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=
m union.=C2=A0 For any rotation of the set about this axis, if the angle is=
 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.

From: Randall Peters= <PETERS_RD@..........>
To:<= /span> "'psnlist@..............." <psnlist@..............>
= Sent: Tuesday, August 16, 201= 1 11:59 AM
Subject: spr= ing I mentioned