The Aging Spring
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.[more]
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.[less]
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.