Hooke's Law for springs is F = k x
where F is the magnitude of the force exerted by the spring,
k is the spring constant for the spring,
and x is the distance the spring has stretched from its equilibrium position.

This recipe freezes most of the protein and then uses bands stretched in opposite directions,
making a tug-of-war on the protein.
By varying the strength of the bands, this recipe gives different equilibrium lengths for the bands.

This recipe shows that the strength of a band squared equals the band's spring constant.
This recipe also shows that if two bands pull in the same direction,
their spring constants (k1 and k2) add together to give the combined spring constant ktotal.
This means that if the two bands have strengths str1 and str2,
ktotal = k1+k2 = str1^2 + str2^2 = strtotal^2,
and this gives a combined band strength of strtotal = sqrt(str1^2 + str2^2).

Amazing to use scripts to demonstrate this ! Not sure this recipe will help us gain points, but, at least, there is something artistic and funny. A real game with no purpose. No purpose can help creativity. That's why I like it.

This routine gives evidence that Foldit bands obey Hooke's Law;
   that is, F = k x where F is the force of the band,
   k = spring constant of band = strength of band squared, and
   x = length band is stretched from its desired (equilibrium) position.
If two bands pull in the same direction, their k's add together
   so that ktotal = k1 + k2 = strength1^2 + strength2^2.
 
Two bands (b1a,b2a) in opposite directions:
 
Here,  F1 = 80 = k1*x1 = (1.0)*(80.00) = (str1)^2*x1 = (1.0)^2*(80.00)
equals F2 = 80 = k2*x2 = (4.0)*(20.00) = (str2)^2*x2 = (2.0)^2*(20.00).
Also,  x1 = 80.00, x2 = 20.00, and x1+x2 = 100.00 = 100.00.
 
Here,  F1 = 90 = k1*x1 = (1.0)*(90.00) = (str1)^2*x1 = (1.0)^2*(90.00)
equals F2 = 90 = k2*x2 = (9.0)*(10.00) = (str2)^2*x2 = (3.0)^2*(10.00).
Also,  x1 = 90.00, x2 = 10.00, and x1+x2 = 100.00 = 100.00.
 
Here,  F1 = 98 = k1*x1 = (1.0)*(98.00) = (str1)^2*x1 = (1.0)^2*(98.00)
equals F2 = 98 = k2*x2 = (49.0)*(2.00) = (str2)^2*x2 = (7.0)^2*(2.00).
Also,  x1 = 98.00, x2 = 2.00, and x1+x2 = 100.00 = 100.00.
 
Here,  F1 = 345 = k1*x1 = (25.0)*(13.80) = (str1)^2*x1 = (5.0)^2*(13.80)
equals F2 = 345 = k2*x2 = (4.0)*(86.20) = (str2)^2*x2 = (2.0)^2*(86.20).
Also,  x1 = 13.80, x2 = 86.20, and x1+x2 = 100.00 = 100.00.
 
Here,  F1 = 662 = k1*x1 = (25.0)*(26.47) = (str1)^2*x1 = (5.0)^2*(26.47)
equals F2 = 662 = k2*x2 = (9.0)*(73.53) = (str2)^2*x2 = (3.0)^2*(73.53).
Also,  x1 = 26.47, x2 = 73.53, and x1+x2 = 100.00 = 100.00.
 
Here,  F1 = 1655 = k1*x1 = (25.0)*(66.21) = (str1)^2*x1 = (5.0)^2*(66.21)
equals F2 = 1656 = k2*x2 = (49.0)*(33.79) = (str2)^2*x2 = (7.0)^2*(33.79).
Also,  x1 = 66.21, x2 = 33.79, and x1+x2 = 100.00 = 100.00.
 
Here,  F1 = 385 = k1*x1 = (100.0)*(3.85) = (str1)^2*x1 = (10.0)^2*(3.85)
equals F2 = 385 = k2*x2 = (4.0)*(96.15) = (str2)^2*x2 = (2.0)^2*(96.15).
Also,  x1 = 3.85, x2 = 96.15, and x1+x2 = 100.00 = 100.00.
 
Here,  F1 = 826 = k1*x1 = (100.0)*(8.26) = (str1)^2*x1 = (10.0)^2*(8.26)
equals F2 = 826 = k2*x2 = (9.0)*(91.74) = (str2)^2*x2 = (3.0)^2*(91.74).
Also,  x1 = 8.26, x2 = 91.74, and x1+x2 = 100.00 = 100.00.
 
Here,  F1 = 3289 = k1*x1 = (100.0)*(32.89) = (str1)^2*x1 = (10.0)^2*(32.89)
equals F2 = 3289 = k2*x2 = (49.0)*(67.11) = (str2)^2*x2 = (7.0)^2*(67.11).
Also,  x1 = 32.89, x2 = 67.11, and x1+x2 = 100.00 = 100.00.
 
Two bands (b1a,b1b) in one direction and one band (b2a) in the opposite direction:
 
Here,  F1 = 454 = (k1a+k1b)*x1 = (1.0+4.0)*(90.74) = [(str1a)^2+(str1b)^2]*x1 = [(1.0)^2+(2.0)^2]*(90.74)
equals F2 = 454 = k2*x2 = (49.0)*(9.26) = (str2)^2*x2 = (7.0)^2*(9.26).
Also,  x1 = x1a = 90.74 = x1b = 90.74, x2 = 9.26, and x1+x2 = 100.00 = 100.00.
 
Here,  F1 = 476 = (k1a+k1b)*x1 = (1.0+4.0)*(95.24) = [(str1a)^2+(str1b)^2]*x1 = [(1.0)^2+(2.0)^2]*(95.24)
equals F2 = 476 = k2*x2 = (100.0)*(4.76) = (str2)^2*x2 = (10.0)^2*(4.76).
Also,  x1 = x1a = 95.24 = x1b = 95.24, x2 = 4.76, and x1+x2 = 100.00 = 100.00.
 
Here,  F1 = 1699 = (k1a+k1b)*x1 = (1.0+25.0)*(65.33) = [(str1a)^2+(str1b)^2]*x1 = [(1.0)^2+(5.0)^2]*(65.33)
equals F2 = 1699 = k2*x2 = (49.0)*(34.67) = (str2)^2*x2 = (7.0)^2*(34.67).
Also,  x1 = x1a = 65.33 = x1b = 65.33, x2 = 34.67, and x1+x2 = 100.00 = 100.00.
 
Here,  F1 = 2063 = (k1a+k1b)*x1 = (1.0+25.0)*(79.36) = [(str1a)^2+(str1b)^2]*x1 = [(1.0)^2+(5.0)^2]*(79.36)
equals F2 = 2064 = k2*x2 = (100.0)*(20.64) = (str2)^2*x2 = (10.0)^2*(20.64).
Also,  x1 = x1a = 79.36 = x1b = 79.36, x2 = 20.64, and x1+x2 = 100.00 = 100.00.
 
Here,  F1 = 1027 = (k1a+k1b)*x1 = (9.0+4.0)*(79.03) = [(str1a)^2+(str1b)^2]*x1 = [(3.0)^2+(2.0)^2]*(79.03)
equals F2 = 1027 = k2*x2 = (49.0)*(20.97) = (str2)^2*x2 = (7.0)^2*(20.97).
Also,  x1 = x1a = 79.03 = x1b = 79.03, x2 = 20.97, and x1+x2 = 100.00 = 100.00.
 
Here,  F1 = 1150 = (k1a+k1b)*x1 = (9.0+4.0)*(88.50) = [(str1a)^2+(str1b)^2]*x1 = [(3.0)^2+(2.0)^2]*(88.50)
equals F2 = 1150 = k2*x2 = (100.0)*(11.50) = (str2)^2*x2 = (10.0)^2*(11.50).
Also,  x1 = x1a = 88.50 = x1b = 88.50, x2 = 11.50, and x1+x2 = 100.00 = 100.00.
 
Here,  F1 = 2007 = (k1a+k1b)*x1 = (9.0+25.0)*(59.04) = [(str1a)^2+(str1b)^2]*x1 = [(3.0)^2+(5.0)^2]*(59.04)
equals F2 = 2007 = k2*x2 = (49.0)*(40.96) = (str2)^2*x2 = (7.0)^2*(40.96).
Also,  x1 = x1a = 59.04 = x1b = 59.04, x2 = 40.96, and x1+x2 = 100.00 = 100.00.
 
Here,  F1 = 2537 = (k1a+k1b)*x1 = (9.0+25.0)*(74.63) = [(str1a)^2+(str1b)^2]*x1 = [(3.0)^2+(5.0)^2]*(74.63)
equals F2 = 2537 = k2*x2 = (100.0)*(25.37) = (str2)^2*x2 = (10.0)^2*(25.37).
Also,  x1 = x1a = 74.63 = x1b = 74.63, x2 = 25.37, and x1+x2 = 100.00 = 100.00.
 
Two bands (b1a,b1b) in one direction, and two bands (b2a,b2b) in the opposite direction:
 
Here,  F1 = 881 = (k1a+k1b)*x1 = (1.0+9.0)*(88.09) = [(str1a)^2+(str1b)^2]*x1 = [(1.0)^2+(3.0)^2]*(88.09)
equals F2 = 881 = (k2a+k2b)*x2 = (25.0+49.0)*(11.91) = [(str2a)^2+(str2b)^2]*x2 = [(5.0)^2+(7.0)^2]*(11.91).
Also,  x1 = x1a = 88.09 = x1b = 88.09, x2 = x2a = 11.91 = x2b = 11.91, and x1+x2 = 100.00 = 100.00.
 
Here,  F1 = 881 = (k1a+k1b)*x1 = (1.0+9.0)*(88.09) = [(str1a)^2+(str1b)^2]*x1 = [(1.0)^2+(3.0)^2]*(88.09)
equals F2 = 881 = (k2a+k2b)*x2 = (25.0+49.0)*(11.91) = [(str2a)^2+(str2b)^2]*x2 = [(5.0)^2+(7.0)^2]*(11.91).
Also,  x1 = x1a = 88.09 = x1b = 88.09, x2 = x2a = 11.91 = x2b = 11.91, and x1+x2 = 100.00 = 100.00.
 
Here,  F1 = 919 = (k1a+k1b)*x1 = (1.0+9.0)*(91.87) = [(str1a)^2+(str1b)^2]*x1 = [(1.0)^2+(3.0)^2]*(91.87)
equals F2 = 919 = (k2a+k2b)*x2 = (64.0+49.0)*(8.13) = [(str2a)^2+(str2b)^2]*x2 = [(8.0)^2+(7.0)^2]*(8.13).
Also,  x1 = x1a = 91.87 = x1b = 91.87, x2 = x2a = 8.13 = x2b = 8.13, and x1+x2 = 100.00 = 100.00.
 
Here,  F1 = 919 = (k1a+k1b)*x1 = (1.0+9.0)*(91.87) = [(str1a)^2+(str1b)^2]*x1 = [(1.0)^2+(3.0)^2]*(91.87)
equals F2 = 919 = (k2a+k2b)*x2 = (64.0+49.0)*(8.13) = [(str2a)^2+(str2b)^2]*x2 = [(8.0)^2+(7.0)^2]*(8.13).
Also,  x1 = x1a = 91.87 = x1b = 91.87, x2 = x2a = 8.13 = x2b = 8.13, and x1+x2 = 100.00 = 100.00.
 
Here,  F1 = 3890 = (k1a+k1b)*x1 = (1.0+81.0)*(47.43) = [(str1a)^2+(str1b)^2]*x1 = [(1.0)^2+(9.0)^2]*(47.43)
equals F2 = 3890 = (k2a+k2b)*x2 = (25.0+49.0)*(52.57) = [(str2a)^2+(str2b)^2]*x2 = [(5.0)^2+(7.0)^2]*(52.57).
Also,  x1 = x1a = 47.43 = x1b = 47.43, x2 = x2a = 52.57 = x2b = 52.57, and x1+x2 = 100.00 = 100.00.
 
Here,  F1 = 3890 = (k1a+k1b)*x1 = (1.0+81.0)*(47.43) = [(str1a)^2+(str1b)^2]*x1 = [(1.0)^2+(9.0)^2]*(47.43)
equals F2 = 3890 = (k2a+k2b)*x2 = (25.0+49.0)*(52.57) = [(str2a)^2+(str2b)^2]*x2 = [(5.0)^2+(7.0)^2]*(52.57).
Also,  x1 = x1a = 47.43 = x1b = 47.43, x2 = x2a = 52.57 = x2b = 52.57, and x1+x2 = 100.00 = 100.00.
 
Here,  F1 = 4752 = (k1a+k1b)*x1 = (1.0+81.0)*(57.95) = [(str1a)^2+(str1b)^2]*x1 = [(1.0)^2+(9.0)^2]*(57.95)
equals F2 = 4752 = (k2a+k2b)*x2 = (64.0+49.0)*(42.05) = [(str2a)^2+(str2b)^2]*x2 = [(8.0)^2+(7.0)^2]*(42.05).
Also,  x1 = x1a = 57.95 = x1b = 57.95, x2 = x2a = 42.05 = x2b = 42.05, and x1+x2 = 100.00 = 100.00.
 
Here,  F1 = 4752 = (k1a+k1b)*x1 = (1.0+81.0)*(57.95) = [(str1a)^2+(str1b)^2]*x1 = [(1.0)^2+(9.0)^2]*(57.95)
equals F2 = 4752 = (k2a+k2b)*x2 = (64.0+49.0)*(42.05) = [(str2a)^2+(str2b)^2]*x2 = [(8.0)^2+(7.0)^2]*(42.05).
Also,  x1 = x1a = 57.95 = x1b = 57.95, x2 = x2a = 42.05 = x2b = 42.05, and x1+x2 = 100.00 = 100.00.
 
Here,  F1 = 4408 = (k1a+k1b)*x1 = (100.0+9.0)*(40.44) = [(str1a)^2+(str1b)^2]*x1 = [(10.0)^2+(3.0)^2]*(40.44)
equals F2 = 4408 = (k2a+k2b)*x2 = (25.0+49.0)*(59.56) = [(str2a)^2+(str2b)^2]*x2 = [(5.0)^2+(7.0)^2]*(59.56).
Also,  x1 = x1a = 40.44 = x1b = 40.44, x2 = x2a = 59.56 = x2b = 59.56, and x1+x2 = 100.00 = 100.00.
 
Here,  F1 = 4408 = (k1a+k1b)*x1 = (100.0+9.0)*(40.44) = [(str1a)^2+(str1b)^2]*x1 = [(10.0)^2+(3.0)^2]*(40.44)
equals F2 = 4408 = (k2a+k2b)*x2 = (25.0+49.0)*(59.56) = [(str2a)^2+(str2b)^2]*x2 = [(5.0)^2+(7.0)^2]*(59.56).
Also,  x1 = x1a = 40.44 = x1b = 40.44, x2 = x2a = 59.56 = x2b = 59.56, and x1+x2 = 100.00 = 100.00.
 
Here,  F1 = 5548 = (k1a+k1b)*x1 = (100.0+9.0)*(50.90) = [(str1a)^2+(str1b)^2]*x1 = [(10.0)^2+(3.0)^2]*(50.90)
equals F2 = 5548 = (k2a+k2b)*x2 = (64.0+49.0)*(49.10) = [(str2a)^2+(str2b)^2]*x2 = [(8.0)^2+(7.0)^2]*(49.10).
Also,  x1 = x1a = 50.90 = x1b = 50.90, x2 = x2a = 49.10 = x2b = 49.10, and x1+x2 = 100.00 = 100.00.
 
Here,  F1 = 5548 = (k1a+k1b)*x1 = (100.0+9.0)*(50.90) = [(str1a)^2+(str1b)^2]*x1 = [(10.0)^2+(3.0)^2]*(50.90)
equals F2 = 5548 = (k2a+k2b)*x2 = (64.0+49.0)*(49.10) = [(str2a)^2+(str2b)^2]*x2 = [(8.0)^2+(7.0)^2]*(49.10).
Also,  x1 = x1a = 50.90 = x1b = 50.90, x2 = x2a = 49.10 = x2b = 49.10, and x1+x2 = 100.00 = 100.00.
 
Here,  F1 = 5253 = (k1a+k1b)*x1 = (100.0+81.0)*(29.02) = [(str1a)^2+(str1b)^2]*x1 = [(10.0)^2+(9.0)^2]*(29.02)
equals F2 = 5253 = (k2a+k2b)*x2 = (25.0+49.0)*(70.98) = [(str2a)^2+(str2b)^2]*x2 = [(5.0)^2+(7.0)^2]*(70.98).
Also,  x1 = x1a = 29.02 = x1b = 29.02, x2 = x2a = 70.98 = x2b = 70.98, and x1+x2 = 100.00 = 100.00.
 
Here,  F1 = 5253 = (k1a+k1b)*x1 = (100.0+81.0)*(29.02) = [(str1a)^2+(str1b)^2]*x1 = [(10.0)^2+(9.0)^2]*(29.02)
equals F2 = 5253 = (k2a+k2b)*x2 = (25.0+49.0)*(70.98) = [(str2a)^2+(str2b)^2]*x2 = [(5.0)^2+(7.0)^2]*(70.98).
Also,  x1 = x1a = 29.02 = x1b = 29.02, x2 = x2a = 70.98 = x2b = 70.98, and x1+x2 = 100.00 = 100.00.
 
Here,  F1 = 6957 = (k1a+k1b)*x1 = (100.0+81.0)*(38.43) = [(str1a)^2+(str1b)^2]*x1 = [(10.0)^2+(9.0)^2]*(38.43)
equals F2 = 6957 = (k2a+k2b)*x2 = (64.0+49.0)*(61.57) = [(str2a)^2+(str2b)^2]*x2 = [(8.0)^2+(7.0)^2]*(61.57).
Also,  x1 = x1a = 38.43 = x1b = 38.43, x2 = x2a = 61.57 = x2b = 61.57, and x1+x2 = 100.00 = 100.00.
 
Here,  F1 = 6957 = (k1a+k1b)*x1 = (100.0+81.0)*(38.43) = [(str1a)^2+(str1b)^2]*x1 = [(10.0)^2+(9.0)^2]*(38.43)
equals F2 = 6957 = (k2a+k2b)*x2 = (64.0+49.0)*(61.57) = [(str2a)^2+(str2b)^2]*x2 = [(8.0)^2+(7.0)^2]*(61.57).
Also,  x1 = x1a = 38.43 = x1b = 38.43, x2 = x2a = 61.57 = x2b = 61.57, and x1+x2 = 100.00 = 100.00.
 
All Done Now.