The European distributor of Nagaoka, Tonar International bv, lists dynamic compliance of 8.5 x 10-6cm/dyne (aka 'cu' or 'compliance units' where 1cu = 1 millionth of a centimetre) for MP-500. If we are to assume that the reference frequency is the typical for Japan 100Hz then we double the stated compliance value for a 10Hz reference.
Therefore, consider the formula for calculating the resonant frequency (Fr) of an arm/cartridge combo:
Fr = 1000/(2π x sqrt(M x C))
Where:
Fr = resonant frequency (in Hz)
M = sum of all mass (tonearm effective mass (including headshell), cartridge weight, plus mounting hardware in g)
C = compliance (at 10Hz)
Example:
Tony's SME with an effective mass of 12.5g and his MP-500 cartridge weighting 8g, with a stated compliance of 8.5 x 10-6cm/dyne (presumably at 100Hz, therefore transformed from 100Hz to 10Hz by doubling the value of 8.5 to 17):
Sum the different masses: 12.5g (tonearm) + 8g (cartridge) + 2.5g (mounting hardware) = 23g.
Then we multiply mass x compliance (the latter @ 10Hz) 23 x 17 = 391.
sqrt of 391 = 19.77
2π x 19.77 = 6.28 x 19.77 = 124.22
1000/124.22 = 8.05Hz, fitting within the desirable 7 - 12Hz range.
Craig