## 2 Experimental Methods
### Variation in Damping
Substituting Equations (3)-(5) into Equation (2), the simplified equation of the system damping coefficient \(c\) can be obtained as  
\[c=c_{\rm m}\left(\frac{R^{*}+c_{0}^{*}}{R^{*}+1}\right) \tag{6}\]  
As shown in Equation (6), in the oscillation system with PTO, the system damping coefficient \(c\) is a function of parameters \(c_{\rm m}\), \(c_{0}^{*}\) and \(R^{*}\). \(c_{\rm m}\) and \(c_{0}^{*}\) are related to the system itself and can be regarded as the internal factors. \(R^{*}\) is impacted by the external load resistance and can be regarded as the external factor. In the present experiment, PTO is based on a fixed-magnetic generator, \(c_{\rm m}\) and \(c_{0}^{*}\) consequently maintain constants. Therefore, \(c\) is just a function of \(R^{*}\), illustrating that the variation in \(c\) can be achieved by adjusting \(R^{*}\). Furthermore, the radius and the rotational inertia of the gears and rotor in PTO system have a great influence on the mass of the oscillation system. [PERSON] (2008) has proved that this impact can be considered as an equivalent mass \(m_{\rm eqe}\). Hence, the mass of oscillation system can be expressed as  
\[m=m_{\rm o}+m_{\rm eqe} \tag{7}\]  
where \(m_{\rm o}\) is the original mass of the oscillation system, which is the sum of prism mass \(m_{\rm pri}\), mass of transmission \(m_{\rm tra}\), and one-third of the spring mass \(m_{\rm spr}\)[PERSON] and [PERSON] (2008). The physical parameters were verified by free-decay tests prior to the experiments. All the damping tests were performed in air at \(K=1200\) N/m and \(m_{\rm o}=16.622\) kg. The average measured value of inner resistance of the generator \(R_{0}\) is 3.3 \(\Omega\). In the test process, every configuration was repeated four times to guarantee the accuracy of results. The final results were determined using a simple averaging method. According to the measured displacements, the system damping ratio \(\zeta\) could be calculated using the logarithmic decrement method:  
Figure 3:0  
where \(A_{i}\) denotes the amplitude in the \(i\)th peak of displacement. Additionally, the natural frequencies \(f_{\rm n}\) were extracted from the time histories of the displacements using FFT (Fast Fourier Transformation). Since the prisms are immersed in air, the added mass can be negligible due to the low density and the viscosity of air. The mass of oscillation system can be calculated by the following expression. Figure 3:1  
The damping coefficient \(c\) of the oscillation system can be calculated by the following expression. Figure 3:2  
The results of free-decay tests are listed in Table 1 and Figure 3:3 In the table, the external load resistance \(R_{\rm L}\), the damping ratio \(\zeta\), and the natural frequency \(f_{\rm n}\) are measured; the load resistance ratio \(R^{*}\), mass of the oscillation system \(m\), damping coefficient \(c\), and the short-circuit equivalent damping coefficient \(c_{0}^{*}\) are calculated using the measured data. As shown in Table 1, \(m\) and \(c_{0}^{*}\) remain approximately constant when \(R^{*}\) varies from 6 to 52 \(\Omega\). The average of \(m\) is 32.90 kg, and the average of \(c_{0}^{*}\) is 6.393. The mechanical damping ratio \(\zeta_{\rm m}\) can be obtained at the open circuit (O/C) case where \(R^{*}\) goes to infinity. The value of \(\zeta_{\rm m}\) is 0.132, which is also presented in Figure 3:4 Then the mechanical damping coefficient \(c_{\rm m}\) can be calculated as 52.22 N\(\cdot\)s\(\cdot\)m\({}^{-1}\). The trends of \(c\) versus \(R^{*}\) based on the test results and calculated results are plotted in Figure 3:5 The calculated results are obtained by Equation (6). The two curves agree very well. The above results from the free-decay tests indicate that using the PTO to control the damping coefficient is reasonable.