FREQUENCY MATCHING - THE WHOLE STORY
BY ERIC H. COOK P.Eng.

INTRODUCTION:
Over the past twenty years "FREQUENCY" has probably become the most used buzzword to hit the golf industrysince the game was invented. Unfortunately it is also one of the most misunderstood words that we use when we talk about golf clubs or golf club shafts. Today I will present a technical definition of frequency, an understanding of what frequency is, what it is not and how it relates to custom club fitting. I will describe the three frequency matching systems presently in use and the relative merits of each system. Finally I will relate frequency to shaft characteristics and discuss how the various systems go about determining the proper frequency for the golfer.

FREQUENCY DEFINED:
Webster's dictionary defines Frequency as; "the number of times any action or occurrence is repeated in a given period". and "in physics,..the number of vibrations or cycles per unit of time". From the second definition we can show that, simply stated, "Frequency is a dynamic (in motion) measurement of shaft flex or stiffness stated in terms of cycles per minute (cpm) of vibration, when the shaft is held firmly in a clamp and the shaft is plucked". The HIGHER the FREQUENCY the STIFFER the SHAFT.


FREQUENCY MATCHED:
The introduction of frequency to the golfing world inevitably brought us the term "Frequency Matched" which has added more confusion. Webster's dictionary defines "Matched" as "...to be equal, similar, suitable, or corresponding to in some way;..". This definition leaves us with a number of possibilities; therefore, Frequency Matched could mean either all the same or all different and as you will see as we proceed, both definitions are used. Think about it and decide for yourself if both definitions can be correct when referring to golf clubs used by any one individual.

The concept of frequency matching is not new but until the introduction of the parallel tip or unitized golf shaft, frequency matching was not a practicable consideration since tapered tip shafts could not be tip trimmed and easily installed in the hosel of the club head.

The book "The Search for the Perfect Swing", published in 1968, suggested that frequency matching could be a better method of matching clubs since this would combine weight, length and stiffness; however, there was no indication as to how this could be done.

It will be both interesting and useful at this point to look briefly at the evolution of golf club matching systems which brought us to the present day.

One of the first patents, related to golf clubs, was issued in the United States to Irving R. Prentiss in 1925. Mr Prentiss matched clubs so that the product of the length and weight was a constant. Note the following quotation from the patent, "It will nearly always be found that a player will have one club in his set of which he is particularly fond and in which he reposes the greatest confidence for the reason that he can consistently play that club successfully". Using this favourite club as a base, Irving goes on to explain the system as a method of matching clubs by dead weight and graduated point of balance. Although this was an improvement at the time, and does not relate to frequency matching, it is interesting to note that all these years later most golfers still have that one favourite club in their set. Nothing much has changed in the last seventy years and very few people have thought about Why that one club is their favourite.

In 1944 Mr. M. Knobel received a patent for a method and apparatus for testing the period of oscillation and, thereby, the moment of inertia of a golf club. Although not related to frequency, the invention purports to provide what is referred to as a measure of feel. Would you not think that the favourite club concept also has something to do with feel?

Mr. T.O. Brandon patented a system in 1958 which relates to correlated and co-ordinated shafts for matched sets of clubs. His invention was based on the premise that the length of a golf club shaft is directly related to the stiffness, weight and shaft characteristics. While this concept was indeed
true, the matching process did not produce frequency matched clubs because the head weight was not considered in the formula. Furthermore, as you will see, matching the shafts by themselves is merely the first step towards achieving frequency matching.

The first indication of a method of frequency matching is described in a patent issued to Malcolm L. Murdock in 1968. This system measures the frequency of a shaft with various head weights attached. Each measured frequency is plotted on a graph opposite to the head weight used. The invention states, "To match a set of clubs it is necessary only to ensure that for a given shaft length of any individual club, a weight of club head is selected such as will give the requisite frequency of vibration to the shaft". While the theory sounds good, the resulting clubs are still mismatched because they would have different Moments of Inertia due to the inconsistency of the headweights required to obtain the frequency.

In a 1975 patent, John Arthur Kilshaw provided a method of matching clubs by both moment of inertia and frequency. The matching was to be done using a mathematical formula and a graph. Once again the theory sounds good but because of shaft inconsistency the results would be largely a matter of luck. In fact the patent content states that actual testing of the frequency of clubs made using the formula showed an accuracy of plus or minus five percent. This means that a calculated 300 cpm shaft could actually be anywhere between 285 cpm and 315 cpm which is far outside a useable tolerance.

In 1978 a United States patent issued to Joseph N. Braly covered a system that matches clubs in accordance with a "...predetermined frequency gradient formed by a plot of shaft frequency and shaft length such that the gradient is a substantially straight line that increases as shaft length decreases and the frequency increments between successive shaft lengths along the gradient are substantially equal...". This approach to frequency matching is in keeping with the traditional manufacturing methods which produce clubs that get progressively stiffer as they get shorter. You may recognize this system as the FM Precision Shaft now produced by Brunswick Golf or the True Temper Dynamic Gold shafts which follow much the same system but use a different identification code.

Finally, the most recent entry into the frequency matching arena is the Swing-Sync Single Frequency System introduced in 1982. This system purports to be a method of frequency matching a set of golf clubs to match the golfer's swing and is covered by a Canadian patent issued in 1986.

We will look at these three systems in more detail, but first I would like to discuss the Theory of Frequency Matching so that you can understand each system, and be able to discuss the relative merits of each based on scientific fact.

THE THEORY OF FREQUENCY MATCHING:
The Professional golfer, Custom Clubmaker or other golf equipment specialist is often called upon to make recommendations to golfers concerning the selection of golf clubs. Aside from the aesthetic qualities of a set of clubs, which is in the eye of the beholder, the objective in recommending a particular type of club to a golfer should be to match the golf club by Total Weight, Head Weight, Length, Grip Size, Lie and Shaft Flex to both the golfer's strength and swing tempo, while maintaining the same feel throughout the set of clubs.

It is a well established fact that during the backswing and the start of the downswing, the weight and motion of the clubhead causes the shaft to bend, thus storing energy in the shaft. If the golfer is to hit a good shot two things must happen during the downswing. The clubhead must return square to the intended line of flight, at separation, if the ball is to be hit at the target, and the stored energy must be transferred to the ball if the golfer is to attain maximum distance from the club being used. Ideally, to achieve these two conditions the shaft should be perfectly straight when the ball leaves the face of the club. To fully understand the significance of the last two statements let's consider the affect of shaft flex on directional control and energy transfer separately, beginning with the transfer of energy.

To quote from the Search for the Perfect Swing, "... One definite finding was that different degrees of whippiness do not very much affect the distance the ball can be sent with any club. In a test using three drivers with different degrees of whip (X,R and L Shafts), golfers of all abilities hit their best drives with each club almost exactly the same distance. This confirms theoretical predictions that variations in shaft flexibility can make only about five yards difference to the best possible drive any golfer can hit. Even this is probably an overestimate, because it assumes that the clubhead is `springing forward' on the shaft as it strikes the ball. In fact there is ample photographic evidence to suggest that for good players and bad, for whippy shafts and stiff shafts - the clubhead has already sprung forward to the limit of its travel by the time it strikes the ball.... In that case clubhead speed at impact would not depend on the type of shaft at all, and the distance obtained would not vary." Remember that this quotation comes from research conducted with unmatched golf clubs and I will show you later that clubhead speed does in fact depend on shaft frequency; however, for the purpose of this discussion the above quotation is fairly accurate if we are considering only the distance that the ball is hit

Now consider the affect of shaft flexibility on directional control. It is well established that the wrong shaft can lead to a 20 to 30 yard variation in the line of a drive. Most amateur golfers will normally hook the ball with a shaft that is too flexible and slice or push the ball with a shaft that is too stiff but this result depends on their swing plane. Obviously you are looking for the shaft that hits the ball straight and lets you control ball flight when you want to do something else. Unless the shaft frequency matches the golfer's swing, directional problems will almost certainly result; therefore, it is important that you understand the relationship between shaft frequency and clubface position in the hitting area.

This relationship can best be illustrated by comparing the head of the club to a weight on the end of a string that you are swinging around in a circle. If you stop swinging the string, the weight will continue around the circle and pass your hand. Similarly, in the golf swing, the clubhead, on the end of the shaft, is trailing the hands until the hands slow down. At this time the clubhead begins to overtake the hands. The lower the frequency (more flexible the shaft) the farther the head goes by the hands, normally causing a closed clubface if the shaft is too soft for the person using it. If the shaft is too stiff, the head does not go as far past the hands and is usually in an open position when it reaches the hitting area.

In summary, the theory of frequency matching suggests that the correct frequency in a golf club is essential to the proper functioning of the club as it relates to the golfer's swing. With that statement in mind lets look, in more detail, at the three frequency matching systems introduced earlier.

THE FM PRECISION SHAFT SYSTEM:
The FM Precision Shaft System was introduced by Dr. Joe Braly in the mid seventies and was the first frequency matching system recognised by the golf industry. He put a repair van on the PGA Tour circuit and by 1978, reportedly, had about 150 Tour players using FM Precision Shafts.

In his patent application Braly says that when he checked the frequency of standard manufactured clubs he found that the frequency varied from one club to another in no consistent way. He then says that when he tested the clubs used by the old masters of the game, like Byron Nelson and Harry Vardon, he found that their clubs varied in frequency by a consistent increment.

This gives a straight line gradient match, wherein each club in the set is incrementally stiffer than the next longer club. See Figure 1. below. This incremental difference appears to be a fairly constant value of about 5 cpm.

In order to pick the FM Precision Shaft that fits you, you are given a group of #5 Irons, coded from 4.5 to 7.5, from which you select the one that you hit the best.
(Figure FM1). From this selection (say 5.5) a set of clubs is assembled which follow the 5.5 gradient line. Using this gradient line the #1 Iron would be 272 cpm and the PW would be 330 cpm, a difference of 58 cpm. Similarly, the Driver would be 240 cpm at 43 inches and the 5 Wood at 41 inches would be 268 cpm, a difference of 28 cpm.

Obviously, each club in the set has a different frequency and therefore a different stiffness of shaft; however, according to Dr. Braly this difference is required in order to match the release point of the club. I was not aware that the golf club released, I have always thought that the golfer did that. I should also point out that the FM System talks about Frequency Matched Shafts not Frequency Matched Golf Clubs.

THE TRUE TEMPER DYNAMIC GOLD SYSTEM:
The True Temper Dynamic Gold System follows the same general theory used by Braly, except that the gradient lines change slope with each different stiffness classification as shown in Figure TT 1. The True Temper system uses a unique identification code such as R100 or S500 etc. Figure TT1, shows the gradient slopes for the R100, S100 and X100 shafts. You can see that the gradient slope increases as the flex category gets stiffer. This suggests that as the shafts get stiffer the incremental difference between clubs should increase. WHY?
True Temper provides five stiffnesses within each designated flex category, with 300 being the center of the available weight distribution. 100 is the most flexible and 500 is the stiffest. This information came from a booklet published by True Temper Sports entitled Frequency Matching wherein FREQUENCY MATCHING is defined as "...a technique used for `fine tuning' the stiffness of golf clubs within a set. The term `frequency matched' is used because measuring the frequency of a golf club is a precise way of determining stiffness. In a frequency matched set of clubs, the frequency or stiffness difference between successive clubs is equal. It does not mean that each club in the set is the same stiffness or frequency. Golf clubs traditionally get stiffer (have a higher frequency) as they become shorter;..". It is interesting to note that this definition was published shortly after the Swing-Sync Single Frequency System was introduced.
27. The definition of "Frequency Matched' used by FM Precision is also based on the "TRADITIONAL" method of making clubs stiffer as they get shorter.

I must agree that both FM Precision and Dynamic Gold shafts are frequency matched; however, I suggest to you that, within any given set of clubs, they are not in fact all matched to the swing of any particular golfer. Let me explain that statement by reviewing the last of the three systems, The Single Frequency System.

THE SINGLE FREQUENCY SYSTEM:
In 1975, after reading "The Search for the Perfect Swing",Bud Malloy, then Head Professional at Hylands Golf Club in Ottawa, began to wonder why most of the golfers that he instructed had a favourite club in their set. He concluded that for some reason this favourite club matched the golfer's swing better than the rest of the clubs in the set. He then wondered if the other clubs in the set could be matched, by frequency of vibration, to this favourite club in some manner. It seemed logical that all clubs in the set should feel the same as that one favourite club but the problem was twofold. Firstly, how could this be done, and secondly, would this approach really meet the requirements of the golfer.

The initial attempt at frequency matching was done using a stroboscope to match a set of three woods. The frequency was adjusted simply by changing the swing weight of the club by adding weight to the head. Although the three clubs were matched by frequency the swing weights varied from D0 for the Driver to over D6 for the 5 Wood. About this time, the introduction of the parallel tip or unitized shaft greatly simplified the frequency matching procedure. Although most heads had to be drilled to accept the unitized shafts it was now possible to start with a head and an uncut shaft and work to the desired frequency in each club.

In the beginning, logic suggested that all clubs should be the same frequency; however, we soon found out that woods and irons made to the same frequency did not work. We agreed that all clubs in the set should feel the same and respond the same way to the golfer's swing. The question was " What does it mean to match a set of clubs"? As I have already said, everyone else in the industry seemed to believe that clubs should get stiffer as they get shorter, the TRADITIONAL WAY, but I don't believe anyone had ever tried to find out just what a golfer really wanted in a matched set of clubs.

We spent the next three years testing golfers at various skill levels with test clubs preset at known frequencies. These test irons included six of each 2, 5, 7, and 9 irons which were precisely matched by swing weight, length etc., with the only variable being the frequency of the shafts.

The frequencies ranged from 280 cpm to 305 cpm with three inches of the butt of the club clamped in the frequency analyser. The clubs were number coded so that the individual did not know the frequency of any club in the test set until after the best club in each group had been selected. Each test candidate hit five shots with each group of six test clubs, starting with the number 9 irons, and were asked to identify the one club in each group that felt the best and produced the most consistent results.

We control tested 35 golfers ranging from Professionals to 30 plus handicap male and female golfers. After recording some 4200 hits, analysis of the test results showed that 87 percent of the test group had selected 3 of the 4 test clubs within a range of 5 cpm of the same frequency. This consistency in selection of frequency becomes very significant when one considers that the difference in shaft frequency between the 3 and 9 irons, in most sets manufactured by the golf industry at that time, varied from 12 to 60 cpm, with an average of 26 cpm. Its still the same today.

FREQUENCY MATCHING AND THE SWING:
Now, how does this single frequency matching system relate to the golfer's swing? With few exceptions, golf teachers have their students try to develop one repeating swing which is used for full shots with all clubs, yet the golfer is provided with a set of clubs that will produce thirteen different results if the same setup and swing is used with each club. Since each club in a standard set of clubs has a different frequency, the golfer must setup differently or swing differently with each club to get consistent results. With standard clubs a slightly different ball position must be used with each club to compensate for the variation in stiffness, since it is virtually impossible to change the way you swing. The ball must be moved back in the stance as the clubs get shorter. The Single Frequency System eliminates this adjustment since all clubs can be played from one of two positions once the correct location is established. All irons and fairway woods are played from the same location and the ball is moved ahead about one inch when the ball is placed on a tee for the driver. With single frequency clubs they all recover at the same place in the swing.

Some articles on the subject have suggested that frequency matching would be of no value to the average golfer because most amateurs do not have a consistently repeating swing. To the contrary, good swing or bad swing, all golfer's have a repeating golf swing. Properly matched clubs eliminate much of the inconsistency that is normally attributed to the swing. Golfers want a set of clubs that react the same way to their swing, regardless of which club is being used. Our tests have shown that any golfer at any level can tell the difference in 5 cpm in a golf shaft so how can they expect to play consistently with a set of clubs that vary by 26 cpm. Every golfer that I have ever met has a favourite club. Its their favourite because they hit more good shots with it than they do with any other club in their bag.

In most cases the favourite club is the same as the frequency selected during the test, providing the person has a correct frequency shaft in the bag. You have all heard the statement that "ninety eight percent of all golfers are playing with the wrong clubs", so it should be no surprise to find out that there are many golfers who do not have a single club in their bag that is actually correct for them. This is a great tribute to either the skill level or the adaptability of the human being, when you consider the scores that have been posted with all of this ill fitted equipment.

You must also understand that FREQUENCY is AMPLITUDE INDEPENDENT. That means that regardless of how far I deflect the shaft the frequency remains constant. When you swing a golf club the shaft doesn't know what you are doing to it, it simply responds to what you are doing. If the shafts in your clubs are all the same frequency they will all respond in the same way to your swing.
39. Therefore, all shots with single frequency matched clubs feel the same from full shots to half shots and all clubs can be hit with equal ease from the 1 Wood through the Sand Wedge.

Finally, during all the years that I have worked with frequency I have found absolutely no correlation between a golfer's selected frequency and any of the criteria normally related to club fitting. In other words, shaft stiffness is not related to age, sex, handicap, size, strength, skill level, clubhead speed or how far you hit your driver. It is related to only one thing and that is HOW YOU SWING. Short of a physical handicap the frequency selected by a golfer will never change and we have ample evidence to show that in fact frequency is genetically related and is hereditary. We have many examples where members of the same family selected the same frequency from the test clubs.

There you have a comparison of the three systems currently claiming to frequency match golf clubs to the individual golfer. While we may agree that they all cannot be correct, since they are somewhat contradictory, we realize that people are all different and no one system will fit everyone. I have no doubt that the Single Frequency System will match more people correctly than either of the other systems that we have discussed; however, there are people out there who cannot or will not learn to use the SWING SYNC Single Frequency System but YOU will never know what you will find until you hit the Test Clubs.

FREQUENCY MISUNDERSTOOD:
As I said earlier, in most cases frequency is misunderstood and has created a great deal of confusion, particularly for the consumer. Consider the case where Joe and Pete are having a game and Joe tells Pete about this new graphite shafted "Whatever it is" that he is hitting so well. Of course Pete immediately wants to try it. He hits one or two drives with Joe's club and thinks it's just great. As soon as the game is over he runs into the shop and orders a club the same as Joe's based on the information printed on the shaft. What is the probability that his club will be the same as the one Joe has. I suggest he would be better off buying a lottery ticket.

Many clubmakers have made a driver for some one that worked very well and then tried to make a 3 wood that gave the same performance. Unless they were using a frequency analyser I suggest that they were something less than totally successful, at least on the first try, although they used the same model shaft from the same manufacturer and followed the trimming instructions to the letter.

Considering everything that is involved in the manufacture of a golf shaft you must agree that the shaft makers do a remarkable job for what we pay for a completed shaft. On that basis alone, and considering normal manufacturing tolerances what range of variation would you expect to find in any group of shafts. If you now relate these variations to the frequency of the completed shaft you will realize that there can easily be an appreciable difference in frequency from one shaft to the next even if they both say FIRM.

This variation is usually greater in graphite shafts than it is in steel, particularly in wrapped graphite which is not usually as consistent as the filament wound variety. It is not unusual to find a frequency variation of 5 to 10 cpm in graphite shafts when you rotate the shaft and measure the frequency in different planes of bending. According to the USGA this variation in frequency from one plane to another is illegal but fortunately for the shaft makers they have never been challenged on this point. If they were I expect about 80% of the graphite shafts would not meet the requirements.

A much larger problem exists when you try and relate one shaft to another that is a different model. For example let's suppose you go to your favourite clubmaker with a Dynamic Regular shaft in your driver and ask to have it replaced with the equivalent stiffness in a Dynalite shaft. You might assume that they should replace the R Shaft with an R Shaft, or if they had a frequency analyser they could measure the frequency of the Dynamic R shaft which might be 255 cpm and match the Dynalite R shaft to the same frequency. The problem is that these two shafts have totally different SHAFT CHARACTERISTICS, such as flex point, torque, weight and step pattern, all of which relate to the equivalent frequency. The fact is that to have the same stiffness in the Dynalite as they measured in the Dynamic they would have to make the Dynalite shaft at a frequency of 240 cpm or 15 cpm less than the Dynamic. This tells us that the Dynalite shaft is relatively stiffer that the Dynamic. I have given you only one example of the difference in shaft characteristics that relate to frequency matching of shafts. Obviously, the clunmaker needs to know the relationship with any shaft that they use, which is part of our research and development, at iso-vibe inc., in support of the Single Frequency Matching System.

I mentioned earlier that our test clubs are made using Dynamic pattern shafts; therefore, we use this shaft as our base. All other shafts that we use are related to the Dynamic Shaft. To do this we make up test clubs with the new shaft and have people with known frequencies hit them in order to select the shaft that most closely matches the shafts they are using. From these results we can then determine the relative equivalent frequency for the new shaft.

To give you a couple of other examples, the TT Lite Shaft is 5 cpm stiffer than a Dynamic and the Activator Graphite, which is now out of production, was 32 cpm stiffer than a Dynamic shaft. As you can see the mistaken idea that 295 cpm in one shaft is 295 cpm in another could create many problems for both the clubmaker and the customer.

Frequency is an absolute measurement of the relative stiffness of shafts within any group of the same make and model but does not necessarily relate to different makes and models of shafts. Each Shaft Characteristic group is unique to itself and the relative stiffness of any group must be established in some way before it can be used successfully.

FITTING FOR FREQUENCY:
I was reading the article in Golf Shop Operations where they were telling us that by the year 2000 clubfitting will be a computerized process that will make buying properly fit golf clubs easier than buying a tailor made suit. All I can say is Good Luck. Think about it for a moment and tell me if you would really want a computer to tell you what golf club feels best in your hands.

The old adage about Garbage-In-Garbage-Out was never more true than it is here. A properly matched club feels good at impact and lets you control ball flight, and what are you going to put into the computer that will allow it to answer those two questions for you. I suggest to you that selection of shaft flex must be a subjective decision by the golfer based on actual feel at impact and results of the hit. These tests must be made with test clubs that have shaft flex as the only variable, so that when the person finds a shaft that works you know why it works.

I have been testing golfers for over twenty years and I would not attempt to suggest the stiffness of shaft that is best for you simply by watching you swing a golf club. The probability that I would be wrong is too great.

Following is a list of the most common methods in use today that purport to determine the stiffness of shaft required by the golfer. They are in no particular order and include a short explanation of the procedure as I understand it, with my own comments about the validity of the procedure used.

THE HENRY GRIFFITTS SYSTEM:
According to the Henry Griffitts philosophy a club fitter should first be a teacher. The teacher then fits the person with the club that best suites their swing style. It seems that they end up fitting everyone with overlength clubs that have upright lies, which in itself sounds like a contradiction. To establish the proper club they have the golfer hit a series of different clubs taken from a test set that includes some 62 clubs. These test clubs have different lies, lengths, shafts and grip sizes with nothing as a common feature; consequently, when the golfer finds the club that works best they have now way of really knowing why it feels better than the rest. In addition to this somewhat random selection, which can vary depending on who is doing the test, the shafts are matched according to the standard manufacturers cutting pattern which produces a gradient match.

THE DYNACRAFT SHAFT FITTING INDEX (DSFI):
This system arrived on the market a few years ago and is the system used by many of the custom club fitters in both the USA and Canada. The shaft selected for the customer is based solely on the CLUBHEAD SPEED generated by the golfer. The DSFI lists the properties of all shafts that relate to a given speed in terms of flexpoint, bendpoint, weight and frequency of the uncut shaft. Once the shaft is selected the shafts are trimmed in accordance with the standard gradient cutting pattern recommended by the manufacturer. Since clubhead speed is not related to shaft stiffness this system cannot be correct more than 30 to 50 percent of the time; however, since they use the gradient system there should always be one club that is correct and a couple of others that are close which is better than the standard OEM product in most cases.

THE TRUE TEMPER DETERMINATOR:
This system was introduced about 1995 and is based on extensive testing by True Temper. They came up with the statement " Its not how fast you swing, it's how you swing it fast". They arrived at this conclusion by measuring acceleration of the clubhead during the swings of some 2800 golfers. Their results prove conclusively that speed itself has nothing to do with the selection of the proper shaft for the golfer being tested. Exactly what we have been saying for the past twenty years.

The Determinator is a mechanical measuring device which measures the maximum acceleration of the clubhead during the swing. You have the golfer swing the determinator ten times and average the readings. Using this average and a chart the clubfitter is supposed to select the stiffness of shaft for the golfer depending on the length of the driver that you want them to use.

I have tested people. whose frequency I know, with the determinator and have not been able to correlate the determinator results with their known frequency. At best the determinator puts you somewhere in the ballpark, within 15 cpm, but certainly cannot suggest a specific frequency for anyone.

COMPUTER BASED MATCHING SYSTEMS:
There are several companies who advertise computer based fitting systems wherein you provide answers to certain questions and the computer program selects the correct specifications for your clubs. while these programs may determine the length, lie and grip size for the subject golfer, there are no questions that can be asked that relate to the stiffness of the shaft that the person should use.

SUMMARY:
There you have it. Gradient Matching, Single Frequency Matching, Shaft Characteristics and Determination of Frequency based on my experience and research.

I trust this will provide some food for thought and generate some questions for further discussion.