On
$Prepar\dot{\ovalbox{\tt\small REJECT}}ng$
Lecture
Notes
$augment\dot{\ovalbox{\tt\small REJECT}}ng$
the
body
of
$know\ovalbox{\tt\small REJECT}$edge
Haiduke Saraf
$\prime$an
$\cup n\dot{\ovalbox{\tt\small REJECT}}$versity
C
$o\ovalbox{\tt\small REJECT}|ege$
Pennsylvania
State
$Univers\dot{\ovalbox{\tt\small REJECT}}ty$York,
$\cup SA$
has2@psu.edu
Abstract
Motivations and Objectives
数理解析研究所講究録
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$ToEditor_{-}RIMS_{-}Augusf2013$
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2.
Physics
of the
problem
and
its formulation
Figure1.
$Two-spr\dot{\ovalbox{\tt\small REJECT}}ng$arrangement
leading
to
a
$comblnat\dot{\ovalbox{\tt\small REJECT}}on$
of
a
$cub\dot{\ovalbox{\tt\small REJECT}}c$and
$qu\dot{\ovalbox{\tt\small REJECT}}nt\dot{\ovalbox{\tt\small REJECT}}c$oscillati
$ons.$
For displacements
$x<L$
the
quantity
$\dot{\ovalbox{\tt\small REJECT}}n$the
parentheses
in
eq
(1)maybe
replaced with
$\frac{1}{2}$$( \frac{\chi}{L})^{2}-\frac{3}{8}$$( \frac{\chi}{L})^{4}+$$y\dot{\ovalbox{\tt\small REJECT}}e|d\dot{\ovalbox{\tt\small REJECT}}ng,$
3.
Analysis
$Accord\dot{\ovalbox{\tt\small REJECT}}ng$
to
the
scenario shown in Fig
1
and
its accompanied
force,
eq
(2),
the
$equat\dot{\ovalbox{\tt\small REJECT}}on$of
$mot\dot{\ovalbox{\tt\small REJECT}}on\dot{\ovalbox{\tt\small REJECT}}s,$$X+\frac{k}{mL^{2}}\nearrow-\frac{3}{4}\frac{k}{mL^{4}}\nearrow=0$
.
(3)
$\mathcal{T}0\Xi ditor$
RIMS Aqgust20l3Decemberl
$1_{-}2013.nb$
$|$alues
$=\{karrow 3.0,$
$\primearrow 6.0\cross 10^{-2},$
$marrow 10.0\cross 10^{-3}\}$
$|$
$ToEditor_{-}RIMS_{-}August20l3$
Decemberl 1
$2013.nb$
$x.m$
Figure3.
$Disp\ovalbox{\tt\small REJECT} ay$of the
$overla\dot{\ovalbox{\tt\small REJECT}}d$osclllations shown
$\dot{\ovalbox{\tt\small REJECT}}nF\dot{\ovalbox{\tt\small REJECT}}g2$.
lt shows
the
Ionger
the
amplitude
the shorter the
$per\dot{\ovalbox{\tt\small REJECT}}od.$$v,m/s$
ToEditor-RIMS-A
uqusf2013Decemberl
$1_{-}2013.nb$
$\iota’.m/s$
4. A Semi-Analytic
method
of solving
DE
of
motion
penod
$S$Figure6. The dots
are
the
$per\dot{\ovalbox{\tt\small REJECT}}ods$and the corresponding
ampl
$\dot{\ovalbox{\tt\small REJECT}}tudes$deduced from
$F\dot{\ovalbox{\tt\small REJECT}}g2$.
The
$so\ovalbox{\tt\small REJECT} idl\dot{\ovalbox{\tt\small REJECT}}ne$is the
$|$
ToEditor-RIMS-A
$ugust201$
3Decemberl
$1_{-}2013.nb$
fitted
curve
$T(amp)=0.0256907amp^{-1}$
x,m
x,m
x,m
$x,m$
Figure7.
$Compar\dot{\ovalbox{\tt\small REJECT}}son$
of the
$numer\dot{\ovalbox{\tt\small REJECT}}csolut\dot{\ovalbox{\tt\small REJECT}}ons$(black curves)vs.
$sem\dot{/}$
-analytic solution
(gray curves).
5. Two
$simi\ovalbox{\tt\small REJECT} ar$nonlinear Oscillators
$E$
Figure8.
$Osci||at\dot{\ovalbox{\tt\small REJECT}}ons$of
an
$e|ectr\dot{\ovalbox{\tt\small REJECT}}c$monopole
within the
$electr\dot{\ovalbox{\tt\small REJECT}}cf\ovalbox{\tt\small REJECT} eld$of acharged ring
$(/eft)$
.
$Osc\dot{\ovalbox{\tt\small REJECT}}Il$atlons of
a
To
$ditor_{-}R1MS_{-}August2013$
Decemberl
1-2013.
$nb$
$magnet\dot{\ovalbox{\tt\small REJECT}}cd\dot{\ovalbox{\tt\small REJECT}}$