Is Power Balance a Valid Criterion for Oscillating System Stability?

[micopl]

Lets consider this definition: If the average power supplied to the system (absorbed power) is less than the average power lost by the system (emitted power) then the system is stable (during the time in which the power was averaged). Is such a definition of stability valid?

 

[chrisbaird]

What kind of system do you have in mind? An exploding gas tank emits more power than it it absorbs, but I would not consider it stable. When you say a system emits more power than absorbs, that word that comes to mind is "active" (as opposed to passive), not "stable". For instance, if you shine a seed laser on a slab of rubber, it is passive and absorbs the energy. This is a passive material. If you shine a seed laser at a properly prepared tank of gas, it will amplify the signal. This is an active material.

Stability is better defined as a centroid of some sort of the system staying constant, such as the combined center of mass of two orbiting masses, or the equilibrium point of an oscillating mass. Stability typically happens in potential wells, whereas unstable equilibrium happens on potential peaks of potential saddle points.

 

[micopl]

I mean oscillating system which can be e.g. a mass connected to a spring, and the other end of the spring is forced with an oscillating force.

 

[chrisbaird]

I don't think such a system could be called unstable for any type case, unless the spring breaks. You could get erratic behavior, if the driving force oscillated slightly faster or slower than a natural frequency, but I would still consider it stable.

 

[PJC01]

I would say that this definition of stability is valid within the context of the specific system being described. In an oscillating system, the balance between absorbed and emitted power is crucial in determining its stability. If the average absorbed power is consistently less than the average emitted power, then the system will eventually lose energy and become unstable.

However, it is important to note that this definition of stability only applies to the time in which the power was averaged. In reality, most systems are subject to fluctuations and variations in power input and output, which can affect their stability. Therefore, it is necessary to consider the overall behavior of the system over time and not just at a single moment in time.

Moreover, other factors such as external influences, internal dynamics, and feedback mechanisms can also impact the stability of an oscillating system. Therefore, while this definition provides a useful starting point for understanding stability, it should not be considered the sole determining factor. A more comprehensive analysis is needed to fully assess the stability of an oscillating system.