On Dick Pierce Professional Audio Developent Wherein we explore soe of the basic physical echanics of tone ars. INTRODUCTION Mechanics is a branch of physics that explores the behavior and analysis of oving asses and the forces associated with these oving asses. Applying the analysis of echanics to tone ars is soething that is an essential part of tone ar design, but is oft neglected outside of the design process. This has lead, aong other things, to a nuber of yths about how tone ars behave and what constitutes the crucial factors affecting their behavior. Here are soe exaples: When calculating the ass of a tone ar, you ust add the tracking force. To reduce the effective ass, you should ake the counterweight less assive. In uch of the analysis below, we ake soe siplifying assuptions. For exaple, when we generally speak of a ass, we assue, for siplicity, that all of the ass is concentrated in one point, or at least in a region that is very sall copared to the other diensions of the proble. We ll also assue that all structures are rigid and all bearings are without friction. In ost cases, the difference that result fro these assuptions lead to analysis results that do not appreciably differ fro physical reality, and are thus good odels of that reality. In other case, we will include the corrections due to asses actually occupying a large extent, and the effects of friction, because they can affect the behavior of the systes we are analyzing in non-trivial ways. I, in no way, intended this to be a coprehensive article on tone ar and turntable design. There are plenty of sources, any of the excellent, on various aspects of tone ar design. There are any articles to be had on design factors to iniize tracking error and other aspects of geoetry, RIAA preaplifier design, tone ar daping and ore. Nor do I intend to preach a particular gospel even in the liited scope of the present topic: I a, for exaple, advocating neither high ar ass or low ar ass as being superior. Rather, I a presenting the basic physics behind why tone ars have the ass that they do, with the hope that ared with this inforation, the reader can better understand the factors involved. Nowhere, necessarily, is there any inforation to be found here on how to design the very best ar: rather, what is presented is the fundaentals needed to do that job. And also I hope that there s enough here to allow the reader to separate the iportant wheat fro the advertising and ythological chaff that oft surrounds discussions on LP playback principals. A QUESTION OF UNITS Throughout this discussion, we ll be using the etric syste of units. More specifically, we ll be using the cgs syste, standing for centieters, gras and seconds. The etric syste of units allows for easy and consistent units calculations. On the other hand, the noral iperial units have little logical relation to one another and are, indeed, a source of great confusion. Revised: Printed: 0-Jan-05 0-Jan-05
The basic unit of length or distance is the centieter, abbreviated as c. A centieter is a little ore than 3/8 of an inch. Fro that, area is easured in square centieters and volue in cubic centieters. The basic unit of ass, a easureent of the aount of atter, is gra. There are about 8 gras in a dry ounce. We ight find it curious that a single cubic centieter of water has a ass of alost precisely gra. In fact, a gra was initially defined as the ass of cubic centieter of water at its axiu density, at about degrees Celsius. Of course, we know of the unit of tie, the second. Fro these basic units, we can cobine the to arrive at the other units that we ll be needing. When an object is oving, or changing its position, we easure that in ters of distance per tie, or centieters per second, or c/s. On the other hand, then the velocity of an object changes, it is said to accelerate, and the acceleration is easured in ters of the change in speed per tie, in c / s/ s, or ore conventionally, c / s. Earth s gravity acts to accelerate objects at the sae rate, an acceleration of 980 c / s often referred to with the sybol g. A force acts upon a ass to cause it to change speed, or accelerate. Specifically, fro Newton, we have the : F a Force is easured in units of gra centieters per second squared, or g c / s. This is a rather cubersoe unit, so we use the units of dynes instead. Before we go further, it s necessary to correct a long-standing isconception about tracking force. Since tone-ar tie ieorial, tracking force has been described in ters of gras. Unfortunately, gras is a unit of ass, not of force, and the use of units of ass to describe force is inappropriate and leads to confusion and incorrect assuptions. When it is said that an ar has been set up with a tracking force of gra, what is really eant is that a a force is set equivalent to that of gra under the influence of gravity. Again, reeber that: F a The acceleration of gravity is 980 c / sec so that gra exerts a force of: F g 980 c /sec 980 dynes So, it is ore correct to talk of a tracking force of 980 dynes rather than gra. Regrettably, the iproper use of gras as a easure of tracking force has becoe all-pervasive and is hard to shake. I would suggest that we ight want to invent a new unit called the gra-equivalent of force, which corresponds to the force exerted by one gra under the influence of gravity at the earth s surface, equal to 980 dynes. Conveniently, though, our choice of units and the planet live on ake the conversion rather easy. gra equivalent tracking force is within % of 000 dynes, aking the conversion pretty easy: gra is about 000 dynes: siple. Throughout the following evaluation, we ll show the tracking force in dynes and gra-equivalent force when convenient. One of the priary advantages of using consistent diensions and units is that it provides a eans of verifying that our work is proceeding correctly along sound lines. We can use a ethod called diensional consistency which verifies that the units and diensions we start with and the operations we perfor on the give us not only the correct nuerical results, but the correct units as well. Let s look at an exaple of diensional consistency. A spring and a ass can for a echanical resonant syste. We are failiar with the forula for the natural frequency of such a syste: F π M C where F is the frequency, M is the ass and C is the copliance. Well, frequency, ass and copliance don t tell us uch, what we need is frequency, ass and copliance in what units. More specifically, the frequency is in units of Hz, or cycles per second, ass (in this context) is in gras, and copliance is in centieters per dyne. But how, you ight ask, does putting ass and copliance together end up in frequency? Because of the correct use of the proper units, that s how. Let s look at this in ore detail. Again, ass is in gras and copliance is in centieters per dyne. The product of these two, M C, cobines the units and creates a new nuber in units of gra centieters per dyne. Well, that sees even ore coplicated until reeber the definition of a dyne: it s a Revised: 0-Jan-05 Page Printed: 0-Jan-05
gra centieter per second squared. So, in equation for, we siply substitute the definition of a dyne: g c g c dyne g c s Now, we can start cancelling out units that appear in both the nuerator and denoinator, since if the appear as factors in both places, the result is one: gras cancel out, centieters cancel out, and we are left with / s in the denoinator. That s the sae as having s in the nuerator. Take the square root of that and you have siply tie, in seconds. Replace everything that used to be under the radical with a nuber in units of seconds, and we get: π s which is in units of per second. The π is the nuber of radians per cycle. Thus, we have started with gras and centieters per dyne and logically ended with cycles per second, or Hz. If, instead of ass, you used weight (which, reeber, is a force), you d find that you d end up in soe weird set of diensions that do not ake logical sense (in this case, the result would be in the reciprocal of the square root of centieter!). By ensuring diensional consistency and thus correct units, we can verify that our path is correct and we end up with results consistent with the physical syste we are dealing with. We ll be using diensional analysis through this and other articles. 3 BALANCE In ost high-quality tone ars, balance and tracking force is achieved by balancing asses relative to the pivot point. Gravity exerts forces on each ass of the tone ar, each of these forces in turn create their own torque around the pivot point. Fg d pivot Torque (designated as G) is a force around a pivot. The aount of torque is equal to the force ties the distance fro the pivot: G F d The force, as entioned, results fro the acceleration of gravity on the ass: F g and g is the acceleration due to gravity, 980 c / sec. As an exaple, say the ass is 5 gras, and the distance d between that ass and the pivot is 0 c (like a phono cartridge ate the end of a tone ar). The force exerted by the ass due to gravity is: F 5g 980 c /sec 4900 dynes and the resulting torque is: G 4900 dynes 0 c 98, 000 dyne c In this case, we have a single source of torque, resulting in an unbalanced force. An unbalanced force eans that the syste will ove. To achieve balance, we ust have an equal aount of torque, but applied in the opposite direction. One way to do this is to have a ass of equal size an equal distance on the other side of the pivot: F d pivot d F The total, or net torque on this syste then is: GNET F d F d The inus sign on the second ter is a result of the torque being applied in the opposite direction. Since, then F F. And since d d then F d F d. If the two ters are equal, then the resulting torque is zero. This is the condition needed to achieve static balance. Achieving static balance can be done with two equal asses equidistant fro the pivot point on opposite sides of the pivot, but that is not the only way. All that is required to achieve static balance is the net su of all torques around the pivot is zero. Revised: 0-Jan-05 Page 3 Printed: 0-Jan-05
Iagine, instead, on the right side of the pivot, we have a ass of 00 gras, but only c fro the pivot. Iagine this arrangeent for a siple, hypothetical tone ar: cart F cart d cart d cw F cw cw The force exerted by that counterweight ass is: FCW 00g 980c /sec 98, 000 dynes Spaced c fro the pivot point, it exerts a torque of: GCW 98, 000 dynes c 98, 000 dyne c And the force exerted by that cartridge ass is: FCART 5g 980c /sec 490dynes Spaced 0 c fro the pivot point, it exerts a torque of: GCART 490 dynes 0 c 98, 000 dyne c precisely equal to the torque exerted by counterweight on other side of the pivot. The su of these two torques, then, becoes: GNET 98, 000 dyne c 98, 000 dyne c 0 The net torque is zero, thus the net forces are zero, and thus the ar is statically balanced. 3. Applying Tracking Force To apply tracking force, the ar is unbalanced usually by oving the counterweight. This results in an unequal application of torque by the cartridge and the counterweight. If the counterweight is oved inwards towards the pivot, it s contributing torque is now reduced resulting in a net downwards force at the cartridge. Let s look at this scenario in an analytical fashion. Take our exaple above, only now lets place the center of ass of the counterweight 0.8 c fro the pivot point, rather than c. The torque it now contributes is: GCW 98, 000 dynes 0. 8c 78, 400 dyne c The net torque then becoes: GNET 98, 000 dyne c 78, 400 dyne c G 9, 600 dyne c NET Then, at the stylus point, 0 c fro the pivot, that unbalanced torque translates into a downward force of: FCART 9, 600 dyne c 0 c F 980 dynes CART And 980 dynes is the force equivalent of gra. By oving the counterweight in a ere (0. c), we ve generated gra equivalent force of tracking weight at the stylus. Now, if we look at the results above, we will see that the net forces resulting fro unbalanced torque goes as a linear function of the distance of the counterweight: 5000 4000 3000 dynes 000 000 3 gra equiv 0 0 0 0. 0. 0.3 0.4 0.5 0.6 0.7 0.8 0.9.0 Pivot-counterweight distance (c) This turns out to be very convenient for calibrating the tracking force. Iagine that the tone ar shaft behind the pivot is threaded, and that each turn of the thread is apart. Siilarly the counterweight is threaded onto this shaft. Rotating the counterweight back and forth on the thread oves the counterweight towards or away fro the pivot. Each turn oves it. But a change in the position of the tone ar results (in our exaple) of a change in force of ½ gra equivalent (490 dynes). Now, adjust the counterweight so that the ar is in perfect balance. Want a gra force equivalent 5 4 Revised: 0-Jan-05 Page 4 Printed: 0-Jan-05
tracking weight of gra? Easy, turn the counterweight on its thread exactly two turns, which oves it (0. c) towards the pivot. How about.5 gra equivalent force? That s three turns. The accuracy of the schee depends only upon the accuracy of the thread and the weight of the counterweight. Both these quantities can be easily designed and controlled during anufacturing to a degree of precision that far exceeds what s necessary in this application. As a result, the tracking force calibrations on tone ars that apply tracking force by rotating a counterweight along a thread are usually very accurate, often ore so than expensive, often frictionladen tracking force gauges. This is contrary to the popular wisdo in the high-end turntable world. 4 ECTIVE MASS The subject of the effective inertial ass of tone ars is an iportant one, but one which sees to be sorely isunderstood, even by alleged experts. As an exaple, one need only look at soe of the clais ade in the popular press. One episode in particular stands out: the head of a copany aking high-quality turntables, in an infaous letter to the editors of High Fi News and Record Review (ca 976), stated categorically that tone ars cannot have ass, since everything is oving around a pivot, all that ass is really translated into oent of inertia. And without ass, the syste can t have a ass-copliance resonance. Unfortunately, the author of this letter failed to get tone ars to subscribe to his theory, as they have behaved before and since in every way as if they did have ass. This confused view of the echanics of tone ars does, however, serve to highlight that the analysis of the effective ass is not necessarily a straightforward exercise. While not necessarily just siple linear echanics. it is still well within the real of high school physics. 4. Moents of Inertia Rotary otion about a pivot point obeys precisely the sae physical laws as linear otion, and can be analyzed in the sae way. If a body of ass is oving at a velocity v, it s kinetic energy E is: E v This is true whether the body is oving in a straight line or whether it is oving in unifor circular otion around a pivot point. In the case of circular otion, we can say that the velocity v is equal to the angular velocity ω and the distance fro the pivot point r: v ωr Now, calculating the energy of such a body erely requires us to use ωr in place of v: E ω r Let s rearrange this equation slightly to give us: E ω r The quantity r is referred to as the oent of inertia of the object, and is an iportant property of all rotating asses. It s norally designated by the sybol I, and, for point objects of ass that are r distant fro the center of rotation, the oent of inertia is calculated as: I r and its units are in gra centieters squared, or gc. Now, this works fine for point asses (those whose ass is concentrated over a distance that is sall copared to r), but tone ars aren t ade out of such objects. Just think about the tone ar tube itself, a tube of soe aterial that has its ass distributed in possibly a coplex fashion over the entire distance between the pivot and the cartridge. Soe portions are close to the pivot, eaning that r is sall, soe portions are far away, and r is large. What is the contribution of such an extended object to the total oent of inertia? Well, let s literally break the proble down and analyze it. Pretend our tone ar tube is a unifor tube 0 c long weighing, say, 3 gras. If all the ass were concentrated at the end, far fro the pivot, it s oent of inertia would be ω is usually expressed in radians per second. A radian is the distance around the circuference of the circle equal to the radius of the circle. Consequently, there are π radians in each full circle or revolution. Revised: 0-Jan-05 Page 5 Printed: 0-Jan-05
I 3g ( 0c) I 3g 400c,. I 00 g c On the other hand, if all the ass was concentrated at the pivot point, it s oent of inertia would be 0. Halfway along, it would be I 3g ( 0c) I 3g 00c,. I 300 g c But, as we know, the ass is distributed uniforly along the length. Let s pretend the ass is concentrated into point asses, each spaced every c along the ar fro the pivot to the end. Point ass nuber, 3 of a gra, is at the pivot point, point ass nuber, having the sae ass as the first, is at the end. The total oent of inertia is siply the su of each one: ITOTAL I + I+ Κ + I The oent of inertia of ass is: 3 I g ( 0c) 0 g c while that of ass is: 3 I g ( 0 c) 09 g c In fact, we can generalize and say the oent of inertia of any segent is: In 3 g n c [ ( ) ] and that the total oent of inertia (in ore general ters and standard notation) is: ITOTAL 3 g[ ( n ) c] n working this out, we end up with a figure of 40gc. We can break it up into saller segents and see what the approxiation works out to. With 0 segents, we get 40gc, 40, we end up with 405gc, 00 yields 40gc. And if we carry the experient far enough, say dividing into,000,000 segents, we get soething like 400. 00 gc. In fact, we can also go look up in an echanical engineering handbook and see what the oent of inertia is for a unifor thin hollow tube pivoted fro one end, and we find: l I 3 which agrees with our little approxiation to a very high degree. While we re there, we ll see oent of inertia calculations for all sorts of shapes of objects. (I have in front of e a copy of Machinery s Handbook, published by The Industrial Press, wherein we find a table spanning several pages illustrating the oents of inertia of dozens of different shapes and profiles). So, for copleteness, we would include these calculations into the total. However, for siplicity, we ll siply confine ourselves to our sipler odel. The iplications of all this are significant, in that it tells us that the energy storage is proportional to the ass, but to the square of the distance of that ass fro the center of rotation. We can think of several intuitive exaples of this property, Flywheels, as in the siple toy gyroscope, try to have all their ass concentrated as far fro the pivot point as possible, to axiize energy storage. These iplication has iportant effect on tone ar design and perforance. Let s take our siple tone ar fro the previous exaple and exaine what the iplications of the placeent of asses relative to the pivot have. Under the assuption that all the portions of our tone ar are rigidly connected together, let s calculate the total oent of inertia. The oent of inertia of the cartridge is: ICARTt 5g ( 0c) ICART 5g 400c I 000 g c CART while that for the counterweight is: 00g ( c) 00g c I 00 g c CW Revised: 0-Jan-05 Page 6 Printed: 0-Jan-05
Hold on a second! The counterweight is 0 ties the ass of the cartridge, yet its oent of inertia is /0 th that of the cartridge. That s because, as we saw above, there s that dependency on the square of the distance fro the pivot. Reeber that the total oent is siply the su of each contributor, so the total is: ITOTAL ICART + ITOTAL 000g c + 00g c I 00g c TOTAL What is iportant fro this analysis is that for ost tone ars, the single largest contributor to the total oent of inertia is the cartridge s, not the counterweight s. And let s look at what first sees to be a copletely counterintuitive result. Let s double the ass of the counterweight to 00 gras. But, reeber, to achieve balance, we ll have to ove it closer to the pivot, in this case fro c to 0.5 c. Now, the contribution to oent of inertia becoes: 00g (. 0 5 c) 00g 0. 5 c I 50 g c CW And the total now becoes: ITOTAL 000g c + 50g c I 050g c TOTAL Thus, the seeingly contradictory result that aking the counterweight heavier reduces the total oent of inertia. 4. And Back to Effective Mass Well, this oent of inertia all sees very interesting, but we are looking for the effective ass. How do we convert fro total oent of inertia back to the effect ass? The iportant issing part of the question is, how do we convert back to the effective ass at the where? The obvious answer, I hope, is at the stylus tip, 0 c away fro the pivot. Reeber that we got to the oent of inertia for a point ass by: I r What we want to know is what is the equivalent ass at the radius r. That s siple (and it s the step that Tiffenbrun forgot to take in is incoplete analysis). Siple re-arrange the equation so that is on one side. Divide both sides of the equation by r and you get: I r So, in our exaple, the ar has a total oent of inertia of 00gc, so the resulting effective ass at the stylus tip, 0 c away fro the pivot, would be: 00gc ( 0 c) 00gc 400c 55. gras And, as we see, the single largest contributor to the total effective ass is the cartridge, not the counterweight. Again, this is as a consequence of the dependency on the square of the distance fro the pivot. Let s look at our second exaple, with the 00 gra counterweight: 050gc ( 0 c) 55. gras Again, soewhat counter-intuitively, the ar with the heavier counterweight ended up with the lower effective ass. Not by a lot, but it s still a real effect. This then contradicts the yth that to lower the ass of a tone ar, all eleents ust have their ass reduced. It further suggests that if you need to lower the effective ass of an ar, you re uch better spending the effort at the end where the cartridge is, not near the pivot or counterweight. 4.3 Tracking Force and Effective Mass One yth that I have heard repeatedly is that to get the total effective ass, you ust add the tracking force to the noral effective ass. This would be true if and only if you got that tracking force siply by adding a ass right to the cartridge, sort of Revised: 0-Jan-05 Page 7 Printed: 0-Jan-05
along the lines of the old trick of taping a penny to the headshell. Most high-quality tone ars achieve positive tracking force by unbalancing the ar, as shown above, oving the counterweight closer to the pivot fro the zero-balance position. We can calculate the effects this has on the effective ass. In our exaple, we had to ove our 00 gra counterweight to a position of 0.8 c away fro the pivot point to achieve a gra equivalent tracking force at the stylus tip. Under that condition, the counterweight s contribution to the total oent of inertia is: 00g (. 0 8 c) 00g 0. 64 c I 64g c CW The total oent of inertia becoes ITOTAL ICART + ITOTAL 000g c + 64g c I 064g c TOTAL And the resulting effective ass, 0 c away fro the stylus tip, becoes: 064gc 400c 56. gras So, quit contrary to the another of the popular yths, in tone ars that achieve tracking force by unbalancing the tone ar, the tracking force is not added to the effective ass. In fact, dialing in the tracking force oving the counterweight closer to the pivot fro the zero-balance state reduces the effective tone ar ass. Siilar to the graph we saw above, we can produce a graph, given our hypothetical tone ar, of effective ass vs tracking force: Mass gras 0 6.00 5.50 5.00 4.50 4.00 0 gra-equivalent force 3 4 5 000 000 3000 4000 5000 dynes Tracking Force Again, the graph shows us the counter-intuitive effect of the ass decreasing with increasing tracking force, even though the dependence is sall, at best. In our exaple, increasing the tracking force fro 000 to 5000 dynes, an increase of 500% or a factor of 5, results in a reduction of ass of only 3%, a negligible change, at the worst. 4.4 A More Coplete Model We have done ost of our exploration aking soe siplifying assuptions: that the only objects contributing to the effective ass are the cartridge and the counterweight. Clearly, in practical tone ars, there s ore than this. There is, at the very iniu. Soe sort of ounting arrangeent for the cartridge, the ar tube, and soe sort of support for the counterweight. There is also whatever object at the pivot point that holds it all together, but, reeber, if it s at the pivot point, its contribution to the effective ass is negligible Let s apply soe practical nubers and see what we ight coe up with for the effective ass for an actual tone ar. I have available a late odel AR tone ar which is easily disassebled and easured. Here s the tally: Revised: 0-Jan-05 Page 8 Printed: 0-Jan-05
Ite Moent of Mass Distance Inertia g c* g c Cartridge 0.3 4540 Mount Ar tube 0.8 8.7 60 Counter 87 ~4 39 weight Counterweight 6 6.5 5 ount Internal wires 0.4 64.5 Signal terinals. 53 Total 5.6g 804 g c * The distance is distance fro the pivot to the center of ass of the object for objects such as the cartridge ount, or the length of the object for the tone ar tube, internal wiring, etc. The stylus-pivot distance of this ar is about.5 c, so that the effective ass of the ar, exclusive of the cartridge or its ounting hardware, is 804 gc 58. g. This is neither a particularly (. 5 c) high-ass nor a particularly low-ass tone ar. If one wanted to, say, reduce the ass of this ar, there are several approaches. You could increase the ass of the counterweight, getting it closer to the pivot, but that would not do uch for you, since the counterweight contributes only 7% of the total effective ass as it is. The biggest gain would be in reducing the aount of ass in the cartridge ounting plate. With soe careful shaving, I would see reoving 5 gras of aterial here. That s 5 gras in effective ass, since it s at the end of the tone ar. Tone ars with asses approaching 5 gras or less are rare and often involve soe significant coproises in strength and rigidity. Those with asses uch exceeding 0 gras significantly liit the range of cartridges that can be used to ones with low copliances. 4.5 Ar Mass and Resonance The significance of the effective ass in relation to the stylus copliance coes fro the fact that the two, together, for a classic echanical resonant syste. It is the cobination of the effective ass and the copliance that deterine the frequency of that resonance: F π M C STYLUS where M is the total effective ass of the ar-cartridge syste, C STYLUS is the echanical copliance of the stylus suspension, and F is the resonant frequency of syste. As long as we aintain consistent units, we can siply plug the nubers in and out coes the resonant frequency in Hertz. Looking at our exaple ar above, the AR, cobined with a 5 g cartridge gives a total effective ass of g. Looking at typical oving-agnet copliance, we find copliance figures of 0 0 6 c / dynes, that is for every dyne of force applied to the stylus, it will deflect 0 illionths of a centieter as a result. That eans, for exaple, that if the tracking force is set to gra equivalent force, or 980 dynes, the stylus deflection will be x C F 6 x 0 0 c / dyne 980 dyne 3 x 98. 0 c or about 0.. The resonant frequency of such a syste will be: F 6 π 0. 8g 0 0 c/ dyne F 4 π 08. 0 gc/ gc/ s F π 44. 0 s F s or Hz. Hz is about ideal for a cartridge/ar resonant frequency, being just about in the ideal range of 7 to Hz. If the effective ass of the ar/cartridge were substantially higher, say, 4 gras, the resonant frequency would be lower, less than 8 Hz. One the other hand, using one of the very highcopliance cartridges, one with a copliance of, say, 40 0 6 c / dyne, would lead to a lower resonance as well, in this case, about 5.5 Hz. Why the resonance should be within these confines is beyond the scope of this article, but suffice it Revised: 0-Jan-05 Page 9 Printed: 0-Jan-05
to say that we are bounded at the top end by the risk of intruding into the usical content of the record, and at the low end by echanical interference due to external vibrations, is-tracking due to warpinduced oveents, and so on. 5 CONCLUSION We ve investigated two area of fundaental echanics as they apply to tone ar properties: the application of lever ars and torque to deterine tracking weight in statically weight-balanced tone ars and the use of concepts of oent of inertia in evaluating the effective ass of tone ars. We have seen that, especially in the evaluation of effective ass, soe of the intuitive assuptions are wrong regarding how each eleent of the ar contributes to the effective ass. For exaple, we see that even though it is the ost assive object in a tone ar, the counterweight, is actually only a inor contributor to the total oving ass. One of the ost iportant concepts to be grasped is that tracking force is not effective ass. We explored how the cartridge ass and stylus suspension copliance interact to for a resonant syste and how that resonance can be calculated. We have also seen that the clai that the tracking force ust be added to the effective ass is siply not supportable. The LP still enjoys a strong and loyal following in soe niche arkets. While it has clearly dropped out of the ainstrea of the usic delivery arket, there are those that are devoted to its survival. Fro a practical standpoint, there are still any recordings and significant perforances that are siply not available on alternate edia (CD, cassette, etc.), eaning that there will, for soe tie to coe, be a need for correct playback of these records. I hope that this discussion, a better understanding of those principals underlying record reproduction can be obtained. Copyright 993-004 by Dick Pierce. Perission given for one-tie nocharge electronic distribution with subsequent follow-ups. All other rights reserved. Revised: 0-Jan-05 Page 0 Printed: 0-Jan-05