Special Case of Partial Fraction Expansion with Laplace Transform Application

Authors

Laurie A. Florio, DEVCOM Armaments Center United States Army Armament Graduate SchoolFollow
Ryan D. Hanc, DEVCOM Armaments Center United States Army Armament Graduate SchoolFollow

Publication Date

6-30-2023

Keywords

ordinary differential equations, Partial Fraction expansion, Laplace Transform

Disciplines

Mathematics | Physical Sciences and Mathematics | Science and Mathematics Education

Abstract

Partial fraction expansion is often used with the Laplace Transforms to formulate algebraic expressions for which the inverse Laplace Transform can be easily found. This paper demonstrates a special case for which a linear, constant coefficient, second order ordinary differential equation with no damping term and a harmonic function non-homogeneous term leads to a simplified partial fraction expansion due to the decoupling of the partial fraction expansion coefficients of s and the constant coefficients. Recognizing this special form can allow for quicker calculations and automation of the solution to the differential equation form which is commonly used to model physical systems.

Recommended Citation

Florio, Laurie A. and Hanc, Ryan D. (2023) "Special Case of Partial Fraction Expansion with Laplace Transform Application," CODEE Journal: Vol. 16, Article 2.
Available at: https://scholarship.claremont.edu/codee/vol16/iss1/2