Physical Principles & Mathematical Derivation
Robert Hooke's linear restoring force F = −kx produces pure sinusoidal Simple Harmonic Motion x(t) = A cos(ω₀t + φ), whose period depends exclusively on mass inertia m and spring stiffness k — completely independent of initial stretch amplitude A!
Questions & Concepts
What physical equation governs Hooke's Law & Mass-Spring Simple Harmonic Motion Simulator?
F = −k × x, ω₀ = √(k / m), T = 2π√(m / k) — Robert Hooke's linear restoring force F = −kx produces pure sinusoidal Simple Harmonic Motion x(t) = A cos(ω₀t + φ), whose period depends exclusively on mass inertia m and spring stiffness k — completely independent of initial stretch amplitude A!
How are the equations of motion integrated in this simulation?
Nonlinear differential equations are integrated at 240–300 Hz substeps using classical 4th-order Runge-Kutta (RK4) to maintain strict Hamiltonian energy accuracy.