In your calculations, be sure the bore diameter, the barrel's profile and section taper lengths and diameters are correct. Use fixed breech end formulas as barrels alone in space have different resonant frequencies than those screwed into receivers solidly affixed to the stock.
The high frequency made by sound waves bouncing back and forth (traveling about 16,000 fps in type 316 stainless steel) are not what barrels whip like fishing rods do when casting lures. Rods and barrels fixed at one end whip at very low frequencies typically under 100 Hz. Example below:
http://www.varmintal.com/amode.htm
There's other examples on his web site.
I'll use the software I asked Tom Irvine's company to make (rifle frequency) below:
http://www.vibrationdata.com/updates.htm.
to calculate a 24" long barrel weight and resonant frequency for a barrel dimensioned as follows:
1.2" dia. x 2" long reinforce (1" long tenon in receiver not used)
1.2" dia. x 2" long x .9" dia. taper
.9" dia. x 19" long x .6 " dia. main taper
.306" bore dia. (.0736 square inch area typical for 30 caliber)
316 stainless steel
Breech fixed
Chamber volume not used. If used, resonant frequency will be a little less. We can compare results. They should be very close, if not the same. Note that the mass of the stock and scope attached to the barrels breech end will alter frequency calculations because they're part of the whole rifle that wiggles when fired. It's best to assume a solid mounted receiver to see what the barrel alone vibrates at when fixed at its breech.
First study on a barrels low frequency vibrations in the vertical plane was made over a century ago. Enjoy the math but the last page is the overall conclusions:
https://archive.org/details/philtrans05900167
99% of all the rifle barrel vibration stuff on the internet is bogus babbling developed to satisfy an incorrect assumption. It's well understood that slower bullets have to be launched at a higher angle than faster ones to strike the same place on target. The only part of the vertical muzzle axis swing that does that is the upswing. It's impossible if bullets leave at the extremes where the axis reverses as half would leave on the upswing and half on the downswing due to normal spreads in barrel time and muzzle velocities.
Fluted barrel stiffness blasphemy is common, too.