Overdamping vs. convergent oscillation

[squeezed90]

I had a question regarding oscillatory motion in a spring-mass-damper system. I understand the concepts of over, under, and critical damping and the criteria which determine them, but I'm wondering if they are equivalent to the concepts of convergent, divergent, and stable oscillation.

I don't think they are, because even underdamping results in a return to the initial state but with oscillation, while divergent and stable oscillations do not.

So I guess my question is, can someone explain the criteria for stable oscillation? If possible, please post a link where I can get more information, I can't seem to find anything online.

Thanks

 

[Bill_K]

Stability theory of dynamical systems is a complex field, since it is usually applied to very general situations which may include damping, driving terms and nonlinearity. I don't know of a simple criterion. The corresponding terms for a linear system are damped, undamped and antidamped. Look up 'Lyapunov stability' on Wikipedia for starters.