Spring-Mass System
Interactive simulation — adjust parameters and watch the visualization update in real time.
Live graphs
How it works
A mass on a frictionless horizontal surface attached to an ideal spring obeys mẍ + cẋ + kx = 0. With light damping, oscillations decay; without driving, energy sloshes between kinetic and potential ½kx².
Key equations
mẍ + cẋ + kx = 0
ω₀ = √(k/m), PE = ½kx²
Underdamped: ωd = √(ω₀² − (c/2m)²), T = 2π/ωd. Undamped motion uses velocity Verlet for better energy behaviour.