Check out the Real Space, Position/Velocity vs Time, Phase Space Projection and Phase Space Orbit views.

The initial state chosen for this display was such that the motion was nearly like the pendulum. The system quickly settled into a rhythm in synchronization with the current through the magnet. Notice that there is one cycle of oscillator motion for one cycle of the forcing function. In the projection of the phase space orbit on the (x,x') plane again the similarity to the pendulum will be obvious.

You may notice that the plot is not perfectly stable at first. If our initial conditions do not lie precisely on the attractor, there will be some transient before the system settles on the attractor. Just click on Color to sort this out.

Just to review the full phase space orbit representation including the time dimension. The white ellipse represents the time axis. The period represented by the length of the elliptical track, the cycle time is the same as the period of the forcing magnetic field. Each time the orbit returns to the (x-x') plane the point is marked in a distinctive color. The position and, velocity axes are reproduced on this sectioning plane. The spots marked on this plane by the returning orbit are the Poincaré section of the orbit, in this case a single point.

The time axis ellipse actually is a circle viewed from in front and above. The x-axis is in the plane of the circular time axis, oriented with positive numbers toward the exterior of the time circle and perpendicular to the time axis at the point of intersection. The x'-axis is perpendicular to both the time circle and the x-axis. It is oriented vertically on the screen with positive values above the time axis and negative values below. One could imagine the (x,x') plane traveling around the time circle with the advancing orbit.