If the damping is too large, then resonance cannot occur. Never the less, "resonant frequency" is widely enough used to qualify as an idiom. Difference between Resonance and Natural Frequency Saturday, August 29, 2015 If you have an electrical circuit consisting of a capacitor (capacitance C) and an inductive coil (inductance L) and you load the capacitor, you will observe a sin-wave oscillation in this circuit as soon as you remove the supply. A cut-off frequency refers to the frequency at which the impulse response of a filter starts to fall off. The resonant frequency is fo. The amazing thing is that every time you hit it, it will vibrate with exactly the same frequency, no matter how hard you hit it. It is very important to understand and measure the natural frequency of a system in order to protect it from such natural disasters. Events such as earthquakes and winds can do destruction on objects with the same natural frequency as the event itself. This means that the amplitude of the vibration stays the same. What about the case of small damping?
The frequency of un-damped oscillations in a system, which has been allowed to oscillate on its own, is called the natural frequency, f0. When a system (e.g. Free vibrations are oscillations where the total energy stays the same over time. Note that resonance can only occur when the natural frequency is greater than the damping rate, multiplied by the square root of 2. That's why "resonance frequency" would be the better choice.
Question: /**/ Natural Frequency Hit anything and it will vibrate. If an object is being forced to vibrate at its natural frequency, resonance will occur and you will observe large amplitude vibrations. The damage was concentrated in a 25 km² area of Mexico City, 350 km from the epicenter(the part of the earth's surface directly above the focus of an earthquake). Natural Frequency & Resonance Name : Date : Level : PhysicsI Teacher : Kim On September 19, 1985, at 7:17 A.M., a Richter magnitude 8.1 earthquake occurred on the Pacific coast of Mexico.
More likely, you mean to describe the frequency of resonance of some system. The natural frequency is a property of the object itself: it will always vibrate at the same frequency independent of how hard or where it is plucked. The introduction of a moderate dampening term  will introduce a real component to the roots and move them such that the resonant frequency is slightly less than the undamped natural frequency. All physical objects have multiple natural frequencies and can resonate under the right conditions. The term resonant (adjective) frequency (noun) implies that it the frequency that is resonating. Resonant frequency vs natural frequency of a driven damped mechanical oscillator .
Natural frequency is directly related with resonance. A force had to be applied to cause the string to resonate and be heard. A stronger dampening term ( )  will decrease the frequency even more but the response at the frequency will be attenuated and have little effect.