Stability Analysis of a Mass-Spring System under the Influence of an Electric Field Using Transfer Function

This research investigates the dynamic stability of a mass-spring system under the influence of an electric field using the analytical transfer function method. The mass-spring system, as a fundamental model in mechanical vibrations, exhibits altered stability criteria when subjected to electrostatic forces. By linearizing the nonlinear governing differential equation of the system, an effective stiffness term incorporating the electric field's influence is derived. The system's transfer function is obtained via Laplace transform, enabling stability analysis in the frequency domain through pole placement. In the non-oscillatory stable state and the damped oscillatory state under weak electric fields, the system remains stable, and the poles are located in the left half of the complex plane. In the marginally stable state at a critical voltage, one of the poles reaches the origin, indicating neutral stability. The instability of the system is such that under strong electric fields, a positive real pole appears, leading to instability. The results highlight the interplay between mechanical damping and electrostatic forces, offering insights for designing microelectromechanical systems where electric fields are utilized for actuation. This study bridges classical mechanics and control theory, providing a framework for stability analysis in electromechanical systems.