## 2 Experimental Setup and Processing Methods
### AVD Conversion Method
\[a(t)=-\omega^{2}G\exp(i\omega t)=\big{(}-\omega^{2}G\big{)}\cdot\exp(i\omega t) \tag{8}\]  
where \(-\omega^{2}G\) is constant and \(\int e^{-i\omega t}dt=\frac{1}{i\omega}e^{-i\omega t}\). Equations (2) and (3) can be expressed by Equations (9) and (10), respectively. \[v(t)=\frac{1}{i\omega}\big{(}-\omega^{2}G\big{)}\cdot\exp(i\omega t) \tag{9}\]  
\[d(t)=\frac{1}{(i\omega)^{2}}\big{(}-\omega^{2}G\big{)}\cdot\exp(i\omega t)=G \cdot\exp(i\omega t) \tag{10}\]The complex constant of Equation (7) can be rewritten as Equation (11). \[v(t)=G\exp(i\omega t) \tag{2}\]0  
By substituting Equation (11) into Equation (10), the displacement in the time domain can be calculated using Equation (12). \[v(t)=G\exp(i\omega t) \tag{2}\]1  
Here, \(H_{2}(\omega)\) is a correction filter in the frequency domain. \[v(t)=G\exp(i\omega t) \tag{2}\]2  
Since it is difficult to set the reference point (fixed point) in order to measure the temporal change, it is necessary to measure the temporal change of the acceleration, and then to calculate the displacement by integrating it twice. However, when the acceleration, including the measurement error, is integrated twice and integrated into the displacement, the displacement includes the amplified additional error, due to the two integral transformations. In this study, numerical integration, such as Fourier transform, has been used to convert acceleration into velocity and displacement. The Fourier transform is more simply a numerical integration; it is the decomposition of a periodic loading into a harmonic series. Here, \(H_{2}(\omega)\) is a correction filter in the frequency domain [32]. Figure 5 shows the flowchart for the conversion of the acceleration data in Method 1. The acceleration data measured in the time domain should be transformed by the Fourier transform function in order to convert them into the frequency domain. \[v(t)=G\exp(i\omega t) \tag{2}\]3  
In addition, \(A_{f}(\omega)\) is calculated again in order to correct the data in the frequency domain; \(H_{2}(\omega)\) is the correction filter multiplied to obtain the corrected Fourier transformed function \(A_{c}(\omega)\). \[v(t)=G\exp(i\omega t) \tag{2}\]4  
Then, velocity and displacement are calculated in the frequency domain. \[v(t)=G\exp(i\omega t) \tag{2}\]5  
\[v(t)=G\exp(i\omega t) \tag{2}\]6  
Finally, to convert them into velocity and displacement in the time domain, the inverse Fourier transform function is used. \[v(t)=G\exp(i\omega t) \tag{2}\]7  
\[v(t)=G\exp(i\omega t) \tag{2}\]8  
In this process, the content of the original signal is modulated on the basis of the transform function, reflecting the system characteristics. After being passed through the high-pass filter used at this juncture, the low-frequency components are removed. This solution, using the time domain method, solves the equation of motion in the time domain directly. In contrast, solutions that use the frequency domain method are obtained by converting the equation of motion in the time domain into the frequency domain. Generally, by using a Fourier transform to convert the equation of motion into the frequency domain, a solution can be found more efficiently than by finding it in the time domain. Moreover, by applying a discrete Fourier transform (DFT) using a fast Fourier transform (FFT) algorithm with a Fourier transform, the integrals used in the Fourier transform can be easily and quickly processed. The second method is time domain analysis. Figure 6 shows the flowchart for the conversion of acceleration data using Method 2. The load magnitude after the first load and the end of the measured load are assumed to be zero. There is zero padding. First, the acceleration (\(a_{0}\)) in the time domain is prepared and integrated so as to obtain the velocity (\(v_{0}\)) and the displacement (\(d_{0}\)). Next, a baseline correction of the initial acceleration (\(a_{0}\)) in the first-order linear equation is performed. \(c_{0}\) and \(c_{1}\) in Figure 6 are the coefficients of the first-order linear equation for the baseline correction.