Mirror Vibration Dynamics on Spring Systems

In this simulation program, we investigate the mechanical interaction between a spring plate and an attached mirror. When the spring undergoes oscillation, it transmits kinetic energy that induces corresponding vibrations in the mirror. Our computational model recreates this physical phenomenon using numerical integration methods to solve the spring-mass-damper system equations. The implementation involves defining spring constants (k), damping coefficients (c), and mirror mass parameters within the simulation environment. The core algorithm calculates displacement vectors using Hooke's Law (F = -kx) combined with Newtonian motion equations. Through real-time visualization, we observe how the mirror's positional harmonics correlate with the spring's oscillation frequency. Furthermore, the program incorporates parametric studies to analyze how different spring types (compression, torsion, leaf springs) and mirror configurations affect vibration responses. The code structure includes modular functions for: 1) Initial condition setup, 2) Time-domain solution using Runge-Kutta methods, and 3) Dynamic visualization routines plotting displacement versus time graphs. This simulation framework provides insights into spring-material properties and mirror dynamics, demonstrating practical applications in optical system stabilization and vibration analysis within physics engineering contexts.