I have said several times that my main complain is that MgR/I is the frequency of a single freely swinging pendulum and nothing, I repeat nothing, more. Now you tell me "you see it is a pendulum"!!!!!! Yes, it is the frequency of a pendulum, if you hold the racquet at the but end between your thumb and forefinger MgR/I=21 means that it will swing with 0.73 Hz. But only if the swings are small and you don't move your hand.
I repeatedly ask for some kind proof that you can apply this formula everywhere like you do, and you reply by telling me to take the physics 101! After a number of years of research and teaching at the post doc level, including helping several student to their PhD:s in mechanical engineering, I think I know my physics 101.
You have obviously seen Rod Cross writings about the double pendulum (I recognize some of the statements, even if you write as if they were your own findings). You probaly saw the word "pendulum" and then you found a formula somewhere on the net that also said "pendulum" and used that without understanding what you did.
Rod Cross model includes some radical simplifications, like one that you don't use your wrist, and should be used carefully. But since you re so attached to it lets assume that it is a perfect description. Then behavior of the racquet involves solving eq A10a and A10b in A double pendulum model of tennis strokes
. And I can assure you that the result won't be MgR/I.
As to your hilarious statement that you need to take the variation in gravity into account. The air resistance of the racquet has a much greater influence than the gravity, shouldn't you include the air pressure and temperature as well?
There are a lot of helpful people at this forum and if you had chosen so you could have received help from them (me included) and maybe made this into something useful where you know how and when to apply it. Instead you have the attitude that you know it all and can apply it everywhere, even when it obvious that you don't have a clue what you are talking about. Pity.
Since you not are interested in any feedback except praise of your great finding I won't bother you with comments any more.
Ph.D. (Aerospace Eng.), M.Sc. (Eng. Physics)