【正文】 Step 2: Determining the most ideal position ?*x and the acceptable most unsatisfied position ?*x Assume that the most ideal position is }min{ *1* xx ?? , and the acceptable most unsatisfied position is }max{ *2* xx ?? 。 2) The process discussed refers to the whole continuous momentary process starting from the moment the bat contacts the ball until the moment the ball departs from the bat。s hands 2) the location which produces maximum batted ball speed 3) the location where maximum energy is transferred to the ball 4) the location where coefficient of restitution is maximum 5) the center of percussion For most bats all of these sweet spots are at different locations on the bat, so one is often forced to define the sweet spot as a region. If explained based on torque, this “sweet spot” might be at the end of the bat, which is known to be empirically incorrect. This paper is going to explain this empirical paradox by exploring the location of the sweet spot from a reasonable angle. Based on necessary analysis, it can be known that the sweet zone, which is decided by the centerofpercussion (COP) and the vibrational node, produces the hitting effect abiding by the law of energy conversion. The two different sweet spots respectively decided by the COP and the viberational node reflect different energy conversions, which forms a twofactor influence. This situation can be discussed from the angle of “spacedistance” concept, and the “Technique for Order Preference by Similarity to Ideal Solution (TOPSIS)” could be used.[2] The process is as follows: first, let the sweet spots decided by the COP and the viberational node be “optional Team 8038 Page 5 of 20 sweet spots”。 4) The coefficient of restitution of the bat bees smaller than before。 e. distance between the undetermined COP and the pivot L (the distance between Block 2 and Block 4 in Fig. 43, that is the turning radius) . Fig. 43 Table 41 Block 1 knob Block 2 pivot Block 3 the centerofmass（ CM） Block 4 the center of percussion (COP) Block 5 the end of the bat ? Calculation method of COP[1][4]: distance between the undetermined COP and the pivot: 224?gTL? (g is the gravity acceleration） （ 43） moment of inertia: 220 4?MgLTI ? (L is the turning radius,M is the mass) （ 44） Team 8038 Page 10 of 20 ? Results: The reaction force on the pivot is less than 10% of the batandball collision force. When the ball falls on any point in the “sweet spot” region, the area where the collision force reduction is less than 10% is ),( LL cm, which is called “Sweet Zone 1”. 2) Determining the vibrational node The contact between bat and ball, we consider it a process of wave the bat excited by a baseball of rapid flight, all of these modes, (as well as some additional higher frequency modes) are excited and the bat vibrates .We depend on the frequency modes ,list the following two modes: The fundamental bending mode has two nodes, or positions of zero displacement). One is about 61/2 inches from the barrel end close to the sweet spot of the bat. The other at about 24 inches from the barrel end (6 inches from the handle) at approximately the location of a righthanded hitter39。 2) When mass M and the location of centerof mass CM changes, batI changes, which is the dominant factor deciding the swing speed. Analysis of corked bat and wood bat [5][6] Table 43 swing period T bat mass M Bat length S CM position d coefficient of restitution BBCOR initial velocity inv swing speed batv ball massballm wood cm cork cm The hitting effect reflects by above physical parameters: Apply these values in formula (411) and (413) 1) Calculate respectively： smBBS /)1( ? smBBS /)2( ? Thus )2()1( BBSBBS ? . )1(BBS represents the maximum battedballspeed of a corked bat, and )2(BBS represents the maximum battedballspeed of a wood bat. Team 8038 Page 16 of 20 Conclusion: when the swing speed ( batv ) and the initial velocity of the ball ( inv ) remain the same, the initial velocity of the wood bat is higher than the corked bat. That is to say that the corked bat does not enhance the “sweet spot” effect. Hence, it is not the reason why Major League Baseball prohibits “corking”. But the change of the momentofinertia caused by the material can explain the prohibit. 2) Calculation of the momentofinertia of two different bats: 2*142)1( cmgI bat ? , 2* 59)2( cmgI bat ? Thus )2()1( batbat II ? . )1(batI is the momentofinertia of the corked bat, and )2(batI is the momentofinertia of the wood bat. Conclusion: the mass and the momentofinertia of the bat reduces after corking, so then swing speed gets faster, which means the professional players are able to watch the ball travel an additional 56 feet before having to mit to a swing. It makes the game unfair to increase the hitting accuracy by corking the bat. Reas。 c. distance between the pivot and the centerofmass d ( the distance between Block 2 and Block 3 in Fig. 43)。 2) Less mass (lower moment of inertia) means faster swing speed。 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 ord