Damped oscillator in phase space
A mass on a spring, drawn not as one curve but as a whole flow. Retune the parameters and watch the trajectory spiral, crawl, or orbit.
- trajectory
- initial state
- equilibrium
- vector field
The arrows show the flow of the system at every point; the bright curve is the path traced from the chosen start. Underdamped (0 < ζ < 1) spirals inward to rest; critical and overdamped (ζ ≥ 1) decay straight in; ζ = 0 orbits forever.
What you're looking at
The horizontal axis is position x; the vertical axis is
velocity v. Every point in this plane is a possible state of
the oscillator, and the amber arrows show where the system moves next
from there. The bright teal curve is the actual path traced from the
starting state you choose (click or drag inside the plot).
The three regimes
The behaviour is governed by the damping ratio
ζ = λ / (2√(k·m)). When 0 < ζ < 1 the
motion is underdamped and spirals inward to rest. At
ζ = 1 it is critically damped, and for
ζ > 1 overdamped — both slide straight
into the origin without overshooting. Set damping to zero and the state
orbits forever on a closed loop.
Want the maths behind the picture? Read Reading a phase portrait.