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.