Oscillator what's the steady state? I'm wondering what's the steady state for an oscillator.
Is it a system without driving force so without external force to disturb the system?
If a system oscillates without driving force can we say the system is in the steady state?
 A: 
Is it a system without driving force so without external force to disturb the system?


If a system oscillates without driving force can we say the system is in the steady state?

These two questions aren't phrased properly. Steady state is not a property of the system. It is a state that the system achieves.
If you want to get real technical, the solution to the differential equation that describes the oscillating system is an equation that contains two terms/parts:

*

*The transient part which decays to zero over time.

*The steady state part does not.

Steady state is reached when the transient part of the equation has decayed to zero leaving only the steady state part remaining.
The less technical way of saying this is that it is when the oscillation starts to behave the same way it would at infinite time (i.e. when it reaches an equilibrium).
If you adhere to this definition, it means...

*

*A system with no losses, after the initial forcing function has been removed, has reached steady state once it begins to oscillate in the same way it would oscillate at infinite time.

*A system with losses with a continually applied (and unchanging) forcing function has reached steady state once it oscillates in the same way it would at infinite time.

*A system with losses, after the forcing function has been removed reaches steady state when it oscillates in the same way it would at infinite time (i.e. which would be when the oscillations stop)

A: Oscillatory dynamical systems return many times in the neighborhood of some reference configuration. In the particular case of a periodic evolution, we speak of steady oscillations. Notwithstanding the opinion of who voted for closing this question as "opinion-based," this definition is not an opinion at all.
Any strictly periodic motion of linear or non-linear oscillators is a steady oscillation.
Periodically forced and damped harmonic oscillators reach a steady state of oscillations after the initial transient has decayed enough to be negligible.
Examples of non-steady oscillations are the motion of a forced harmonic oscillator at a resonance (diverging oscillations) or quasi-periodic motions like the superposition of two incommensurate frequencies harmonic motions.
A: For an oscillator (damped and also driven), the solution to the motion equation has two parts, a transient part (dependent of the initial condition - position and velocity - of the particular problem) and a steady-state part (which is dependent of the driving force). They must be used together to fit the physical boundary conditions of the problem.
The total solution is of the form:
$$x(t) = x_{transient}(t) + x_{steady-state}(t)$$
