MH's ideal coil and voltage question

[poynt99]

Whether right or wrong, decaying oscillations of a resonant system are often referred to as still resonating.

By the definition given in the attachment, an LC circuit is a resonant system, as is also an air resonant cavity.

I suspect that everything that can resonate has an energy exchange process within itself, even after the stimulus is removed.

[MileHigh]

From HyperPhysics:

http://hyperphysics.phy-astr.gsu.edu/hbase/sound/reson.html#resdef

[The first definition that they give:]

Resonance

In sound applications, a resonant frequency is a natural frequency of vibration determined by the physical parameters of the vibrating object. This same basic idea of physically determined natural frequencies applies throughout physics in mechanics, electricity and magnetism, and even throughout the realm of modern physics.

[The second definition that they give, the one you are obsessing on:]

Ease of Excitation at Resonance

It is easy to get an object to vibrate at its resonant frequencies, hard at other frequencies. A child's playground swing is an example of a pendulum, a resonant system with only one resonant frequency. With a tiny push on the swing each time it comes back to you, you can continue to build up the amplitude of swing. If you try to force it to swing a twice that frequency, you will find it very difficult, and might even lose teeth in the process!

[MileHigh]

https://en.wikipedia.org/wiki/Tuning_fork

Tuning fork

A tuning fork is an acoustic resonator in the form of a two-pronged fork with the prongs (tines) formed from a U-shaped bar of elastic metal (usually steel). It resonates at a specific constant pitch when set vibrating by striking it against a surface or with an object, and emits a pure musical tone after waiting a moment to allow some high overtones to die out. The pitch that a particular tuning fork generates depends on the length and mass of the two prongs. It is frequently used as a standard of pitch to tune musical instruments.

[What they say later is that the pitch is also determined by the springiness of the metal of the tuning fork, where they discuss Young's modulus.]

The main reason for using the fork shape is that, unlike many other types of resonators, it produces a very pure tone, with most of the vibrational energy at the fundamental frequency, and little at the overtones (harmonics)

[MileHigh]

http://www.giangrandi.ch/electronics/ringdownq/ringdownq.shtml

Measuring the Q-factor of a resonator with the ring-down method

Introduction

Resonance is a very common phenomenon, especially in electronics, acoustics, mechanics and optics. When a resonance is desired, special devices are built, called resonators, that have the property of naturally oscillating at some frequency, called resonant frequency, with (much) greater amplitude than at others.

All resonators are characterized by their resonant frequency f0 and their quality factor Q: this page is about a simple method of measuring Q, called the ring-down method.

In electronics, LC circuits are a common kind of resonator, often called resonant circuit, tuned circuit or tank circuit. They are all composed by an inductor (labelled L) and a capacitor (labelled C) connected together. The resistor (labelled R) is responsible for the losses and the final Q-factor: it's often ignored or omitted and rarely added as a physical component, but always present as any losses in the resonator will appear as a resistor. So, every practical LC circuit is actually an RLC circuit, even if just called LC, as it's also the case in this page. Usually, the inductor is responsible for the majority of the losses.

This page is mainly oriented on electrical LC circuits, but the ring-down method applies to all kinds resonators, because the equations describing their behavior have the same form.

All the previous examples were electrical circuits. Let's have a look now at a mechanical resonator, as the ring-down method applies to almost any resonator. I choose a 440 Hz tuning fork used by guitar players to tune their instrument. To measure the amplitude of the oscillations it has been coupled to a piezoelectric transducer and connected to the oscilloscope, as shown in the picture below. The piezoelectric transducer works here as a microphone. Here, the choice of the probe is not important, but the way to hold the fork in place is critical: I ended up tying it to a long wooden stick with thin copper wire, being careful in not tightening it too much.

[MileHigh]

Here we go again:

An LC circuit is a resonant circuit that acts as an electrical resonator that resonates at the resonant frequency and manifests the phenomenon of resonance.

A tuning fork is a resonant system that acts as a mechanical resonator that resonates at the resonant frequency and manifests the phenomenon of resonance.

A wine glass is a resonant system that acts as a mechanical resonator that resonates at the resonant frequency and manifests the phenomenon of resonance.

A bell is a resonant system that acts as a mechanical resonator that resonates at the resonant frequency and manifests the phenomenon of resonance.

All of the above systems are modeled by the attached circuit.  This is a simplified model that does not include the resistor.