Simple Harmonic Motion
Pull a mass on a spring away from equilibrium and release it — adjust mass, spring stiffness, and damping to see undamped, underdamped, critically damped, and overdamped motion.
Preview — sign up free to change the numbers yourself
What you can adjust
- Mass
- 0.1 – 10 kg
- Spring constant (k)
- 1 – 100 N/m
- Initial displacement
- 0.05 – 2 m
- Damping (c)
- 0 – 20 Ns/m
How far the mass is pulled from equilibrium before release.
0 = undamped (oscillates forever). Below the critical value the mass oscillates with decaying amplitude (underdamped); at or above it, the mass returns to rest without overshooting (critically damped / overdamped).
About this simulation
What it shows
A mass on a spring is pulled away from rest and released, and its position is drawn over time. Damping can be added to make the swings die away.
The key idea
The spring pulls back in proportion to the stretch, so the period is 2π√(m/k) however far you pull it. Damping removes energy: light damping shrinks the swings, strong damping stops them overshooting.
Try this
Leave Damping (c) at 0, then raise it above about 9 Ns/m (the critical value for the default mass and spring): the mass returns to rest without overshooting.