# Mechanical Harmonics

I like a little song and dance so I thought listening to how a monopole sounds might be fun. I found something on my main source of reference, Wikipedia:

Consider a spring, fixed at one end and having a mass attached to the other; this would be a single degree of freedom (SDoF) oscillator. Once set into motion it will oscillate at its natural frequency. For a single degree of freedom oscillator, a system in which the motion can be described by a single coordinate, the natural frequency depends on two system properties: mass and stiffness; (providing the system is undamped). The radian frequency, ωn, can be found using the following equation:

Where: k = stiffness of the spring m = mass ωn = radian frequency (radians per second)

The monopole has zero stiffness. However massive, the radian frequency will always be 0. A spatial measurement as “radian” does not seem to apply. In effect it is likely to behave as a Bose-Einstein Condensate, but not close to zero Kelvin, but at exactly Zero K. It has zero viscosity. We should also remember that the monopole would have zero degrees of freedom expressed in two coordinates. This comes from how it rolls.

From the radian frequency, the natural frequency, fn, can be found by simply dividing ωn by 2π. Without first finding the radian frequency, the natural frequency can be found directly using:

Where: fn = natural frequency in hertz (cycles/second) k = stiffness of the spring (Newtons/meter or N/m) m = mass(kg) while doing the modal analysis of structures and mechanical equipment, the frequency of 1st mode is called fundamental frequency.

Dividing ωn = 0 by 2π gives another zero. Dividing 1 with 2π  = 0.1591549430918953 Assuming Pi = 3 we get 0.16666….
Something makes it not settle on .16 sharp….go look for that, please.

But the quantity 1 being divided can be redefined as 2 qualities. Reason is that a singularity has zero quantitative properties. It is all unified polarized actions. The natural frequency of a singularity/monopole would then be: 2/2π = 0.3183098861837907. Here perhaps keeping Pi fractioned makes sense since we’re close to a fundamental function. I suggest we understand this 2/2π  as:
* Two polarized actions being (a) linear contraction of pole with (b) circular pole extension. Linear contraction of pole is fundamental, self-referent gravity.
Circular extension of pole is fundamental, self-referent currency.
One is Magnetic and One is Electric.
One is of its own electromagnetism.
* Dividing is of One self-breaking in two Ones. The two Ones are of the same nature. The first Second is a clone of the first One. So 1 pole/extension becomes; 1a pole/extension + 1b pole/extension.
* The Pi value is tricky, but I have this idea of mine. The seemingly infinite fractions are probably an artifact of measurement, not being able to cover the actual quantum “tunneling”. But the basic 3 is not all that clear. Since I reject all quantities in a single monopole, it has only eigenvalues of quality, 3 is not a number of radians. Nor will I have values of space in a unit that generates space. So for now, I assume 3 to be related to the monopoles mode of oscillations and how the actual breaking of its own symmetry plays out. More on that later…

I know nothing of programming code, but I find this of potential interest:
Q: I would like to fit a curve with curve_fit and prevent it from becoming negative. Unfortunately, the code below does not work. Any hints? Thanks a lot!
A: Your model actually works fine as the following plot shows. I used your code and plotted the original data and the data you obtain with the fitted parameters:

This is the input values on the X-axis: xData = [0.0009824379203203417, 0.0011014182912933933, 0.0012433979929054324, 0.0014147106052612918, 0.0016240300315499524, 0.0018834904507916608, 0.002210485320720769, 0.002630660216394964, 0.0031830988618379067, 0.003929751681281367, 0.0049735919716217296, 0.0064961201261998095, 0.008841941282883075, 0.012732395447351627, 0.019894367886486918, 0.0353677651315323, 0.07957747154594767, 0.3183098861837907]

Last in line is exactly 2/2π = 0.3183098861837907 What makes me interested are the words: curve, negative. Also that the guy asking is surprised it doesn’t work, and the answer saying that it actually works fine. It seems the one asking didn’t like the graph X-axis starting at -0.05. So he got some help making the same plot look nicer:

Same values, same outcome, but not interfering with our mathematical preferences. Presto, the ugly negative has magically disappeared, as it is always made to disappear.

Back to the harmonic oscillator, there’s a quirk to be recognized and dealt with. If the unit has 0 radian frequency, but a “natural” frequency of actions unified in one action (not as radiation), how does it sound? In this unit, there seems to be no steady pulse distinguished. If we could stand beside it and listen to it, hypothetically, there would perhaps be just one big bang of “0.3183098861837907”, whatever that is.
Oh, that’s 1/2π  = 0.1591549430918953 doubled….but what IS it? It seems to show up in inversed Gaussian distributions and that could be a pointer.

I intuitively like the idea of everything inversed at the point of singularity monopole evolution. And Gaussian distributions are what we have in reality. So why not crunch the numbers and have relations be outside-inside and with signs reversed?
If I knew programming, that’s what I would take as a starting point.

I also stumble over the notion of a missing fundamental, and again, such “gaps” makes me curious. So I learn that: A harmoic sound is said to have a missing fundamental, suppressed fundamental, or phantom fundamental when its overtones suggest a fundamental frequency but the sound lacks a component at the fundamental frequency itself. The brain perceives the pitch of a tone not only by its fundamental frequency, but also by the periodicity implied by the relationship between the higher harmonics; we may perceive the same pitch (perhaps with a different timbre) even if the fundamental frequency is missing from a tone.

For example, when a note (that is not a pure tone) has a pitch of 100 Hz, it will consist of frequency components that are integer multiples of that value (e.g. 100, 200, 300, 400, 500…. Hz). However, smaller loudspeakers may not produce low frequencies, and so in our example, the 100 Hz component may be missing. Nevertheless, a pitch corresponding to the fundamental may still be heard.

What my mind hears is the sound of entanglement. Hey guys and gals, after the bang of the true first harmonic, everything is a symphony of overtones which some call Cymatics. The higher harmonics are of the phantom fundamental which we cannot hear.
We cannot hear it because it is not a physical value itself.
It is the fundamental force of dual action that makes all actions valuable.
It permeates the whole universe in all directions.
It is not a detectable pulse that sweeps over the real surface in steady frequency.
It is not apart from all detectable frequencies.
It is a part of all detectable frequencies.
The phantom frequency it what drives all frequencies of spin.
It is the spinor of the spin.
It is the hidden work within the visible workers.
The phantom dissipates itself, breaks itself into realized overtones.
Its higher harmony is all there is.
A beautiful choir, made to sing a requiem for the dying phantom of the universal opera.
A phantom that will rise again, and again, and again …
It makes the phonons sing.
It makes the excitons exciting.
It is the superconducting of empirical reality.

And all of this from looking up “fundamental frequency of mechanical systems” on Wikipedia. Another productive lunch break I think.