# Two-Degrees-of-Freedom (2 DOF) Magnetic Spring-Based Electromagnetic Energy Harvester
## 8 Conclusions  
This study proposed and analysed a two-degrees-of-freedom (2 DOF) magnetic spring-based electromagnetic energy harvester through an integrated approach combining analytical modelling, numerical simulation, prototyping, and experimental validation. The dual-floating-magnet configuration enabled the system to harness two resonant modes, offering a broader frequency bandwidth and increased energy-harvesting potential compared to single-degree-of-freedom (SDOF) designs. The nonlinear magnetic restoring forces were modelled using fitted polynomials, and system dynamics were solved using the state-space approach in MATLAB with the ODE23t solver, chosen for its capacity to handle moderately stiff electromechanical systems. Analytical results for induced voltage and system response were compared against experimental measurements, showing good agreement in both waveform and amplitude trends, with peak-induced voltages reaching approximately 7.2 V (analytical) and 7.0 V (experimental) under 15 N excitation.  
While the model demonstrated strong predictive capability, certain discrepancies remain between the simulated and experimental results. These differences are attributed to idealised assumptions in the modelling process--such as the perfect alignment of magnetic components, neglect of minor frictions, uniform magnetic field distribution, and simplified coil dynamics--which are challenging to replicate precisely in physical prototypes. These assumptions introduce uncertainty, especially under high displacement or nonlinear regimes, and highlight the scope for further refinement.  
Future work will aim for the following objectives:  
* Improve the modelling of magnetic interactions through more accurate finite element- or machine learning-assisted characterisation.
* Incorporate real-world effects such as friction, misalignment, and coil saturation.
* Optimise circuit load configurations for efficient power conditioning.  
Despite its limitations, the proposed system confirms that 2 DOF magnetic spring-based architectures are promising for broadband, low-frequency vibration energy harvesting. This work contributes both a robust modelling framework and valuable experimental validation, laying a foundation for more advanced and scalable harvester designs.  
Conceptualization, R.A., I.H. and K.M.; methodology, R.A. and K.M.; software, R.A.; validation, R.A.; formal analysis, R.A.; investigation, R.A.; resources, R.A.; data curation, R.A.; writing--original draft preparation, R.A.; writing--review and editing, I.H. and K.M.; visualization, R.A. and K.M.; supervision, I.H. and K.M.; project administration, K.M.; funding acquisition, K.M. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The data presented in this article are available on request from the corresponding author.  
The authors gratefully acknowledge the Australian Government Research Training Program Scholarship for [PERSON]'s study at Curtin University, Australia.  
The authors declare no conflicts of interest.