The Nature of Natural Frequency

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I've been told that the natural frequency of an oscillator is the frequency an oscillator will oscillate at when left to itself. Is this referring to the frequency of an ideal oscillator subject to ONLY a restoring force. Because all REAL oscillators are subject to damping and, when left to themselves, will oscillate at a frequency different than the ideal case. Even if the difference is small for many cases, it is still different. So is the "natural frequency" the frequency a REAL oscillator will oscillate at when left to itself or is it the frequency of the ideal oscillator with no damping? Please don't refer me to a Wikipedia page. Thank you
 
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cdot said:
I've been told that the natural frequency of an oscillator is the frequency an oscillator will oscillate at when left to itself. Is this referring to the frequency of an ideal oscillator subject to ONLY a restoring force. Because all REAL oscillators are subject to damping and, when left to themselves, will oscillate at a frequency different than the ideal case. Even if the difference is small for many cases, it is still different. So is the "natural frequency" the frequency a REAL oscillator will oscillate at when left to itself or is it the frequency of the ideal oscillator with no damping? Please don't refer me to a Wikipedia page. Thank you

When you are told that "... natural frequency of an oscillator is the frequency an oscillator will oscillate at when left to itself.. ", were you also told that this is the ideal condition in which damping and other factors are not being considered?

Everything here has a proper context. If not, then we do not know what the "boundary conditions" are to be able to answer such a thing.

Zz.