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.
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.

THINGS TO TRY

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

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.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.