If you are using a Japanese cartridge you will have to double the value from 100hz to 10 hz!
For example: Say we have an arm of with a published Effective mass of 12 grams and a Japanese cartridge weight of 10 grams, with a compliance of 5cu/dyne/100 Hz. Effective Mass of the arm is another topic in its own right and often not published by the arm manufacturer or not published accurately. But for our example we are using a trusted arm manufacturer with good engineering design. We want to know the RF of the tonearm/cartridge combo. The first thing we have to do is to transform the compliance from 100 Hz to 10 Hz by doubling the value of 5, which will become 10. Next we will add up the different masses: 10 g (stylus) + 12 g (arm) +1 g (screws) + other things (like finger lift, in this case let us say they are zero) = total 23 g. Then we multiply 10 x 23 = 230 The square root of 230 is around 15.17. Finally: 159 ÷ 15.17 = 10.48 Hz, a value that places itself in the desired interval of 8 -12 Hz. Another quick way to check compatibility is to plot the predicted resonance using the graph below. Add the weight of cartridge and screws to the Effective Mass of the Arm (manufacturer should publish this). Look across to the Dynamic Compliance (manufacturer should publish this) and hopefully it falls somewhere in the 8-12hz zone.
Here is a calculation chart!