Mass with a Spring and a Rubber Band

This system consists of a mass attached to both a spring and a rubber band subject to an external force proportional to , where is the angular frequency. The other controls are the damping factor and the restoring forces and . The spring obeys Hooke's law, as does the rubber band when it stretches, but not when it contracts. Systems of this type have been suggested as possible causes of the collapse of the Tacoma Narrows Bridge.


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The equation of motion is
The gravitational acceleration is approximated as 10 .
[1] P. Blanchard, R. L. Devaney, and G. R. Hall, Differential Equations, 4th ed., Boston: Brooks/Cole, 2012, pp. 454–456.
[2] Tacoma Narrows Bridge Collapse "Gallopin' Gertie." [Video]. (Dec 9, 2006)
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