The Aging Spring

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The dynamical system governed by the following time-varying ordinary differential equation is a variation of the classic forced mass-spring-dashpot system with mass , dashpot constant , constant stiffness , and forcing term . Aging springs are characterized by a stiffness decaying with time. Here an exponential decay from an initial value at time zero to an asymptotic value is considered.

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Mathematica can integrate this equation exactly, but the solution in general is a huge expression involving BesselJ and Gamma functions, together with their integrals; it is very difficult to imagine their behavior as time advances.

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Contributed by: Adriano Pascoletti (March 2011)
Open content licensed under CC BY-NC-SA


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This Demonstration was stimulated by the paper:

T. J. Lardner, "Resonance and the Aging Spring," ASME Jnl. of Applied Mechanics, 69(3), May 2002 pp. 397-398.



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