# Pendulum with Direction Field

Physics-based simulation of a pendulum, showing both a phase graph and the direction
field (or slope field) associated with the differential equation.

Click the "Sim" tab to access parameters such as: gravity, mass or friction (damping).
Drag the pendulum to change the starting position. Or click below to set some
predefined initial conditions.

See the page about the
single pendulum
for more about how pendulums work and the math behind this simulation. This simulation
is identical to that one, but adds a graph of the
direction field
(AKA slope field) of the differential equation. This direction field is shown
overlapping the phase space
graph of angular velocity vs. angle. At each point, the path of the pendulum in phase
space is along the direction field.

Also available:
source code,
documentation and
how to customize.

## Experiments to try:

- Notice that the path through phase space is always along the direction field.
- Which parameters (damping, gravity, mass, length) change the direction field?
Why do they or don't they change the direction field?
- Try bigger faster motions of the pendulum (drag the pendulum to a high starting
point, or give it a high start velocity). Notice that it still moves along the
direction field in phase space.
- Turn on "show energy". When is kinetic energy highest? When is potential energy
highest?