Anharmonic Oscillator

[studiot]

19 minutes ago, Kartazion said:

Ok. But it was for information. What electronic circuits are you talking about?

Impulse function sometimes uses RC without L, and the Heaviside step function uses a simple switch.

Simple ones can be constructed with various semiconductor devices for example

 

 

The point  of the step function is that  it (the step) is always  finite, unlike   the Delta impulse function.

 

I also mentioned Gibbs phenomena.

Did you miss that?

[Kartazion]

17 minutes ago, studiot said:

I also mentioned Gibbs phenomena.

Did you miss that?

Yes.

Interesting the unijunction transistor. But it does not pass from one signal to another. In addition the signals A and B are symmetrical, while my principle is first one then the other.

A simple flip-flop or latch should be enough.

[studiot]

2 hours ago, Kartazion said:

Yes.

 

So what about  it?

2 hours ago, Kartazion said:

Interesting the unijunction transistor. But it does not pass from one signal to another. In addition the signals A and B are symmetrical, while my principle is first one then the other.

A simple flip-flop or latch should be enough.

 

I  don't  understand the connection.

[Kartazion]

1 hour ago, studiot said:

I  don't  understand the connection.

The connection between what?

1 hour ago, studiot said:

So what about  it?

The signal from A and B, when it is different from zero, is symmetrical. So it can't work for my oscillator.

In any case for the circuit that you proposed to me... 
'We do not see, by clearness (you have to guess), the effect of Gibbs phenomena. '

It is necessary that when A is true (1), then B = 0, and not -1.
And when B = -1 then A = 0.

[Kartazion]

I did not explain myself well with my example of -1.
I confused the tesion + - with the high and low alternation of a square signal with as zero medium.
But I understand that the signal is either 0 volt (-) or Vcc (+).

[studiot]

4 hours ago, Kartazion said:

I did not explain myself well with my example of -1.
I confused the tesion + - with the high and low alternation of a square signal with as zero medium.
But I understand that the signal is either 0 volt (-) or Vcc (+).

 

That's good you saw that for yourself.

So your 'signal'  is actual a  binary T or F in digital space.

Yes in this non physical space you can have  perfect  rectangular, pulse and square waves.

But I did not think we were talking about such spaces.

And my UJT  oscillator does  not need a signal to drive it. It is self oscillating.

 

The appearance  of Gibbs depends  upon the number of terms in Fourier series.
It appears as finite damped ringing (overshoot and undershoot) for a finite number of terms.
For infinite terms it appears as an infinite vertical line.

 

The Fourier series for a square wave is special because something special happens with it.

The  whole of the rest of linear algebra is based  upon the space of piecewise continuous funtions.
This provides inherited properties, existence and uniqueness theorems we  forget and take for granted.
The most important of these is one which guarantees that whenever we add two or more continuous functions from the space we will get another continuous function from that space.

But when we add the trigonometric functions to model a square wave we step ouside the space and the normal conditions for Fourier series.

This condition states "There should be a finite number of discontinuites in the waveform being modelled"

But a square wave has an infinite number of discontinuities.

 

[Kartazion]

11 hours ago, studiot said:

But I did not think we were talking about such spaces.

The rest, if you wish, will be made of integrated circuit and 'digital space'.

 

11 hours ago, studiot said:

And my UJT  oscillator does  not need a signal to drive it. It is self oscillating.

Yes normal, it works alone thanks to the charge and discharge of the C capacity which acts on the transitor, hence the more or less sawtooth wave. Besides, its usefulness would be useful as a clock. It reminds me of the principle of NE555 with the RC setting.

 

11 hours ago, studiot said:

But a square wave has an infinite number of discontinuities.

The discontinuity happens to be the logical change of state of a square wave. It's the plot of the vertical on the oscilloscope, no?

[studiot]

24 minutes ago, Kartazion said:

The discontinuity happens to be the logical change of state of a square wave. It's the plot of the vertical on the oscilloscope, no?

Yes, but that plot on the scope is a 'perfect' finite step function, whereas a perfect fourier  square wave has infinities at those horizontal coordinates.

[Kartazion]

Here is version two of the classic harmonic oscillator. This version remains primitive, but functional.

On 3/11/2020 at 1:47 AM, Kartazion said:

You will see a very basic diagram, but its principle is that there. 

Its clock is clocked at regular intervals. The bottom Johnson counters integrated circuit advances the particle from left to right, and the top one from right to left.

 

 

Do you validate this principle of this mechanical / classic oscillator?

Or is there already such a mechanical / classical oscillator studied in physics?

[studiot]

8 hours ago, Kartazion said:

Here is version two of the classic harmonic oscillator. This version remains primitive, but functional.

 

 

Do you validate this principle of this mechanical / classic oscillator?

Or is there already such a mechanical / classical oscillator studied in physics?

A self  reversing linear motor ?

[Kartazion]

15 minutes ago, studiot said:

A self  reversing linear motor ?

Yes, if we want, a self reversing linear motor, which suddenly becomes an oscillator.

[Kartazion]

It is simple and efficient.

Do you validate this principle of this classic oscillator? 

I want your opinions:

studio?
Mordred?
swansont?
Strange?
Markus Hanke?

and others ...

[Kartazion]

Silence is acceptance.

[swansont]

I don't know what your point is. The animation does not reflect the system you had previously described. Ignoring the value of the oscillation frequency, you had described something that spent far more time at the extrema of the system.

[Kartazion]

1 hour ago, swansont said:

I don't know what your point is. The animation does not reflect the system you had previously described. Ignoring the value of the oscillation frequency, you had described something that spent far more time at the extrema of the system.

Yes it is for the start. I started with a harmonic oscillator which goes smoothly in terms of frequency.

It then suffices to make this oscillator anharmonic, with a viscosity at the limit switch, and at a higher frequency.

If you want I make you the diagram of this anharmonic and faster oscillator. But the result and at very high frequency would be the same.
Namely a mass density distributed at the ends.

Spoiler

 

I would have hoped that you would be able to see where I was coming from

Spoiler

 

[Kartazion]

This is the effect of Kartazion.

Here is the first equation:

[math]\frac{total\ mass}{number\ of\ positions}=density\ per\ position[/math]

 

This equation is true if the time granted by position is equivalent for each position.
It may happen that the particle is stopped longer in one position at the expense of the other.
In this case, the equation is no longer valid.

[Kartazion]

######################################################

We can consider that the oscillator uses an iteration principle.
Is the oscillator mathematically expressible as an iterated function?

[Kartazion]

Here is the program in html/css description language of the anharmonic oscillator that I have described.
It alternates, and by its entire path, the particle between its two poles.
At very high frequency, the conclusion and the aim of this experiment is to clearly demonstrate the duplication of the particle, and this in several places.

--> See the animation

 

<html>
<head>
  <link rel="stylesheet" href="oscillator.css"></head>
<body>
  <div id="velocity_1">
</div>

 

#velocity_1 {
    width: 20px;
    height: 20px;
    border-radius: 20px;
    background: black;

    position: relative;
        
    animation-name: oscillator;
    animation-duration: 2s; 
    animation-iteration-count: infinite;
}

@keyframes oscillator {

 0% {
        transform: translateX(0px);
    }

30% {
        transform: translateX(0px);
    }

40% {
        transform: translateX(500px);
    }

80% {
        transform: translateX(500px);
    }

90% {
        transform: translateX(0px);
    }
}

 

[Kartazion]

On 3/23/2020 at 7:18 PM, swansont said:

… The animation does not reflect the system you had previously described. Ignoring the value of the oscillation frequency, you had described something that spent far more time at the extrema of the system.

And now you are convinced the expected effect?

As planned, and at a very very high frequency, I do with a particle, several points of different static mass.

 

[swansont]

50 minutes ago, Kartazion said:

And now you are convinced the expected effect?

As planned, and at a very very high frequency, I do with a particle, several points of different static mass.

 

I've written you off as a lost cause.

[Kartazion]

26 minutes ago, swansont said:

I've written you off as a lost cause.

Technically speaking, could you develop what you mean?

I'm wrong?

[Strange]

16 minutes ago, Kartazion said:

Technically speaking, could you develop what you mean?

I'm wrong?

I think it is more a case of being impervious to being shown to be wrong.

[swansont]

35 minutes ago, Kartazion said:

Technically speaking, could you develop what you mean?

I'm wrong?

Right and wrong can't be assigned when the situation is as ambiguous as your discussion is. You have not presented a clear problem, have not been consistent in what you are asking for. You seem to be quoting from various web pages as if you know what you're talking about, and then post things that suggest you don't.

It's like trying to hit a moving target that moves erratically if not randomly. I can't hit that target. IOW, I can't give you the answers you are looking for, with the presentation you have provided.

You have a code, you say. If that tells you position as a function of time, integrate that twice (while applying the initial conditions or other boundary conditions) and you will have acceleration as a function of time. F = ma. You'll have the force needed to produce that motion. (if you have velocity as a function of time, you only have to integrate once). That's if it's an object with mass. But you have also discussed electrical/digital behaviors, which don't have to follow Newton's laws of motions (see above comment about inconsistency)

 

[Kartazion]

58 minutes ago, swansont said:

You have not presented a clear problem, have not been consistent in what you are asking for. 

Really.

58 minutes ago, swansont said:

It's like trying to hit a moving target that moves erratically if not randomly. I can't hit that target. IOW, I can't give you the answers you are looking for, with the presentation you have provided.

I always claim the same idea.

59 minutes ago, swansont said:

 You seem to be quoting from various web pages as if you know what you're talking about, and then post things that suggest you don't.

I am trying to understand what I find. This is why I present it here on this forum to have your opinions.

1 hour ago, Strange said:

I think it is more a case of being impervious to being shown to be wrong.

Be impervious to its operation.

Edited April 1, 2020 by Kartazion

[Kartazion]

Here, this time, a code in javascript that simulates the displacement of a particle according to the principle of an anharmonic oscillation.
This program tries to be able to measure the duplication of the particle on several given points.

When you increase the speed to 40, you will achieve perfect harmony.

--> See the animation

 

<html>
<head>
    <meta charset="utf-8">
    <meta name="viewport" content="width=device-width">
    <title>Anharmonic Oscillator</title>
    <style>
         
        #contentContainer {
            width: 200px;
            height: 600px;
            overflow: hidden;
            display: flex;
            align-items: center;
        }
 
        #particle {
            width: 20px;
            height: 20px;
            background-color: black;
            border-radius: 50%;
        }
 
    </style>
</head>
 
<body>

<h3>Anharmonic Oscillator</h3>

<p>
  <input type="button" onClick="stop()" value="stop">
  <input type="button" onClick="start()" value="start">
  <input type="button" onClick="velocity()" value="speed"> x<span id="_power">0</span><br>
<p>
  Counter:  <span id="clock">0</span><br>
</p>
</p>

<div id="contentContainer">
    <div id="particle"></div>
</div>

<script>
/*##########################################*/
  
var unity = 0;
var _unity = 0 ;
var power = 0;
var nb_power = 0;
var particle = document.querySelector("#particle");

particle.style.transform = `translate3d(${50}px, ${_unity}px, 0)`;

/*##########################################*/

function animate() {
unity += 10;
document.getElementById("clock").innerHTML = unity;

if ( unity <=200 ) {
_unity -= 10;
particle.style.transform = `translate3d(${50}px, ${_unity}px, 0)`;
}
if ( unity >= 400) {
_unity += 10;
particle.style.transform = `translate3d(${50}px, ${_unity}px, 0)`;
}
if ( unity >= 600) {
_unity -= 10;
if ( unity == 800 ) {
unity = 0;
}
}
if (power == 1) {
 requestAnimationFrame(animate);
} 
}

/*##########################################*/

function stop() {
power = 0;
nb_power = 0;
unity = 0;
_unity = 0;
document.getElementById("_power").innerHTML = nb_power;
document.getElementById("clock").innerHTML = 0;
}
function start() {
if (power == 0) {
power = 1;
nb_power = 1;
document.getElementById("_power").innerHTML = nb_power;
animate();
}
}
function velocity() {
if (power == 1) {
if (nb_power == 60) {
stop();
} else {
nb_power += 1 ;
document.getElementById("_power").innerHTML = nb_power;
animate();
}
}
}
</script>

</body>
</html>

 

Edited April 4, 2020 by Kartazion