Electron. J. Diff. Equ.,
Vol. 2009(2009), No. 141, pp. 115.
Precise asymptotic behavior of solutions to
damped simple pendulum equations
Tetsutaro Shibata
Abstract:
We consider the simple pendulum equation
where
,
, and the friction term
is either
or
.
Note that when
and
, we have well known
original damped simple pendulum equation.
To understand the dependance of solutions, to the damped simple
pendulum equation with
, upon the term
,
we present asymptotic formulas for the maximum norm of the solutions.
Also we present an asymptotic formula for the time at which
maximum occurs, for the case
.
Submitted April 21, 2009. Published November 7, 2009.
Math Subject Classifications: 34B15.
Key Words: Damped simple pendulum; asymptotic formula.
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Tetsutaro Shibata
Department of Applied Mathematics, Graduate School of Engineering
Hiroshima University, HigashiHiroshima, 7398527, Japan
email: shibata@amath.hiroshimau.ac.jp

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