## PSN-L Email List Message

Subject: Re: spring I mentioned
From: Pete Rowe ptrowe@.........
Date: Tue, 16 Aug 2011 12:28:35 -0700 (PDT)

```Ah hah. I got it. The key is visualizing a cosine not a sine!!=0AThanks for=
the mental exercise.=0APete=0A=0A=0A=0A________________________________=0A=
From: Randall Peters =0ATo: "'psnlist@................
" =0ASent: Tuesday, August 16, 2011 11:59 AM=0ASubj=
ect: spring I mentioned=0A=0A=0ASorry, Charles and Pete,=0A=C2=A0=C2=A0=C2=
=A0=C2=A0 that I didn=E2=80=99t do a very good job of describing it; so let=
me try again.=C2=A0=C2=A0 A picture would be =E2=80=98worth a thousand wor=
ds=E2=80=99, but I don=E2=80=99t want to go there unless we have to.=0AEach=
of the four strips is formed to exist in an unloaded shape like I mentione=
d=E2=80=94approximately one cycle of a cosine.=C2=A0 After shaping all four=
strips to be identical, they are then welded or glued together at their en=
ds in pairs, yielding two identical spring components. =C2=A0There are two =
ways a strip pair could be welded at their ends, one being with a strip lyi=
ng on top of another, so the pair are in contact virtually everywhere.=C2=
=A0 That is not the choice used.=C2=A0 Rather from that starting arrangemen=
t, flip one of the two so that when they come together, they touch only at =
their ends, where they are then welded. =C2=A0Each end of these two identic=
al components (four ends total) will look kinda like what you would see fro=
m the =E2=80=98sharp=E2=80=99 side only if you were to imagine a plane pass=
ing through the center of a water drop about to break away from the spigot.=
=C2=A0 =0AIf you can visualize their shape, then now take one of these two =
welded structures and insert it inside the other one at right angles until =
their centers meet.=C2=A0 The insertion will meet a resistance force only a=
s the pair approach their final resting place.=C2=A0 There, with the planes=
of the two components resting at right angles to each other, is realized t=
he 4-fold rotational symmetry I mentioned.=C2=A0 In other words, visualize =
an axis that passes through the centers of both the top union and the botto=
90 degrees, the spring will look the same from a fixed position of view.=
=C2=A0 In solid state physics we call this a 4-fold rotational symmetry, be=
cause 4 such indistinguishable rotations bring it back to where you started=
Ah hah. I =
got it. The key is visualizing a cosine not a sine!!Thanks for the mental exercise.PeteFrom: Randall Peters=
<PETERS_RD@..........>To:<=
/span> "'psnlist@..............." <psnlist@..............>=
Sent: Tuesday, August 16, 201=
1 11:59 AMSubject: spr=
ing I mentioned<!--=0A#yiv67=
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><div class=3D"yiv670659552WordSection1"><div class=3D"yiv670659552MsoNorma=
l">Sorry, Charles and Pete,</div><div class=3D"yiv670659552MsoNormal">&nbsp=
;&nbsp;&nbsp;&nbsp; that I didn=E2=80=99t do a very good job of describing =
it; so let me try again.&nbsp;&nbsp; A picture would be =E2=80=98worth a th=
ousand words=E2=80=99, but I don=E2=80=99t want to go there unless we have =
to.</div><div class=3D"yiv670659552MsoNormal">Each of the four strips is fo=
rmed to exist in an unloaded shape like I mentioned=E2=80=94approximately o=
ne cycle of a cosine.&nbsp; After shaping all four strips to be identical, =
they are then welded or glued together at their ends in pairs, yielding two=
identical spring components. &nbsp;There are two ways a strip pair could b=
e welded at their ends, one being with a strip lying on top of another, so =
the pair are in contact virtually everywhere.&nbsp; That is not the choice =
used.&nbsp; Rather from that starting arrangement, flip one of the two so t=
hat when they come
together, they touch only at their ends, where they are then welded. &nbsp=
;Each end of these two identical components (four ends total) will look kin=
da like what you would see from the =E2=80=98sharp=E2=80=99 side only if yo=
u were to imagine a plane passing through the center of a water drop about =
to break away from the spigot.&nbsp; </div><div class=3D"yiv670659552MsoNor=
mal">If you can visualize their shape, then now take one of these two welde=
d structures and insert it inside the other one at right angles until their=
centers meet.&nbsp; The insertion will meet a resistance force only as the=
pair approach their final resting place.&nbsp; There, with the planes of t=
he two components resting at right angles to each other, is realized the 4-=
fold rotational symmetry I mentioned.&nbsp; In other words, visualize an ax=
is that passes through the centers of both the top union and the bottom uni=