Question

Natural frequency seems to be a poorly defined concept [closed].

Per wikipedia:natural frequency, also known as eigenfrequency, is the frequency at which a system tends to oscillate in the absence of any driving force. Let's take a wine glass as an example. The wine glass sits on a table, it is not visibly moving. But since natural frequency exists, therefore it is oscillate on some minute scale. Where does the oscillation come from? Is it from the electrons and protons that are whizzing inside of the glass and getting excited due to stochastic heat? Is it because protons are hitting the surface of the glass? Or is it oscillating due to the minor tremor in the earth? Or perhaps the minute attractive force exerted upon it by all other objects? In each case, it is clear that there is a driving force: heat, proton's impact force, tremor. So clearly natural frequency must be associated with a type of oscillation that's not any one of the above. So where does the oscillation come from instead? It seems that given any source of this oscillation, you can identify a driving force. Hence such driving force is never absent, hence there is no natural frequency. Are all objects naturally oscillatory and that natural frequency is like a fundamental aspect of an object, such as its 'mass'? If so, can we identify this natural frequency in some way? E.g., I want to know my body's natural frequency at this moment. The Wikipedia definition of natural frequency is a poor one, since (as you point out) it implies that a system canonlyoscillate at its natural frequency if there is no driving force. This is incorrect - if the driving force is periodic and its frequency is equal to the natural frequency then the system will oscillate strongly at its natural frequency - this is called resonance. A better definition (taken fromhere) is The frequency or frequencies at which an object tends to vibrate when hit, struck, plucked, strummed or somehow disturbed. Are all objects naturally oscillatory and that natural frequency is like a fundamental aspect of an object, such as its 'mass' ? Yes. Every system will have some natural frequency or a spectrum of natural frequencies, and this is a fundamental attribute of the system. If so, can we identify this natural frequency in some way ? For a simple system it may be possible to calculate its natural frequency or frequencies from first principles. For example, the natural frequency of a plucked string depends on its length, its tension and its mass per unit length following relationships known asMersenne's laws. For more complex systems, natural frequencies can be determined experimentally by subjecting the system to driving forces with a range of frequencies and looking for signs of resonance. The problem with an eigen-frequency is that it is exact, and the phase space to hit an exact frequency is 0, but if you do hit it, the response diverges...classically. In quantum mechanics, the eigen frequency corresponds to a stationary state that never changes and never interacts. That's obviously not how reality works. IRL, the exact states are approximation, and there is some interaction that broadens the response (in frequency space). Classically, that is dissipation (see:QQ-factor). In quantum mechanics, it is some perturbing interaction. For example: the background electromagnetic field, which couples atomic orbitals (which are no longer exact solutions to Schrodinger's approximately, good enough). In atomic physics, see: natural line width (in: ) Much of this is covered in the Fokker-Planck flucation dissipation theory (start from: –Planck_equation), which is simply too huge a topic to cover here. A complete answer would contain a large portion of Thorne and Blanford, see 6.8:

Answer 1

Natural frequency is the rate at which a system vibrates when not subjected to external forces or damping. It's a fundamental property of physical systems. Resonance occurs when an external force drives a system at its natural frequency, leading to an increase in oscillation amplitude.

Step-by-step explanation:

Natural frequency refers to the inherent tendency of an object to oscillate at a particular frequency when it isn't influenced by external forces.

When a system oscillates freely without any driving force (like wind or a push) or damping forces (such as friction or air resistance), it does so at its natural frequency. This concept is important in understanding various physical phenomena.
In cases where an external periodic force is applied to a system, and this force happens to match the system’s natural frequency, the system will resonate.

This means that the oscillations within the system can dramatically increase in amplitude. An everyday example of this is when a singer hits a note that causes a glass to vibrate and, if the note is sustained at the glass’s natural frequency, potentially shatter.
The natural frequency is not something easily observed in stationary objects like a wine glass on a table. Instead, the minute vibrations they may experience from external sources are not the object’s natural oscillations.

The concepts of free, forced, and damped oscillation are key to understanding the different behaviors that can occur when different kinds of forces act upon a system.
In practice, identifying a system’s natural frequency can be complex. For simple systems like a plucked string, physics provides formulas like Mersenne's laws to calculate this frequency.

For more complex structures, experimental methods involving driving forces of different frequencies can be used to find the point of resonance, which signals the natural frequency.