2004 Spring Beauty in Modeling Contest

Rules
Spring Problem
Judges
Prizes
FAQ

Draft Rules:

  1. (Entry) A valid entry consists of
    1. a clearly written solution to the Spring problem with any accompanying materials,
    2. a clear indication of the division and participant name(s) with contact information and one person indicated as the primary contact, and
    3. the appropriate entry fee ($2 per participant).
  2. (Format) Written solutions should be typed and accompanied by any computer code or other supporting materials. Coding should be completely and carefully explained and documented. Clarity in presentation will comprise a significant portion of the judging criteria. All materials may be submitted on a single cd if that is preferable to the participants and aids in making a clear presentation of results.
  3. (Divisions) An entry may be designated as RESTRICTED or OPEN.

    The RESTRICTED DIVISION is intended for undergraduates from Georgia Tech, but in principle undergraduates from another institution may also participate. All participants in this division must be undergraduates and must not obtain direct assistance from any (human) source other than those listed as participants on the contest entry. These provisions are subject to the spirit and letter of the Georgia Tech Honor Code.

    The OPEN DIVISION is for anyone who wishes to participate.

    Individual or Team entries are permitted in either division.

    No single person may be listed on two distinct contest entries. If a single person enters twice, both submissions will be disqualified with no refund of entry fee.
  4. Prizes will be awarded to the primary contact listed on the contest entry. The primary contact is solely responsible for distributing prize money to other team participants.


All entries must be received by March 25, 2004.

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Judges: Solutions will be judges on beauty, elegance, and accuracy by
  1. Wenjing Ye (Mechanical Engineering)
  2. Predrag Cvitanovich (Physics)
  3. John McCuan (Mathematics)
  4. John Pelesko (Mathematics, University of Deleware)
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Prizes: Cash prizes will be given to the top three entries in each division according to the formula

First Prize = $(50 + n/2)
Second Prize = $(25 + n/3)
Third Prize = $(15 + n/5)

where n is the total number of participants in the division.

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Spring Problem




Shown above is a slinky type spring with the ends held (at the same height and depth) in vertical planes 172 mm apart.

Problem: Describe the shape of the same spring if the ends are held in a different position, which we now describe.

Position of the ends

Notice that the position of the ends may be specified by the center of a circle (the circle of the end), a plane in which the circle is held, and a normal to that plane pointing toward the spring (on the circle of the end). Taking the z-direction coming out of the picture and the y-direction to be vertical, the positions we wish to specify are given in this way by
left center: (0,0,0) right center: (179,158,0)
left plane: y = 0 right plane: y = (16x + 1086)/25
left normal: (0,-1,0) right normal: (-16,25,0)

where the x,y,z-coordinates have the x and z directions horizontal; all dimensions are given in millimeters.

(For example, the data for the first positions described are
left center: (0,0,0) right center: (172,0,0)
left plane: x = 0 right plane: x = 172
left normal: (1,0,0) right normal: (-1,0,0).)

Physical dimensions of spring: You may assume the solution spring lies in |z| < 14.15 mm.

FAQ
Any questions concerning the problem may be sent to mccuan@math.gatech.edu and they will be posted with responses here.

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