tone arm with 10gr mass with 15 gram weight cartridge?

μm/mN=...X10-6cm/dyn=cu

effective mass of tonearm, cartridge mass and cartridge compliance, should produce the desired resonance frequency.

and at the end of the day if sound quality is good (most important) then you forgett all the formulas.

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!

http://www.mh-audio.nl/Calculators/RF.html

Just do it.

Keep in mind that any published figure for tonearm effective mass must be accompanied by some other information, if we are to make sense of it. We need to know whether the published figure includes a "typical" cartridge and the mass of the OEM headshell. As soon as you use a different aftermarket headshell, the EM would be altered. If your cartridge is unusually heavy or light, that too might change the result. Every single cartridge is not going to have a compliance exactly as stated by the maker of that particular cartridge; there can be significant sample to sample variation. Finally, the counter-weight has a variable effect on EM; the CW adds to EM in relation to its weight times the square of the distance between its center of mass and the pivot.  So to minimize EM, you want the heaviest CW that works to counterbalance, so it can be as close as possible to the pivot.  As someone else pointed out, the actual leeway for arriving at a calculated resonant frequency that falls within the acceptable range of 7 to 12Hz is quite wide, referring to the (probably inaccurate) numbers that you finally decide to plug in to the equation. Which is why I say, "Just do it". Unless there is a huge and obvious disconnect between compliance and EM, you’ll be OK.

so for the actual mass of my arm to do all those calculationsת i need to add to the official spec of the manufacturer the weight of the screws and the lifter.
the headshell in my case ( well tempered) is part of the arm so i assume i was already taken into account.
i admit that i'll need to read yours explanation several times to completely understand it 😃
right now i am thinking about 3 carts, neither is Japanese.
Van den Hul DDT-II Special Moving Coil 
 Benz Micro Wood SL
E.A.T. JO N°5 CARTRIDGE.
the last one weight 15 g, while the first two are lighter, VDH 8.2 g, and benz micro *9 g.
so that was my major reason for asking that question .
also the EAT has COMPLIANCE, DYNAMIC/LATERAL           12 μm/mN
wile the VDH states- 

Compliance  15 without specifying which kind of value is it
so i'm confused with all that different values. 

I've used carts with 12-16g mass (16+ grams for Benz LPS) on my 9.5g EM Clearaudio tracer arm.  I just had to use the additional counterweight.  It sounded great, tracked well, and the resonance frequency as measured by the HiFi News test record was a hair over 7hz.  A bit low but turned out fine.