Nutation frequency for a weighted gyroscope

Question

So, I've been led to believe that the frequency of nutation of a gyroscope can be calculated using the formula

In which the I's are the moments of inertia around the principal axes and omega-3 is the angular velocity of the disk of the gyroscope. But the moments of inertia around the principal axes of a cilinder are

and working this out for a gyroscope with a disc of 1.5 kg, a radius of 11.5 cm and a height of 2,5 cm I get:

(There was a math error here, it's gone now) Which would mean the frequency of nutation is 2 times higher than the angular velocity, which does not match observation. What am I doing wrong? Thank you in advance.

The gyroscope used.

Cleonis · Answer

I can confirm that the nutation frequency is proportional to the angular velocity of the spinning gyroscope.

Article:
precession and nutation of a gyroscope, by Eugene Butikov
In the above article it is discussed that the nutation frequency is the same frequency as the frequency of torque-free precession because it is in fact the torque-free precession. (The torque-free precession of the entire precessing assembly.)

Also:
Documentation for an educational set containing a gimbal mounted gyroscope and weights that can be added to the gimbal mounting, altering a specific moment of inertia, thus altering the nutation frequency:
Laws of gyroscopes

My understanding is that if the gyroscope wheel is mounted on a long axis that axis has a significant effect on the nutation frequency.

Nutation frequency for a weighted gyroscope

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