## 3 Results  
### Physical Constants of the System  
Firstly, it was necessary to carry out a numerical study to verify the sensitivity of the energy-controlling parameters, namely the stiffness constant and the mass of the system. To this end, tests were carried out without any contact to investigate the damping and dynamic characteristics of the system. Thus, to calculate the system's physical constants, the system's energy dissipation was characterized by acquiring the system's response in free vibration, which is visible in Figure 3.  
There was a response characterized by an oscillatory movement of constant frequency and an exponential decrease in the amplitude of the maximum peaks over time. This means that energy dissipation occurs fundamentally in viscous form and can be modelled by an under-damped system in free vibration. Thus, the law of motion of this system is given by Equation (2). \[x(t)=x_{0}e^{-\xi_{0}w_{a}t}cos(w_{a}t) \tag{2}\]  
Considering the law of motion only for the values of the maximum peaks, where cos (\(w_{a}t\)) = 1 occurs, Equation (3) was obtained. \[x(t)=x_{0}e^{-\xi_{0}w_{a}t} \tag{3}\]  
The damped natural frequency of the system \(w_{a}\) can be calculated by Equation (4)  
\[w_{a}=\frac{2\pi}{T_{a}} \tag{4}\]  
where \(T_{a}\) is the average period, measured directly from the curve in Figure 3. It results in a damped frequency value of system \(w_{a}\) of 123.10 rad/s\({}^{2}\), which is considered to be equal to the vibration frequency of system \(w_{n}\). Considering the value of the vibration frequency \(w_{n}\) and that the exponential adjustment of the maximum peaks of the curve in Figure 3 is represented by an equation similar to Equation (3), it is possible to obtain the value of the damping factor \(\xi\). In this case, the value of 7.14 \(\times\) 10\({}^{-3}\) was obtained. Now, knowing the value of the vibration frequency of system \(w_{n}\) and the spring stiffness constant \(k\), it is possible to obtain the value of the mass of system \(m\) using Equation (5). \[w_{n}=\sqrt{\frac{K}{m}}\ \Leftrightarrow m=\frac{k}{w_{n}^{2}} \tag{5}\]  
The value of the spring stiffness constant \(k\) was experimentally obtained in previous studies, corresponding to 265 N/m. Thus, the extracted value of the mass of system \(m\) is \begin{table}
\begin{tabular}{c c} \hline
**p1 in Water at 25 \({}^{\circ}\)C** & **Fatty Acid Depleted—5.3, Endogenous Material—4.7; 4.9** \\ \hline Refractive index increment (578 nm) \(\times\) 10\({}^{-3}\) & 1.90 \\ Optical absorbance, A\({}_{229\,\mathrm{nm}}\) (1 g/L) & 0.667 \\ Mean residue rotation [m\({}^{\prime}\)]\({}_{233}\) & 8443 \\ Mean residue ellipticity & 21.1 [\(\theta\)]\({}_{209\,\mathrm{nm}}\); 20.1 [\(\theta\)]\({}_{222\,\mathrm{nm}}\) \\ Estimated \(\alpha\)-helix, \% & 54 \\ Estimated \(\beta\)-form \% & 18 \\ \hline \end{tabular}
\end{table} 
Table 1: Cont. 17.49 g. Finally, it is possible to calculate the damping constant \(c\) using Equation (6), where a value of 0.031 Ns/m was obtained. \[\xi=\frac{c}{2\sqrt{kn}}\ \Leftrightarrow c=2\xi\sqrt{km} \tag{6}\]  
Based on the above, the physical constants characteristic of the experimental method are presented in Table 2.  
It should be noted that three tests were carried out, with the values considered the average of those obtained in the different tests. The constants obtained present a ratio between the standard deviation and the mean of the order of magnitude of \(10^{-3}\), as it is much lower than \(10^{-1}\), the results are considered a good experimental approximation. By substituting the physical constants of the system in Equation (2), the theoretically expected response curve is obtained. By comparing this curve with those obtained experimentally for the different tests, as visible in Figure 4, very low RMSE values were identified, in the order of \(10^{-2}\), meaning a high similarity between the results. The physiological operating conditions of contact lenses allow us to conclude that contact occurs under lubricated conditions.