Physical Principles & Mathematical Derivation
From suspension bridges (Tacoma Narrows) and seismic building dampers to quartz crystal clocks, mechanical resonance occurs when periodic external forcing pumps energy in phase with natural velocity, peaking sharply when fd ≈ f0.
Questions & Concepts
What physical equation governs Driven Harmonic Oscillator & Mechanical Resonance Simulator?
A(ω) = (F₀ / m) / √[ (ω₀² − ω²)² + (c·ω / m)² ] — From suspension bridges (Tacoma Narrows) and seismic building dampers to quartz crystal clocks, mechanical resonance occurs when periodic external forcing pumps energy in phase with natural velocity, peaking sharply when fd ≈ f0.
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.