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🧪 Mathematics Differential Equations Simulation

Interactive mass-spring-damper simulator for the second-order linear ODE my'' + cy' + ky = 0: adjust mass, damping and stiffness, watch the characteristic roots move on the complex plane, and see the exact analytic solution animate an overdamped, critically damped, underdamped or undamped mass in real 3D.

Mathematics2DModerate60 FPS📱 Mobile-adapted

This simulator makes the second-order linear differential equation my″ + cy′ + ky = 0 physically tangible as a mass on a spring with a damper. Instead of integrating step by step, it solves the equation exactly through its characteristic roots, plotted live on the complex plane, and animates the resulting closed-form y(t) driving a real 3D mass through overdamped, critically damped, underdamped and undamped regimes as you drag the mass, damping and stiffness sliders.

⚙ Under the hood

This simulation demonstrates differential equations and their solutions through interactive visualizations. It allows users to explore different types of differential equations and their behavior.

Differential EquationsSecondOrderSolutions

2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install