Did you know, what is a thought experiment, gedanken experiment?
It is a non-existent practice, an otherworldly experience, the imagination of what is not really there. Thought experiments are like daydreams. They give birth to monsters. Unlike a physical experiment, which is experienced check hypotheses, the "thought experiment" magically replaces experimental verification with desired, untested conclusions, manipulating logical constructions that actually violate logic itself by using unproved premises as proven ones, that is, by substitution. Thus, the main task of the applicants of "thought experiments" is to deceive the listener or reader by replacing a real physical experiment with his "doll" - fictitious reasoning on parole without physical verification itself.
Filling physics with imaginary, "thought experiments" has led to an absurd, surreal, confusing picture of the world. True explorer must distinguish such "wrappers" from real values.

Relativists and positivists argue that the "thought experiment" is a very useful tool for testing theories (also arising in our minds) for consistency. In this they deceive people, since any verification can only be carried out by a source independent of the object of verification. The applicant of the hypothesis himself cannot be a test of his own statement, since the reason for this statement itself is the absence of contradictions visible to the applicant in the statement.

We see this in the example of SRT and GR, which have turned into a kind of religion that governs science and public opinion. No amount of facts that contradict them can overcome Einstein's formula: "If the fact does not correspond to the theory, change the fact" (In another version, "Does the fact not correspond to the theory? - So much the worse for the fact").

The maximum that a "thought experiment" can claim is only the internal consistency of the hypothesis within the framework of the applicant's own, often by no means true, logic. Compliance with practice does not check this. A real test can only take place in a real physical experiment.

An experiment is an experiment, because it is not a refinement of thought, but a test of thought. Thought that is consistent within itself cannot test itself. This has been proven by Kurt Gödel.

The waves look like

Equations of a plane monochromatic electromagnetic

Instantaneous values ​​at any point are related by the relation

oscillate in the same phases, and their

The plane perpendicular to the propagation velocity vector

The magnetic fields are mutually perpendicular and lie in

Electromagnetic waves are transverse,

The environments are determined by the formula

The phase velocity of electromagnetic waves in various

Wave.

The space process and is an electromagnetic

Point to another. This periodic in time and

Spreading in the surrounding space from one

Mutual transformations of electric and magnetic fields,

electromagnetic field, then a sequence arises

To excite a variable with vibrating charges

Maxwell's equations for the electromagnetic field. If

The existence of electromagnetic waves follows from

Electromagnetic waves

Shimi, will be weak. Thus, for example,

The voltage created on the capacitor by other components

Exceeding the value of this component, while

Ideal stresses, the desired component. Having set up

A complex voltage equal to the sum of several sinusoidal

The phenomenon of resonance is used to isolate from

Equal to the value of the inverse quality factor of the circuit, i.e.

Relative width of the resonance curve

The quality factor of the circuit determines the sharpness of the resonant

Loop resistance.

So the quality factor is inversely proportional to

With cut U

The capacitor can exceed the applied voltage, i.e.

The resonant properties of the circuit are characterized by the quality

A steady current in a circuit with a capacitor cannot flow.

Ires LC

Coincides with the natural frequency of the circuit

Therefore, the resonant frequency for the current strength

Rice. 1.22

R1< R2 < R3

   . (1.96)

At ω →0, I= 0, since at a constant voltage

ness Q, which shows how many times the voltage on

 (1.97)

At low damping ω res≈ ω0 And

Q  1 (1.98)

curves. On fig. 1.23 shows one of the resonance curves

for the current in the circuit. Frequencies ω1 And ω2 correspond to the current

max II 2 .

 

contour (by changing R And C) to the required frequency

, you can get a voltage on the capacitor in Q once



tune the radio to the desired wavelength.

    1 0 2

mmax I

Rice. 1.7

Fig.1.23

 , (1.100)

 - speed of electromagnetic waves in vacuum.

since the vectors E

And H

electrical and

wave formation, forming a right-handed system (Fig. 1.24). At

this vectors E

And H

0 0   E N. (1.101)

cos() m Е  Е t  kx  , (1.102)

cos() m H  H t  kx  , (1.103)

where ω is the wave frequency, k = ω/υ = 2π/λ is the wave number, α-

Fig.1.24

Electromagnetic waves carry energy. Volumetric

Definition

Initial phase of oscillation is a parameter that, together with the amplitude of oscillations, determines the initial state of the oscillatory system. The value of the initial phase is set in the initial conditions, that is, at $t=0$ c.

Consider harmonic oscillations of some parameter $\xi $. Harmonic oscillations are described by the equation:

\[\xi =A(\cos ((\omega )_0t+\varphi)\ )\ \left(1\right),\]

where $A=(\xi )_(max)$ - oscillation amplitude; $(\omega )_0$ - cyclic (circular) oscillation frequency. The parameter $\xi $ lies within $-A\le \xi \le $+A.

Determination of the oscillation phase

The entire argument of the periodic function (in this case, the cosine: $\ ((\omega )_0t+\varphi)$), which describes the oscillatory process, is called the oscillation phase. The magnitude of the oscillation phase at the initial moment of time, that is, at $t=0$, ($\varphi $) is called the initial phase. There is no established phase designation, we have initial phase denoted by $\varphi$. Sometimes, to emphasize that the initial phase refers to the time $t=0$, the index 0 is added to the letter denoting the initial phase, for example, $(\varphi )_0.$

The initial phase unit is the angle unit, radian (rad) or degree.

The initial phase of oscillations and the method of excitation of oscillations

Let us assume that for $t=0$ the displacement of the system from the equilibrium position is equal to $(\xi )_0$, and starting speed$(\dot(\xi ))_0$. Then equation (1) takes the form:

\[\xi \left(0\right)=A(\cos \varphi =\ )(\xi )_0\left(2\right);;\] \[\ \frac(d\xi )(dt) =-A(\omega )_0(\sin \varphi =\ )(\dot(\xi ))_0\to -A(\sin \varphi =\frac((\dot(\xi ))_0)(( \omega )_0)\ )\ \left(3\right).\]

We square both equations (2) and add them:

\[(\xi )^2_0+(\left(\frac((\dot(\xi ))_0)((\omega )_0)\right))^2=A^2\left(4\right). \]

From expression (4) we have:

Divide equation (3) by (2), we get:

Expressions (5) and (6) show that the initial phase and amplitude depend on the initial conditions of oscillations. This means that the amplitude and the initial phase depend on the way the oscillations are excited. For example, if the weight of a spring pendulum is deflected from the equilibrium position and by a distance $x_0$ and released without a push, then the equation of motion of the pendulum is the equation:

with initial conditions:

With this excitation of vibration spring pendulum can be described by the expression:

Addition of oscillations and initial phase

An oscillating body is capable of taking part in several oscillatory processes simultaneously. In this case, it becomes necessary to find out what the resulting oscillation will be.

Let us assume that two oscillations with equal frequencies occur along one straight line. The equation of the resulting oscillations will be the expression:

\[\xi =(\xi )_1+(\xi )_2=A(\cos \left((\omega )_0t+\varphi \right),\ )\]

then the amplitude of the total oscillation is equal to:

where $A_1$; $A_2$ - amplitudes of folding oscillations; $(\varphi )_2;;(\varphi )_1$ - initial phases of summed oscillations. In this case, the initial phase of the resulting oscillation ($\varphi $) is calculated using the formula:

The equation for the trajectory of a point that takes part in two mutually perpendicular oscillations with amplitudes $A_1$ and $A_2$ and initial phases $(\varphi )_2and(\varphi )_1$:

\[\frac(x^2)(A^2_1)+\frac(y^2)(A^2_2)-\frac(2xy)(A_1A_2)(\cos \left((\varphi )_2-(\ varphi )_1\right)\ )=(sin)^2\left((\varphi )_2-(\varphi )_1\right)\left(12\right).\]

In the case of equality of the initial phases of the oscillation components, the trajectory equation has the form:

which indicates the movement of a point in a straight line.

If the difference between the initial phases of the added oscillations is $\Delta \varphi =(\varphi )_2-(\varphi )_1=\frac(\pi )(2),$, the following formula becomes the trajectory equation:

\[\frac(x^2)(A^2_1)+\frac(y^2)(A^2_2)=1\left(14\right),\]

which means the motion path is an ellipse.

Examples of problems with a solution

Example 1

Exercise. Oscillations of the spring oscillator are excited by a push from the equilibrium position, while the load is given an instantaneous speed equal to $v_0$. write down initial conditions for such an oscillation and a function $x(t)$ describing these oscillations.

Solution. Message to the load of the spring pendulum instantaneous speed equal to $v_0$ means that when describing its oscillations using the equation:

initial conditions will be:

Substitute into expression (1.1) $t=0$, we have:

Since $A\ne 0$, then $(\cos \left(\varphi \right)\ )=0\to \varphi =\pm \frac(\pi )(2).$

Let's take the first derivative $\frac(dx)(dt)$ and substitute the time $t=0$:

\[\dot(x)\left(0\right)=-A(\omega )_(0\ )(\sin \left(\varphi \right)\ )=v_0\to A=\frac(v_0) ((\omega )_(0\ ))\ \left(1.4\right).\]

It follows from (1.4) that the initial phase is $\varphi =-\frac(\pi )(2).$ Let us substitute the resulting initial phase and amplitude into equation (1.1):

Answer.$x(t)=\frac(v_0)((\omega )_(0\ ))(\sin (\ )(\omega )_0t)$

Example 2

Exercise. Two vibrations in the same direction add up. The equations for these oscillations are: $x_1=(\cos \pi (t+\frac(1)(6))\ );;\ x_2=2(\cos \pi (t+\frac(1)(2))\ )$. What is the initial phase of the resulting oscillation?

Solution. Let's write the equation harmonic vibrations X axis:

Let's transform the equations given in the condition of the problem to the same form:

\;;\ x_2=2(\cos \left[\pi t+\frac(\pi )(2)\right](2.2).\ )\]

Comparing equations (2.2) with (2.1), we obtain that the initial phases of the oscillations are:

\[(\varphi )_1=\frac(\pi )(6);;\ (\varphi )_2=\frac(\pi )(2).\]

We depict in Fig. 1 a vector diagram of oscillations.

$tg\ \varphi $ total fluctuations can be found from Fig.1:

\ \[\varphi =arctg\ \left(2.87\right)\approx 70.9()^\circ \]

Answer.$\varphi =70.9()^\circ $

Oscillation phase (φ) characterizes harmonic oscillations.
The phase is expressed in angular units - radians.

For a given oscillation amplitude, the coordinate of an oscillating body at any time is uniquely determined by the cosine or sine argument: φ = ω 0 t.

The oscillation phase determines the state of the oscillatory system (the value of the coordinate, velocity and acceleration) at a given amplitude at any time.

Oscillations with the same amplitudes and frequencies may differ in phase.

The ratio indicates how many periods have passed since the start of oscillations.

Graph of the dependence of the coordinate of the oscillating point on the phase




Harmonic oscillations can be represented both using the sine and cosine functions, because
sine differs from cosine by shifting the argument by .



Therefore, instead of the formula

x = x m cos ω 0 t


it is possible to use the formula to describe harmonic oscillations



But at the same time initial phase, i.e. the value of the phase at time t = 0, is not equal to zero, but .
IN different situations it is convenient to use sine or cosine.

What formula to use in calculations?


1. If at the beginning of oscillations the pendulum is taken out of the equilibrium position, then it is more convenient to use the formula using the cosine.
2. If the coordinate of the body at the initial moment would be equal to zero, then it is more convenient to use the formula using the sine x \u003d x m sin ω 0 t, because in this case, the initial phase is equal to zero.
3. If at the initial moment of time (at t - 0) the oscillation phase is equal to φ, then the oscillation equation can be written as x \u003d x m sin (ω 0 t + φ).


Phase shift


Oscillations described by formulas in terms of sine and cosine differ from each other only in phases.
The phase difference (or phase shift) of these oscillations is .
Graphs of the dependence of coordinates on time for two harmonic oscillations shifted in phase by :
Where
graph 1 - oscillations that occur according to a sinusoidal law,
graph 2 - oscillations that occur according to the law of cosine