So you have to make a recording with a line in. A microphone won't work. Some modern higher end laptops have a 3,5mm jack that can sense what kind of 3,5mm plug is inserted and when it's a stereo plug it asks if it's a headphone or line in. Most other laptops have a combo jack but that is purely suited for a headset. So a microphone plus headphones, no line in.
But if you manage to get a recording by line in, this is what you have to do:
So this is a screenshot in my mothers tongue, but I guess you'll understand. You make the recording (the wave pattern you see). make it at least 1 minute, and select the track (ctrl+a). Some versions have a select limit of little over 2min, so any recording under 2min is ideal.
Then go to analyze->display spectrum.
Then you get this:
Set the sample size to 65536 (bottom arrow; higher numbers gives too much information)
put your cursor on the highest peak in the low frequencies (red arrow), so there will be a distinct peak, around 4-12Hz.
The peak will give the frequency in the bottom (other red arrow). This is a rounded value, in the graph you can see that the actual peak is somewhere between 8 and 9Hz (the red line), but who's counting.
Regarding your effective mass, I estimate that the effective mass of that arm including that headshell will be between 16 and 24gram.
If your headshell is already 21.15-5.8=15,35gram (that's including wires and mounting hardware (0,5gr), then chances are the complete arm is 20gr or more.
Not all the headshell weight is directly transferrable to the same effective mass, as half of it sits a little bit closer to the fulcrum point, but you might loose 1 or 2 grams because of that.
If you can weigh your counterweigth and measure it's distance to the fulcrum point (ideally: the distance between fulcrum point and 2/3 of the depth of the counterweigth), then I can make a fairly exact calculation of the effective mass.
Because the counterweight is moved forewards or more to the back depending on if you mount a heavier or lighter cartridge, the effective mass also changes slightly with that. But I expect your future cartridge will be in the ballpark of that 5,8 grams.
But for a arm like that I would recommend a medium to low compliance cartridge. Or a cartridge with a damping brush