There will be several natural frequencies corresponding to the many different vibration patterns possible.
If you can associate a stiffness with the mass, then w=sqrt(k/m).
If the deflection caused by gravity is representative of the vibration, then measure the static deflection and natural frequency can be calculated from that.
Most times a "bump test" is used to determine the natural frequency of something. You whack it with a hammer and measure the frequency of the response.
Also lots of computational techniques are available which would require a lot more info from you.
Pete is correct, but you can do a little more calculation. The stiffness of the individual components of the the table can be calculated with beam equations. For instance the stiffness of the table top could be describe as a beam between two support so K= 48EI/L^3. You would then need to do the same kind of calculation for each leg, and add up the stiffnesses, remembering that springs in parallel add directly while springs in series add such that 1/Ktot= 1/K1 +1/K2+1/K3.....+1/Kn. You would have to start by deciding which natural frequency to calculate as there is most likely a different one for each direction X,Y,and Z.
If you look in a mechanical engineering design book, you should be able to find a table of beam equations for the restraints in your situation and come up with a stiffness of the table. Figureing out how much of the tables mass is really contributing modally to a given natural frequency is another question.
I would be really interested to know why you are doing this.
Let me know if you want more help.
SMS,
Thanks for the help. This table is to support several flexures that have an optics table on top. Acutuators attached to the table will provide tilt in the x and y directions. We just want to make sure that the frequency is higher than the one that we will be opporating with, something like 8 hz.
You should also take into account that the table will probably by sitting on a floor which will itself be flexible (unless your table is sitting on a seismic block)
Well, that tells me a bit more. w=(1/2pi)*sqrt(K/M),and w= 8HZ as a minimum, so K/M=Kg/W has to be more than 25,627. If we assume that say 60% of the table weight is in the top, and use that as the modal weight, then the modal Weight is 0.6*600 or 360lbs. Solve for K= 25,627*W/g and you get a minimum required stiffness of 23,890 lb/in. So if you go back to those beam equations I told you about and calculate a stiffness that is at least 15% greater than 23,890 you should be all right.
The only problem is you did not tell me how heavy the optics gismo on the table is, so I have not accounted for the modal weight contribution of the gizmo. If it is heavy that contribution might be significant.
