## 3 Results and Discussion
After removing the force, the pendulum will start generating electricity when it reaches a certain angle, and the potential energy of the pendulum is used to generate electricity. Therefore, the power generation of the pendulum is the same as the potential energy difference of the pendulum, which initiates the power generation and potential energy of the equilibrium position. \[W_{out}=\Delta U=mg\Delta h=mgl(1-\cos\theta) \tag{7}\]  
Equation (7) represents the amount of change in potential energy, that is, the amount of power generated by potential energy, where m is the mass of the pendulum, \(1\) is the length of the pendulum, and g is the gravitational acceleration. The height difference between the angle at which the pendulum starts generating power and the equilibrium position is given by \(\Delta\)h, and it corresponds to the difference in y-axis position between the power generation start position from the equilibrium position, as shown in Figure 2. The input and output work can be derived using a mathematical model of the pendulum which begins to develop when the displacement of the pendulum reaches a certain angle. Using this, the power generation efficiency corresponding to the pendulum mass m, pendulum length l, and power generation angle \(\alpha\) can be derived. Figure 4 shows the time required to reach the power generation angle according to the pendulum mass and length. It can be observed that the longer the length and the greater the mass of the pendulum, the longer it takes to reach the generating angle. In addition, the pendulum length was short, there was no significant difference in the time required for the different pendulum mass values to reach the power generation angle. Once the time to reach the power generation angle is determined, the input and output of the generator can be calculated using Equations (6) and (7), and the power generation efficiency can be defined as follows:  
\[\eta=\frac{W_{out}}{W_{in}} \tag{8}\]  
Figure 4: Time to reach the angle of generation according to the mass and length of the pendulum. Equation (8) expresses the efficiency of the generator, Here, \(W_{in}\) is the amount of work input until the pendulum reaches the power generation angle derived from Equation (6), and \(W_{out}\) is the power generation energy of the pendulum at the power generation angle derived from Equation (7). Using Equation (8), the efficiencies according to the length of the pendulum, mass of the pendulum, and angle of power generation can be obtained. Figure 5 shows the power generation efficiency depending on the mass and length of the pendulum, where the power generation angle \(\alpha\) was fixed at \(\pi/6\). The efficiency tends to increase as the pendulum mass increases, but drops sharply at approximately 1 kg, 6 kg, and 10 kg. These are the points at which the time to reach the power generation angle mentioned in Figure 3 and Table 1 changes non-linearly. This can occur when fixing the generation angle and is a consideration in generator design. The pendulum length does not affect the efficiency, but only the period of the pendulum. Figure 6 shows the dependence the efficiency on the length of the pendulum and power generation angle \(\alpha\), when the mass m of the pendulum was fixed at 1 kg. Figure 6 also shows that the efficiency does not change linearly with the generation angle. It can be seen that the generation efficiency is low at the generation angle \(\alpha\) values of \(\pi/30\), \(\pi/12\), and \(2\,\pi/15\). Interestingly, the length of the pendulum has no effect on the power generation efficiency, only on the period of the pendulum. Figure 7 is a color map showing the efficiency depending on the mass of the pendulum and the power generation angle \(\alpha\), where the pendulum length l was fixed at 1 m. On this color map, the white circles indicate points of maximum generator efficiency for a certain section; a pendulum mass of 4 kg and the generation angle \(\alpha\) of 7 \(\pi/60\) characterize one of the maximum efficiency points.