Natural frequency of hydraulic axis

Hello sir,
I am Dinesh from Servocontrols.

Recently, I came across one natural frequency formula from rexroth trainers guide

Approach with Rexroth Trainers guide

Which differs slightly from the formula that Peter has mentioned in many hydraulic articles.

Approach with Delta

I just want to know, why is that difference?

It is a bit difficult to tell what the Rexroth formula is exactly without seeing their definitions. I believe the two formulas are the same, just with the Rexroth version using some slightly different terminology.

They use Eoil which I presume is a measure of the stored energy in the oil, and then substitute H/2 x AR to denote the volume. I take this to mean some kind of rod area by perhaps a height? It is not clear from context. In any case, it appears to arrive at the same expression, just with slightly different symbols for the various terms.

I recommend this thread, Computing the Natural Frequency of the Cylinder and Load, to see a worked out example.