## 2 Experimental Methods
### Variation in Stiffness  
In most of the previous studies [5; 6; 7], the variation in system stiffness is achieved by adjusting physical springs. But the change of springs has a great impact on the equilibrium position of the prism immersed in water due to the buoyancy and gravity. In order to solve this problem, some scholars changed the layout of the direction of the cylinder, and some developed virtual system such as VCK (virtual damper-spring system) [30; 31] to vary system stiffness. In the present investigation, a new spring system is established to solve the problem mentioned above. The components of the system are shown in Figure 6. A duralumin plate is rigidly fixed on the transmission. Multiple columns with equally spaced mount points are arranged longitudinally on the duralumin plate. The corresponding mount points are also arranged at the upper section and lower section of the frame. The upper mount point, the mount points in the columns, and the lower mount point are in a vertical line. During the experiment, the upper side of the lower springs and the lower side of upper springs can be selected as the best mount point to suspend. According to the linear superposition principle of spring stiffness, different system stiffnesses can be implemented by using different groups of springs. The stiffness of a spring group with \(n\) springs is the sum of each spring stiffness \(k_{\mathrm{spr}i}\). The requirements in the following expressions need to be satisfied by hanging the springs. \[\sum_{i=1}^{N}f_{\mathrm{ui}}-\sum_{j=1}^{M}f_{\mathrm{uj}}=(m_{\mathrm{o}}-m _{\mathrm{d}})\mathrm{g} \tag{11}\]  
\[f_{\mathrm{uj}}=k_{\mathrm{ui}}\Delta x_{\mathrm{ui}};\ f_{\mathrm{ji}}=k_{ \mathrm{ij}}\Delta x_{\mathrm{ij}} \tag{12}\] \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(R_{\mathrm{L}}/\Omega\) & \(R^{*}\) & \(\zeta\) & \(f_{n}/Hz\) & \(m/kg\) & \(c/N\cdot s\cdot m^{-1}\) & \(c_{0}^{*}\) \\ \hline
6 & 1.818 & 0.400 & 0.957 & 33.17 & 159.64 & 6.797 \\
11 & 3.333 & 0.292 & 0.965 & 32.66 & 115.63 & 6.262 \\
16 & 4.848 & 0.252 & 0.955 & 33.35 & 100.92 & 6.454 \\
20 & 6.061 & 0.232 & 0.959 & 33.03 & 92.52 & 6.448 \\
22 & 6.667 & 0.222 & 0.959 & 33.03 & 88.56 & 6.334 \\
52 & 15.758 & 0.172 & 0.967 & 32.48 & 68.00 & 6.061 \\ \(\infty\) (O/C) & \(\infty\) & 0.132 & 0.966 & 32.56 & 52.22 & - \\ Average & - & - & 0.961 & 32.90 & - & 6.393 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The complete results in free-decay test by varying the load resistance. Figure 5: Damping coefficient of the oscillation system \(c\) versus load resistance ratio \(R^{*}\). \[\sum_{i=1}^{N}k_{ui}+\sum_{j=1}^{M}k_{uj}=K \tag{13}\]  
where \(k_{ui}\) and \(k_{ij}\) denote the stiffness of the \(i\)th upper extensional spring and \(j\)th the lower extensional spring, respectively. \(\Delta x_{ui}\) and \(\Delta x_{ij}\) denote the extended lengths of the \(i\)th upper extensional spring and \(j\)th the lower extensional spring, respectively. \(N\) and \(M\) denote the total numbers of the upper extensional springs and the lower extensional springs. \(m_{d}\) is the displaced mass of the prism [23]. In order to ensure the accuracy of the spring system, the linearity of five spring groups were verified by loading different weights. The weight varied from 0 to 24 kg, and the variations of the loading weight versus the measured static expanded displacement in different configurations are depicted in Figure 7. The relationships between the loading weight and static expanded displacement are obviously linear, indicating that the stiffness has a great linearity. The mechanical damping ratios \(\zeta_{m}\), the mechanical damping coefficients \(c_{m}\), the natural frequency of the oscillation system \(f_{n}\), and the mass of oscillation \(m\) are verified using the free-decay tests as well. All the tests were performed in air at the open circuit (O/C) configuration. The original mass \(m_{o}\) is 16.622 kg, and the test methods and the calculation of the corresponding parameters are all similar to the description in Section 2.3.