Phase Portraits

Position and velocity together

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• The phase plane plots velocity against position: each solution is a path.
• Conserved energy makes paths follow energy curves: loops for swings, open curves for whirling.
• The separatrix divides behaviours; friction makes paths spiral into a stable equilibrium.

Steps

1. What do you need to know?
2. The phase plane
3. The pendulum’s portrait
4. Over the top
5. Small and large swings
6. Adding friction