Simulations — TgN Virtual Lab
Interactive mechanics simulations. Adjust parameters and observe animation and real-time graphs simultaneously.
Equations solved with 4th-order Runge–Kutta (RK4) numerical integration — reference: myphysicslab.com
Equation of Motion
m · ẍ = −k · x − c · ẋ
m = mass (kg) • k = stiffness (N/m) • c = damping • x = displacement from equilibrium
Single Spring–Mass System
Spring – Mass – Damper — 1 DOF
Animation
Graph
Equation of Motion (Non-linear)
θ̈ = −(g/L) · sin(θ) − (c/mL²) · θ̇
g = 9.81 m/s² • L = length (m) • θ = angle from vertical (rad) • m = mass (kg)
Simple Pendulum
Non-linear ODE with damping
Animation
Graph
Equations of Motion (2 DOF)
m₁ẍ₁ = −k₁x₁ − k₂(x₁−x₂) − cẋ₁
m₂ẍ₂ = −k₂(x₂−x₁) − cẋ₂
Normal modes: in-phase and anti-phase coupled oscillation
Coupled Spring–Mass System
Two masses connected by springs — normal modes
Animation
Graph