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On Preparing Lecture Notes : augmenting the body of knowledge (Study of Mathematical Software and Its Effective Use for Mathematics Education)

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(1)

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

(2)

$|$

$ToEditor_{-}RIMS_{-}Augusf2013$

Decemberl 1

$20l3.nb$

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)

(3)

$\mathcal{T}0\Xi ditor$

RIMS Aqgust20l3Decemberl

$1_{-}2013.nb$

$|$

alues

$=\{karrow 3.0,$

$\primearrow 6.0\cross 10^{-2},$

$marrow 10.0\cross 10^{-3}\}$

(4)

$|$

$ToEditor_{-}RIMS_{-}August20l3$

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

$per\dot{\ovalbox{\tt\small REJECT}}od.$

$v,m/s$

(5)

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

(6)

$|$

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

(7)

To

$ditor_{-}R1MS_{-}August2013$

Decemberl

1-2013.

$nb$

$magnet\dot{\ovalbox{\tt\small REJECT}}cd\dot{\ovalbox{\tt\small REJECT}}$

poIe

within the magnetic

$f\prime eld$

of

a

$Ioop\dot{\ovalbox{\tt\small REJECT}}ng$

current

$(r\dot{\ovalbox{\tt\small REJECT}}ght)$

6.

Conclusions and Remarks

7.

A

Potential

Extension

for the

Future

Investigation

Conducive Publications

AcknowIedgement

References

参照

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