## 3 Results
### Detailed Analysis of the Typical Cycle of a Repetition for a 10 kg Load
#### 3.1.2 Evaluation of the Superposition of the Relevant Repetitions  
The idea of overlapping the concentric phase of R2 and R24 allowed us to understand how the bicep muscle adapted during exertion in a typical extended set, with MNR = 25. Figure 6 presents the superposition of the forces' evolution for the initial and final repetition in the case of the 10 kg machine load.  
In the case of a 10 kg load, we can observe some differences between the first and last relevant repetitions. It can be seen that the time taken to reach the maximum value of the force was longer at the beginning. Additionally, the slope of the ascending curve (i.e., the geometric place of the mean values of the micro cycles) was less inclined in R2,  
Figure 5: Evolution of forces versus time—10 kg load for cycle of an initial repetition (a) and of a final repetition (b).  
Figure 6: Superposition of the forces’ evolution at the initial and final repetitions—10 kg load.  
which proves that, towards the end, a fatigue threshold was reached, which causes an increase in the execution speed on the concentric phase of the repetition cycle. Hence, the third hypothesis was validated.  
A polynomial regression was found that presents the evolution of the forces in time, for each initial and final repetition. In Figure 6, those regressions are represented by a red line. Identifying one type of regression could lead to the identification of different strategies for changing the way the exercise is performed. For the initial repetition, the regression that best fits the average values of the forces is presented in Equation (1). The coefficient of determination (R square) is 0.729 and interprets, as a percentage, how representative the regression line is for the investigated data (72%).  
\[F_{R2}=0.052-0.0005\cdot t+6\times 10^{-5}.t^{2}-8\times 10^{-7}.t^{3}+3\times 10^{- 9}.t^{4} \tag{1}\]  
Based on the polynomial regression developed, the impulse was calculated by integration. For the period of reaching the highest force (i.e., 0.8 s), in the case of an initial repetition, the impulse was 0.041 kN's.  
The polynomial regression that best fits the measured average values for the final repetition is presented in Equation (2). R square for this regression is 0.607.  
\[F_{R24}=0.058-0.0004\cdot t+7\times 10^{-5}.t^{2}-3\times 10^{-6}.t^{3}+4\times 1 0^{-8}.t^{4} \tag{2}\]  
Based on Equation (2), the impulse developed at a final repetition, in 0.41 s, decreased at 0.023 kN's. It can be observed that the impulse was 50% lower in the case of the final repetition.  
Table 3 presents the results obtained from the paired \(t\)-test application. It can be observed that, for the first relevant repetition, the mean of the maximum force values was 0.127 \(\pm\) 0.004 kN, an 8% lower value than the mean of the final repetition of the exercise set, which was 0.138 \(\pm\) 0.006 kN.  
There was a significant average difference between R2_Fmax and R24_Fmax (t29 = 8.14, \(p\leq\) 0.001), and R2_Fmax was 0.011 points lower than R24_Fmax. The second hypothesis was validated; there was a statistically significant difference between the maximum forces developed during the initial and final repetitions of the exercise set.  
[PERSON]'s d was calculated in order to find the size of the difference between the means. The value was, in this case, \(-\)2.15, meaning a large effect size and a practical significance.