Explanation Given: The given functions are, F ( s ) = s + 4 s 2 + 8 s + 25 , G ( s ) = s e − π / 2 s 2 + 16 Approach: By the Convolution Theorem, L − 1 [ F ( s ) G ( s ) ] = L − 1 [ F ( s ) ] ∗ L − 1 [ G ( s ) ] Calculation: Consider the given functions, F ( s ) = s + 4 s 2 + 8 s + 25 , G ( s ) = s e − π / 2 s 2 + 16 Use Convolution Theorem as follows, L − 1 [ F ( s ) G ( s ) ] = L − 1 [ s + 4 s 2 + 8 s + 25 ] ∗ L − 1 [ s e − π / 2 s 2 + 16 ] = e − 4 t cos 3 t ∗ e − π / 2 cos 4 t = f ∗ g By the definition of Convolution product theorem, ( f ∗ g ) ( t ) = ∫ 0 t f ( t − τ ) g ( τ ) d τ The value of e − 4 t cos 3 t ∗ e − π / 2 cos 4 t is calculated as follows,

Differential Equations and Linear Algebra (4th Edition)

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ISBN: 9780321964670

Author: Stephen W. Goode, Scott A. Annin

Publisher: PEARSON

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Chapter 10.9, Problem 24P

To determine

To express:

The L−1[F(s)G(s)] in terms of a convolution integral.

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Chapter 10.9, Problem 23P

Chapter 10.9, Problem 25P

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To express: The L − 1 [ F ( s ) G ( s ) ] in terms of a convolution integral.

Solution Summary: The author explains how to express the L-1left in terms of a convolution integral using the Convolution Theorem.

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To express:

The L−1[F(s)G(s)] in terms of a convolution integral.

Want to see the full answer?

Chapter 10 Solutions

To express: The L − 1 [ F ( s ) G ( s ) ] in terms of a convolution integral.

Solution Summary: The author explains how to express the L-1left in terms of a convolution integral using the Convolution Theorem.

Concept explainers

Videos

To express: The L−1[F(s)G(s)] in terms of a convolution integral.

Want to see the full answer?

Chapter 10 Solutions

To express:

The L−1[F(s)G(s)] in terms of a convolution integral.