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Spring in Field of Two Magnets

​
x(0)
0.1
′
x
(0)
-0.2
a
1
b
0.1
t
35.
This Demonstration shows the solution for the following system. An iron mass is constrained to slide on the
x
axis. The mass is attached to a spring anchored above the
x
axis and subject to an external force with amplitude
b
(red arrow), conforming to Hooke's law. The mass is also attracted to two long bar magnets with their poles shown as orange squares, placed at a distance
a
below the
x
axis. To a reasonable approximation, each magnet attracts the mass with a force proportional to the inverse square of its distance to the pole. Different types of qualitative behavior, including chaotic motions, can be seen in the phase portraits.
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