## 4 Simulation and Experiment Analysis
### Simulation Analysis  
Main parameters values of the LOLS are shown in Table 1.  
Based on the mathematical model and the block diagram of the LOLS built above, the simulation analysis of the dynamic performance of the LOM with external spring force load can be finished as shown in Figure 13, and the simulated spring stiffness is 133.33 N/mm, 66.67 N/mm and 33.33 N/mm corresponding to amplitude force of 400 N, 200 N and 100 N, respectively.  
As can be seen in Figure 13, spring forces affect both phase responses and amplitude responses as the phases advance by 8.78\({}^{\circ}\), 5.62\({}^{\circ}\) and 0.65\({}^{\circ}\), and the amplitude responses reduce by 5.5%, 4.1% and 2.7%, corresponding with amplitude forces of 400 N, 200 N and 100 N respectively, compared with no load. So phase advances and amplitude attenuation extend as the simulated spring stiffness becomes bigger.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Simulation Model Parameters** & **Value** \\ \hline Force constant coefficient of the LOM \(K_{\text{e1}}\)/(N/A) & 32 \\ Force constant of the VCM \(K_{\text{e2}}\)/(N/A) & 25 \\ Spring stiffness k/(N/m) & 18,141 \\ Damping force of the LOM \(f_{\text{c1}}\)/N & 50 \\ Damping force of the VCM \(f_{\text{c2}}\)/N & 10 \\ Mover mass of the LOM \(m_{\text{l}}\)/kg & 1.28 \\ Mover mass of loading mechanism \(m_{\text{2}}\)/kg & 1.1 \\ Resistance of the LOM \(R_{\text{l}}\)/\(\Omega\) & 2.6 \\ Resistance of the VCM \(R_{\text{2}}\)/\(\Omega\) & 1.2 \\ Coil inductance of the LOM \(L_{\text{l}}\)/H & 0.024 \\ Coil inductance of the VCM \(L_{\text{2}}\)/H & 0.0033 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Main parameters of the LOLS.  
Figure 12: Block diagram of the linear oscillating load system (LOLS).  
Similarly, the dynamic performance of the LOM with external damping force loads is depicted in Figure 14, corresponding with the amplitude damping forces of 200 N and 400 N respectively.  
As it can be seen in Figure 14, damping forces have an effect on amplitude responses particularly as the amplitude responses reduce by 6.1% and 11.5% corresponded with the amplitude damping forces 200 N and 400 N respectively, compared with no load. Damping forces merely affect the amplitude responses; as the amplitude damping force is bigger, the amplitude attenuation is bigger.  
Similarly, the dynamic performance of the LOM with external rectangular force loads is depicted in Figure 15, corresponding to the amplitude rectangular forces of 200 N and 400 N respectively.  
As can be seen in Figure 15, rectangular forces have effects on the position outputs, especially on the amplitude responses as these reduce by 16.6% and 8.5% correspo  
Figure 14: Position outputs under different damping loads.  
Figure 13: Position outputs under different spring loads.  
Figure 15: Position outputs under different rectangular loads.  
rectangular forces of 200 N and 400 N respectively, compared with no load. Rectangular forces have effects on the amplitude responses more seriously than effects of damping forces at the same force load amplitude.  
For these three types of force load, damping force and rectangular force only has effects on the amplitude response as the bigger the amplitude force is, the bigger the amplitude attenuation, while the spring force have effects not only on the amplitude response but also on the phase response as the bigger the amplitude force is, the bigger the amplitude attenuation and phase advance are. Because the spring stiffness is increased owing to the added spring load, to raise the cut-off frequency of the LOM leads to smaller phase lag.