With great pleasure I just re-read the contribution of Nigel Cooper,"Radial Variation in the Vibrations of the Cochlear Partition" in the Proceedings of the International Symposium on Recent Developments in Auditory Mechanics", H. Wada et al., Eds., World Scientific, 2000, pp. 109-115. I tried to derive myself the formula y = 323*(x^2/16 - ...) in Figure 4. I agree with the _expression_ in brackets, but suspect that the number 323 should be replaced by 320. That yields an area of 1.0 between the beam center-line and the x-axis, and so a mean displacement of 1.0.
(Yesterday I tried to contact Nigel privately, without success).
With best wishes,