Bessel’s Differential Equation and the Aging Spring Problem
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Date
2014-08
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Addis Ababa University
Abstract
In this paper we study the aging spring equation without damping
X= (t) + e−at+b x(t)=0 ,
or the most general one with damping
(t) + dx= (t) + e−at x(t)=0
which is a special cases of homogeneous linear second order ODE with variable coefficients.
We will show that, with a suitable change of variables, this equation of aging spring problem
can be transformed into Bessel differential equation and hence the solution can be expressed
in terms of Bessel functions
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Keywords
Bessel’s Differential Equation, And the Aging Spring Problem