[this was actually an interview question for me at blue or!g!n]
Rather than just applying formulas blindly, here is a different approach:
BASIC CONCEPT:
A fin has several different vibration modes. The ones to worry about are the first bending mode and the torsional mode. In a way, you can think of the fin as a resonator which wants to vibrate at certain frequencies in certain ways. The way that it actually bends in real life is a combination of all of the modes that are excited.
SOOO, imagine that the fin were a tuning fork. You could hit it (impulse) and it will resonant to its natural frequency. You could also just go over to it and sing the same note and the fork would begin to resonate if you were matched up with its tone well enough. Another way to make it resonant is to bombard it with white noise, which excites ALL frequencies. However, since it only wants to resonate it its primary modes, it just makes the tone it was designed to make.
A fin is like the tuning fork, though it has several difference frequencies it wants to resonate at. The different frequencies are associated with different mode shapes... bending, torsion, etc.
The crazy thing is that WIND IS LIKE WHITE NOISE. So as wind rushes by a fin it excites all frequencies but the only ones that build up are the primary modes... and that is what normal fin flutter is.
Now, this is all with the assumption you don't have blunt trailing edges, which create unsteady shedding vortex motion that can be very bad if it crosses over a fin mode (The shedding vortex frequency changes with airspeed so even if your fin starts to resonate with it for a split second the results can be disastrous.)
So how does an engineer calculate the resonant modes? For the first mode (bending) you basically pretend that the fin is a cantilever beam and for the cross section, shape, and modulus calculate the effective spring constant k. You can also calculate an effective fin inertial mass m. Then the calculation for the natural frequency is
f=2*pi *sqrt(k/m)
The torsional mode is a little more difficult since you need to calculate the effective torsional stiffness and effective torsional inertial mass. The frequency calculation is the same, however. Unless you've taken a continuum mechanics class, this calculation is above most hobbyists.
If you have access to Anysis, Solidworks FEA, or Abaqus or any other linear FEA software you could just plug in the shape (in modal analysis mode), add some material properties, fix the one side, and out would spit all the frequency modes. You probably wouldn't care about anything less than, say, 100Hz or so though. (the amplitudes get very small the higher up you go since the damping remains constant and the mechanical energy dissipates quicker)
So there you go. I just saved you $200,000 in education expenses. jk jk.
