# Influence of the Motion of a Spring Pendulum on Energy-Harvesting Devices
## 1 Introduction  
Energy harvesting (EH) has been a substantial aspect of research work in the previous few years. It transforms the surrounding energy presented on Earth into electrical power to drive autonomous electronic devices or circuits [1, 2]. This energy can be harnessed from solar energy, thermal energy, and the most vital source for harnessing, kinetic energy, especially from vibrational motion [3]. EH depending on vibration can drive devices like sensors and wireless electronics as well as monitoring applications [4]. Its mechanism's models depend on the uses of electromagnetic, piezoelectric, and hybrid electromagnetic devices. In [5], [PERSON] et al. designed an electromagnetic generator to convert the environment vibrational energy into an electrical one to power sensor devices. The response of a harvester of energy is investigated in [6]. In [7], the authors computed the coupling due to the electromagnetic energy harvesters and deduced the resonant harvesters' output voltage. A prototype was designed in [8] to harvest energy from the speed of passing vehicles and control their speed simultaneously. In [9], the authors investigated a self-powered and self-operating tracking system based on an electromagnetic hybrid friction blue energy-harvesting module, theoretically and experimentally. The unique spin of the designed gyro enables the system to search for the energy of low-frequency wave and non-uniform vibration with high efficiency. A hybrid designed propeller wheel was reported in [10] with a nano-coupled triboelectric generator and an electromagnetic generator that can harvest the wind's energy even in a weak airflow. At the same time, [PERSON] et al. [11] harvested energy from low frequency. They used a piezoelectric energy harvester (PEH) with stoppers and tuned the device at monostable mode to avoid problems in a bistable or tristable system. A multi-mode PEH with analytical modeling is investigated in [12] to produce different close peaks of the voltage output from the vibrational sources. In [13], theoretical and experimental broadband PEH studies depend on kinetic energy with a triple well potential generated by the magnetic field. The mathematical model is examined to show the response of tristable energy generators. A comparison between three nonlinear planar springs, namely bi-leg, quad-leg, and pent-leg designs, is presented in [14] to examine the influence of the interaction of a vibration mode to extend the operating frequency range of the PEH. In [15], the authors answered the question: How can the electricity be generated from a mechanical structure driven by vapor momentum? They investigated a design of an energy harvester that experimentally depends on vapor-induced vibration for the heat pipe application. The velocity of the vapor impacted the induced power of the device. A report on a cost-effective wearable PEH using electrophoresis, conductive fabrics, and coated with nickel-copper-polyester is presented in [16]. The finite element method (FEM) was used in [17] to obtain the numerical results of the effectiveness of the piezoelectric layer's length and thickness on the von Mises stress. The influence of increasing the seismic mass's thickness on the cantilever structure's resonance frequency was studied in [18], in which the FEM was applied to achieve numerical results. It is observed that the resonance frequency of the cantilever decreased with increasing size of the seismic mass. The authors [19] presented the design, manufacture, and testing of an underground double-axis PEH based on the piezoelectric stack. A modified numerical method was utilized in [20] to obtain the solutions of second-order boundary value problems of ordinary differential equations (ODEs) directly for Dirichlet and mixed cases. In addition, a hybrid single-step implicit block method was used to solve the nonlinear differential equation of a circular sector oscillator in [21]. Significant success was achieved in solving the stiff ODEs using the hybrid single-step implicit block method.