## 3 Results and Discussion  
As explained in Section 2, the pendulum movement can be found using Equation (5). Applying a force with the same frequency as the pendulum's resonant frequency causes the pendulum to diverge over time, which can be used to reach the angle for power generation. The solid line in Figure 2 is a graph representing the \(\theta\) value of Equation (5), the horizontal axis represents time, the vertical axis represents the angle \(\theta\) of the pendulum, and \(\alpha\) is the angle at which power generation start. When the pendulum angle reaches angle \(\alpha\) in the forward or reverse direction, power generation begin, and when the pendulum stops at the equilibrium position, the force is applied again to move the pendulum. To obtain the amount of work at this time, it is first necessary to determine the time it takes for the pendulum angle theta to reach the start angle of power generation. In Figure 2, where the solid and dotted line meet, the value of the horizontal axis can be obtained and derived. From Equation (5), the time taken for the pendulum to move to the angle for power generation is determined by the mass of the pendulum \(m\), the length of pendulum \(l\), and the power generation angle \(\alpha\). Figure 2: Angular displacement of the pendulum \(\theta\). Figure 3 shows the displacement of the pendulum for the following masses: 1 kg, 1.4 kg, 1.8 kg, 2.2 kg, and 2.4 kg depicted using solid lines and symbols. In addition, the angle \(\alpha\) at which power generation starts can be determined by the user. An arbitrary value \(\pi/6\) was used in Figure 3. The power generation time (\(t_{1}\) to \(t_{5}\)) can be derived from the intersection of the solid line and the dotted lines. Table 1 lists the time required to reach the power generation angle for each mass. Table 1 summarizes the power generation time according to the mass of the pendulum with \(\pi/6\) determined by the power generation angle, which is \(\Delta t=t_{n+1}-t_{n}\). Based on the time required to reach \(\alpha\), as listed in Table 1, it can be observed that as the mass increases, the time to reach the power generation angle also increases. From the \(\Delta t\) values in Table 1, it can be confirmed that \(t_{n}\) increases in intervals of approximately 1.05 s as the mass of the pendulum increases; however, the interval between 1.4 kg and 1.8 kg is 1.88 s. From this, it can be seen that \(T_{\alpha}\) does not change linearly as the mass increases, but there is a section in which it increases nonlinearly. A phenomenon in which the efficiency of the generator decreases occurs in such a nonlinear part, and the specific content of efficiency will be discussed in this section. As described in the earlier, when determining the design parameters and deriving the time taken to reach the development angle, the amount of work performed by the MG until the pendulum starts to develop can be also determined. \[W_{in}=\int_{0}^{T_{\alpha}}M(t)\cdot\dot{\theta}\,dt \tag{6}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Mass of Pendulum** & **Time to \(\alpha\) (\(T_{\alpha}\))** & \(\Delta\)\(t\) \\ \hline \(t_{1}\) & 1 kg & 3.42 s & - \\ \(t_{2}\) & 1.4 kg & 4.49 s & 1.05 s \\ \(t_{3}\) & 1.8 kg & 6.37 s & 1.88 s \\ \(t_{4}\) & 2.2 kg & 7.42 s & 1.05 s \\ \(t_{5}\) & 2.4 kg & 8.46 s & 1.04 s \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Power generation angles by mass. Figure 3: Absolute value of pendulum displacement with mass. Equation (6) derives the amount of work from the moment the pendulum receives the force at the equilibrium position to the end of the movement. Here, M(t) is the torque, \(T_{\alpha}\) is the time taken to start generation, \(\dot{\theta}\) is the speed of the pendulum. The forces are in the form of torque and are developed in response to clockwise (\(-\)) and counterclockwise (\(+\)) bi-directional displacements.