> '` bjbj$$ .FF4\\\\p8L$hBj
j
j
BW
j
:
j
`p T\
m0
u
u
u
YBB
j
j
j
j
888$\888\$0TAP 303- 3: Modelling springs and masses
This file is provided for use with:
HYPERLINK "TAP303-2-Mass-spring-SHM.doc" TAP 303-2: Oscillating freely
A Modellus model to look at the relationship between f, k and m
This model allows you to alter the spring constant and mass of an oscillator, looking at changes in the motion.
The Modellus model is below
EMBED Package
Practical advice
This model looks at the relationship:
EMBED Equation.3
This could be used after the free oscillator has been introduced. You could use it to supplement work done in the laboratory in describing the motion, both in relating all the kinematic variables, and in relating the characteristics of the oscillation to the dynamic variables. It could form the basis for a useful homework exercise. Alternatively you could demonstrate some of the features of the model using it to introduce the topic. If so, a real system should be demonstrated also. At some stage the students should analyse real data.
This model is deliberately simple, and probably should not be used to replace laboratory work on this topic. It may, however, form a useful focus for discussion, or private study. The chance to play the motion back step by step, talking through the changes to understand the dynamics, relating this to the average time for a complete oscillation, and to interact with a range of masses and spring constants should not be missed.
More confident students, or those with more time to spend here, could adapt the model to form a presentation, adding vectors to the animation, and perhaps slowing it down by making the time steps finer grained, to form a tool to help them explain the relationship between the quantities.
Alternative approaches
This model could be introduced much later when a lot of practical experience has been gained and students know about (k/m) 1/2, as you may choose to base an introduction entirely on laboratory work
.
Social and human context
This step-by-step understanding, in which every change is linked to a prior sufficient cause, is central to the theme of the clockwork Universe and Laplaces thought: All the effects of nature are only the mathematical consequences of a small number of immutable laws. Mass and spring oscillators can be used to model everything from car suspensions to molecular vibrations. It is important that you get a feel for the physics involved. In this activity, a model is employed to highlight some of the important physical ideas involved in studying simple oscillating systems.
Modellus
Modellus is available as a FREE download from HYPERLINK "http://phoenix.sce.fct.unl.pt/modellus/" http://phoenix.sce.fct.unl.pt/modellus/ along with other sample files and the user manual
External reference
This activity is taken from Advancing Physics chapter 10, 130L
OPz{|P Q q r RV12ghre]Thdh!m>0Jhdh!m>H*jihdh!m>EHU<jeRF
hdh!m>B*OJPJQJUV^JnH phtH jhdh!m>UjUF
hdh!m>Ujhdh!m>U*j
hdh!m>B*CJU^JaJphjhdh!m>UhNbh!m>0JjhNbUhNbjhNbUh!m>hdh!m> )*NOP p q
gd!m>gd!m>gd!m>gd!m>gd!m>gd!m>h!m>hdh!m>jhdh!m>U,1h. A!"#$%DyKF
TAP303~3.DOC>8TAP303-2-Mass-spring-SHM.docBDd
0
#A24N0HWk+eV,Ib$=۬lsW̒U
**IjҐѫYJ55Ēk
D66~ͪ$fˬCT)%=8KGgIuu^baJ9A:Y\{$1
%1+ˬBx5$su76'~Yeg@%ifNbU%1U^__O̒p=Ybt@٣a$f3KRSvmIb$wR.oֵzYK'5_=YU̒,Ig24̒F=8axf=G,YMkKNY̪$f5`Vdtf Y %ˬ3ʙli%Ьרc rO\ՃݏTgK:Y
/OBV:|`aKb^V[Z1+||XDRIg awxLµ
[RaF1kEwxP%Mq0+Xؒj
sv&rDfXؒ
Gr:>>%mfv_4faKlVfu]-lI;0<7<[$faK%1Kؒ-lI,aKb%1M,(YͰeIj-GbV3lY,a[[%Y,Ib$fI$Y%I̒$fIb$1K%Y,Ib$fI$Y%I̒$fIb$1K%Y,Ib$fI$Y%I̒$fIb$1K%Y,Ib$fI$Y%I̒$fIb$1K%Y,Ib$fia/!$Une>,fYzY,1Yb,f1Kb,fYb,1Y%fYj۬rYbZ(fYjlBUߚ
,1Yb,f1Kb,fYleբVb$XbXb,f1Y̪%f1Yb,f1Yb,f1Yb,lYjϬY|IکŬRfeu^V͚Zצo[֮b[s/!~FނwA1Y2kJ.+ՃmŬ
Gw
N{{Q
Uج:urZ,fHbjY=~0YZ1Df]NQYjݬkNdY#1kgEd,1Yb%fy,f1Kb1+xfU*'r^IOLfZ0kYH?Ǭ"H5aZ&n+6f5}7NTCR?^>f,klxJ+|Of=߬\cVV2UˬP?ծYɗZt?Z*NɵthlxYw'le~pvY `M%fA@,f1Ԑ9YbV{YD,f1YE}SΙ`9zp52EuN_]By:x9oqxf>z銟CdFf=9L6{[fs֡R?ʬWqtϗ]"2:aRoe?fv#l~728cf:1FYgx#Zǳ@YX]|-}wMx fR'B_]=muz6dNgTeOȚ8
Ƭ-1Y,B2K*A(B4EHYPU",iRbn#f,HRۃDJ,IYP̒(&fINYR{Y>̒,ܐb'1Kxr@]R0IҮͲ,eAY2N$G1KJpf9Yb%1K,1K$fYbޫ v-Uz9`Z5⾾>wKhv+fuKFm[>g!vsfY7+^o_9㯟U݆z}V>Hg1uy(ýLmGww_һ{f-Q|Up6zW%0)桻+ff~ASw۩˻
>&SGz#f|XmVbכٙLj:e_,ήKg7#fGp:YEU;}W͊!-fiƬJ9k&<>&n:~.{Tfl0vt(~:9exʽa{Uf)e}rt
B={ **cҦf`{UVEo2KE=~kh,AfMmZ*[o,i]d%I̒$fIb$5`!oz~T4ՍDd
0
#A2 0qR%`
`!0qR%}}x}RJ@ݴA(J_Q{*ނ Sb?d)aGҋe>ޖ2l҈}ݝ7ͦ'h ܸM\8qkn9
ZG㓒?>Otmx!girjzc1TNR%e=xpbl탵14CVm "Ҿv3b&uiZEJu<}ֿ[#P>E.@7پ8Ms722E!!7Keʰ&oAnp>HZW)8$Xi
L~]ZHAg@j/+/Jo.:(Z!
^,@9D
7}~`ܗտWbCgDd
0
#A2<j2O|N[k i%p`!j2O|N[k i%pxR2 ix?O@Ɵ+B%Q LL?DANNN.~g'f0ir+
P)ew]ːb[* )N)V6ErJCVNkIKKÇNmc!UPu&II9ɕ@ÖcUx`GLΥ_6_Y%mk
s+iI]lL7HV|Q:| Lw '.I?߉NOjXfz˵7gKeYAnF/7sC(Z>aB.E^ŏɇCC]m'`Laq9pʄl**/nVYkN-*F>)I
> 2BwTZ!&}gDd
l\
c$A??#"`2eG?[FS`!eG?[FN8YxuQJQ=wF5-D,V2I !6(c~V
beaiag?P3;3@.**imFW_b"<]k!=ۚ[R)V6oR*I9[~R:ۤĵwuv7Normal CJOJPJQJ_HmH sH tH DA@DDefault Paragraph FontRiRTable Normal4
l4a(k(No ListhOh!m>ItemH1$7$8$H$35B* CJOJQJ\^J_HaJmH phsH tH JOJ!m>TAP ParaxB*CJOJQJ^JphFOF!m>TAP Subx5B*OJQJ^Jph4U@!4!m> Hyperlink >*ph
"& "&)*NOPpq
r r v:r v:r v:r v:r v:r r v:r &r v:r v:r r v:r ir v:r v:r r v:r v:r v:r v:r r v:r v:r r v:r v:r r v:r v:r r )*NOPpq
000000000000000000000000000000000
O{q1
g
X::X8@0(
B
S ?BM100039!:
"
?*urn:schemas-microsoft-com:office:smarttagsstockticker$EX`
OO!m>NbO
51@D:@UnknownGz Times New Roman5Symbol3&z Arial3z Times"qhQtFo o !r43qHX ?!m>2(TAP 303- 3: Modelling springs and massesmxgvysCompObjq
FMicrosoft Office Word Document
MSWordDocWord.Document.89q