ) } − f ( 0 ) if the function f ( t ) is piecewise continuous. Similarly for second derivative of the function L { f ″ ( t ) } = s 2 L { f ( t ) } − s f ( 0 ) − f ′ ( 0 ) . Calculation: Consider function f ( t ) as t cosh k t and obtain the first and second derivative of the function as follows: f ( t ) = t cosh k t f ′ ( t ) = cosh k t + k t sinh k t f ″ ( t ) = k sinh k t + k sinh k t + k 2 t cosh k t = 2 k sinh k t + k 2 f ( t ) Now, apply the derivative transform theorem as, L { f ″ ( t ) } = L { 2 k sinh k t + k 2 f ( t ) } s 2 L { f ( t ) } − s f ( 0 ) − f ′ ( 0 ) = 2 k L { sinh k t } + k 2 L

5th Edition

ISBN: 9780321974235

Author: Calvis

Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)

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Problems on Growing Functions

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Chapter 7.2, Problem 30P

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Program Description: Purpose of the problem is to derive the formula that L{tcoshkt}=s2+k2( s 2 − k 2 )2 .

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Chapter 7.2, Problem 29P

Chapter 7.2, Problem 31P

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Chapter 7 Solutions

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Program Description: Purpose of the problem is to derive the formula that L { t cosh k t } = s 2 + k 2 ( s 2 − k 2 ) 2 .

Solution Summary: The author explains the purpose of the problem, which is to derive the formula that Llefttmathrmcosh

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Program Description: Purpose of the problem is to derive the formula that L{tcoshkt}=s2+k2( s 2 − k 2 )2 .

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Chapter 7 Solutions