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.PeteFrom:Randall Peters= <PETERS_RD@..........>To:<= /span>"'psnlist@..............." <psnlist@..............>= Sent:Tuesday, August 16, 201= 1 11:59 AMSubject:spr= ing I mentionedSorry, Charles and Pete, = ; that I didn=E2=80=99t do a very good job of describing = it; so let me try again. 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.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. 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. 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. That is not the choice = used. 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.  = ;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.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. The insertion will meet a resistance force only as the= pair approach their final resting place. 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. In other words, visualize an ax= is that passes through the centers of both the top union and the bottom uni= on. For any rotation of the set about this axis, if the angle is 90 d= egrees, the spring will look the same from a fixed position of view. In soli= d state physics we call this a 4-fold rotational symmetry, because 4 such i= ndistinguishable rotations bring it back to where you started.The l[ Top ] [ Back ] [ Home Page ]