^^^ Any way to get to it by using size / weight / etc.?
One way is to perform what's called a Modal analysis using Finite Element Analysis. Chances are you don't have $20k to buy the software and $6k for a good enough computer.
I suggest you google "Model analysis" and see if there are any published solutions for the more "canned" simple shapes. There may be closed solutions for shapes such as cylinders, square plates, etc.
If the object is a simple shape, you can do that calculation by hand.
Example or link to information on how to do this please?
Robert D. Blevins. Formulas for Natural Frequency and Mode Shape, Krieger Pub Co (January 1, 2001).
You could post a drawing of the object.
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