Double-Spring Pendulum

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This Demonstration shows the motion of a double-spring pendulum. Despite its simplicity, typical chaotic behavior can occur. The animation shows the interactions of the two bobs connected by the spring, with and without the action of gravity.

Contributed by: Chihiro Ito and Reiho Sakamoto  (August 2019)
Open content licensed under CC BY-NC-SA


Parameters in the Demonstration:

The labels and stand for the upper and lower bobs.

1. Coordinates for the two bobs. The origin of the upper spring is .

The upper bob:

The lower bob:


: length of the spring

: angular displacement of the spring

2. The Lagrangian of the model:


: the mass of the bob

: constant of the gravitation

: spring constant

: length of the spring at equilibrium, with


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