【正文】 z is the distance from the pivot point where the ball hits the bat； inlv is the ining ball speed； batv is the bat swing speed just before collision. The following formulas are got by sorting the above variables[1]: gLM gdIT b a t ?? 22 ?? ……………………… ………………… … （ 48）224? gTMdILC O P b a t ??? ………………………………… ……… …… （ 49） Team 8038 Page 15 of 20 ? ? batAinA veveBBS ??? 1………………… ……………………… （ 410） Associating the above three formulas with formula (46) and (47), the formulas amongBBS , the mass M , the centerofmass (CM ), the location of COP, the coefficient of restitution BBCOR and the momentofinertia of the bat batI are: batin vk kB B C O Rvk kB B C O RBBS )11(1 ? ???? ?? ……………………… （ 411） 224?MgdTIbat ?………………………………… ………………………… （ 412） Mmk ball?……………………………………………………………… （ 413） It can be known form formula (411), (412) and (413): 1) When the coefficient of restitution BBCOR and mass M of the material changes, BBS will change。s right hand. Fig. 44 Fundamental bending mode 1 (215 Hz) The second bending mode has three nodes, about inches from the barrel end, a second near the middle of the bat, and the third at about the location of a righthanded hitter39。 b. length of the bat S (the distance between Block 1 and Block 5 in Fig 43)。 5) Less mass means a less effective collision； 6) The moment of inertia bees smaller.[5][6] By analyzing the changes of the above parameters of a corked bat, whether the hitting effect of the sweet spot has been changed could be identified and then the reason for prohibiting “corking” might be clear. Analysis of Problem III First, explain whether the bat material imposes impacts on the hitting effect。 then, the sweet spot could be located by sequencing the sweet zones of the two kinds on the bat. Finally, pare the maximum hitting effect of this sweet spot with that of the end of the bat. Analysis of Problem II Problem II is to explain whether “corking” a bat enhances the “sweet spot” effect and why Major League Baseball prohibits “corking”.[4] In order to find out what changes will occur after corking the bat, the changes of the bat’s parameters should be analyzed first: 1) The mass of the corked bat reduces slightly than before。 For office use only T1 ________________ T2 ________________ T3 ________________ T4 ________________ Team Control Number 8038 Problem Chosen A For office use only F1 ________________ F2 ________________ F3 ________________ F4 ________________ Team 8038 February 23, 2020 Summary Baseball is a popular batandball game involving both athletics and wisdom. There are strict restrictions on the material, size and manufacture of the bat. It is vital important to transfer the maximum energy to the ball in order to give it the fastest batted speed during the hitting process. Firstly, this paper locates the centerofpercussion (COP) and the viberational node based on the single pendulum theory and the analysis of bat vibration. With the help of the synthesizing optimization approach, a mathematical model is developed to execute the optimized positioning for the “sweet spot”, and the best hitting spot turns out not to be at the end of the bat. Secondly, based on the basic model hypothesis, taking the physical and material attributes of the bat as parameters, the moment of inertia and the highest batted ball speed (BBS) of the “sweet spot” are evaluated using different parameter values, which enables a quantified parison to be made on the performance of different bats. Thus finally explained why Major League Baseball prohibits “corking” and metal bats. In problem I, taking the COP and the viberational node as two decisive factors of the “sweet zone”, models are developed respectively to study the hitting effect from the angle of energy conversion. Because the different “sweet spots” decided by COP and the viberational node reflect different form of energy conversion, the “spacedistance” concept is introduced and the “Technique for Order Preferenceby Similarity to Ideal Solution (TOPSIS) is used to locate the “sweet zone” step by step. And thus, it is proved that the “sweet spot” is not at the end of the bat from the two angles of specific quantitative relationship of the hitting effects and the inference of energy conversion. In problem II, applying new physical parameters of a corked bat into the model developed in Problem I, the moment of inertia and the BBS of the corked bat and the original wood bat under the same conditions are calculated. The result shows that the corking bat reduces the BBS and the collision performance rather than enhancing the “sweet spot” effect. On the other hand, the corking bat reduces the moment of inertia of the bat, which makes the bat can be controlled easier. By paring the two Team 8038 Page 2 of 20 conflicting impacts prehensively, the conclusion is drawn that the corked bat will be advantageous to the same player in the game, for which Major League Baseball prohibits “corking”. In problem III, adopting the similar method used in Problem II, that is, applying different physical parameters into the model developed in Problem I, calculate the moment of inertia and the BBS of the bats constructed by different material to analyze the impact of the bat material on the hitting effect. The data simulation of metal bats performance and wood bats performance shows that the performance of the metal bat is improved for the moment of inertia is reduced and the BBS is increased. Our model and method successfully explain why Major League Baseball, for the sake of fair petition, prohibits meta