The magnitude of electromagnetic oscillations. Analogy between mechanical and electromagnetic oscillations - Knowledge Hypermarket. Possible Applications of Oscillations

Development of a methodology for studying the topic "Electromagnetic oscillations"

Oscillatory circuit. Energy transformations during electromagnetic oscillations.

These questions, which are among the most important in this topic, are dealt with in the third lesson.

First, the concept of an oscillatory circuit is introduced, an appropriate entry is made in a notebook.

Further, in order to find out the cause of the occurrence of electromagnetic oscillations, a fragment is shown, which shows the process of charging the capacitor. The attention of students is drawn to the signs of the charges of the capacitor plates.

After that, the energies of the magnetic and electric fields are considered, the students are told about how these energies and the total energy in the circuit change, the mechanism for the occurrence of electromagnetic oscillations is explained using the model, and the basic equations are recorded.

It is very important to draw students' attention to the fact that such a representation of the current in the circuit (the flow of charged particles) is conditional, since the speed of electrons in the conductor is very low. This method of representation was chosen to facilitate understanding of the essence of electromagnetic oscillations.

Further, the attention of students is focused on the fact that they observe the processes of converting the energy of an electric field into magnetic energy and vice versa, and since the oscillatory circuit is ideal (there is no resistance), the total energy of the electromagnetic field remains unchanged. After that, the concept of electromagnetic oscillations is given and it is stipulated that these oscillations are free. Then the results are summed up and homework is given.

Analogy between mechanical and electromagnetic oscillations.

This question is considered in the fourth lesson of the study of the topic. First, for repetition and consolidation, you can once again demonstrate the dynamic model of an ideal oscillatory circuit. To explain the essence and prove the analogy between electromagnetic oscillations and oscillations of a spring pendulum, the dynamic oscillatory model “Analogy between mechanical and electromagnetic oscillations” and PowerPoint presentations are used.

A spring pendulum (oscillations of a load on a spring) is considered as a mechanical oscillatory system. Identification of the relationship between mechanical and electrical quantities in oscillatory processes is carried out according to the traditional method.

As it was already done in the last lesson, it is necessary to remind the students once again about the conditionality of the movement of electrons along the conductor, after which their attention is drawn to the upper right corner of the screen, where the “communicating vessels” oscillatory system is located. It is stipulated that each particle oscillates around the equilibrium position, therefore, fluid oscillations in communicating vessels can also serve as an analogy for electromagnetic oscillations.

If there is time left at the end of the lesson, then you can dwell on the demonstration model in more detail, analyze all the main points using the newly studied material.

The equation of free harmonic oscillations in the circuit.

At the beginning of the lesson, dynamic models of an oscillatory circuit and analogies of mechanical and electromagnetic oscillations are demonstrated, the concepts of electromagnetic oscillations, an oscillatory circuit, the correspondence of mechanical and electromagnetic quantities in oscillatory processes are repeated.

The new material must begin with the fact that if the oscillatory circuit is ideal, then its total energy remains constant over time

those. its time derivative is constant, and hence the time derivatives of the energies of the magnetic and electric fields are also constant. Then, after a series of mathematical transformations, they come to the conclusion that the equation of electromagnetic oscillations is similar to the equation of oscillations of a spring pendulum.

Referring to the dynamic model, students are reminded that the charge in the capacitor changes periodically, after which the task is to find out how the charge, the current in the circuit and the voltage across the capacitor depend on time.

These dependencies are found by the traditional method. After the equation for the oscillations of the capacitor charge is found, the students are shown a picture that shows the graphs of the charge of the capacitor and the displacement of the load versus time, which are cosine waves.

In the course of elucidating the equation for oscillations of the charge of a capacitor, the concepts of the period of oscillations, cyclic and natural frequencies of oscillations are introduced. Then the Thomson formula is derived.

Next, the equations for fluctuations in the current strength in the circuit and the voltage on the capacitor are obtained, after which a picture is shown with graphs of the dependence of three electrical quantities on time. Students' attention is drawn to the phase shift between current fluctuations and charges by its absence between voltage and charge fluctuations.

After all three equations are derived, the concept of damped oscillations is introduced and a picture is shown showing these oscillations.

In the next lesson, a brief summary is summarized with a repetition of the basic concepts and tasks are solved to find the period, cyclic and natural frequencies of oscillations, the dependences q(t), U(t), I(t), as well as various qualitative and graphical tasks are studied.

4. Methodical development of three lessons

The lessons below are designed as lectures, since this form, in my opinion, is the most productive and leaves enough time in this case to work with dynamic demos. ion models. If desired, this form can be easily transformed into any other form of the lesson.

Lesson topic: Oscillatory circuit. Energy transformations in an oscillatory circuit.

Explanation of new material.

The purpose of the lesson: explanation of the concept of an oscillatory circuit and the essence of electromagnetic oscillations using the dynamic model “Ideal oscillatory circuit”.

Oscillations can occur in a system called an oscillatory circuit, consisting of a capacitor with a capacitance C and an inductance coil L. An oscillatory circuit is called ideal if there is no energy loss in it for heating the connecting wires and coil wires, i.e., the resistance R is neglected.

Let's make a drawing of a schematic image of an oscillatory circuit in notebooks.

In order for electrical oscillations to occur in this circuit, it is necessary to inform it of a certain amount of energy, i.e. charge the capacitor. When the capacitor is charged, the electric field will be concentrated between its plates.

(Let's follow the process of charging the capacitor and stop the process when the charging is completed).

So, the capacitor is charged, its energy is equal to

therefore, therefore,

Since after charging the capacitor will have a maximum charge (pay attention to the capacitor plates, they have charges opposite in sign), then at q \u003d q max, the energy of the electric field of the capacitor will be maximum and equal to

At the initial moment of time, all the energy is concentrated between the plates of the capacitor, the current in the circuit is zero. (Let's now close the capacitor to the coil on our model). When the capacitor closes to the coil, it begins to discharge and a current will appear in the circuit, which, in turn, will create a magnetic field in the coil. The lines of force of this magnetic field are directed according to the gimlet rule.

When the capacitor is discharged, the current does not immediately reach its maximum value, but gradually. This is because the alternating magnetic field generates a second electric field in the coil. Due to the phenomenon of self-induction, an induction current arises there, which, according to the Lenz rule, is directed in the direction opposite to the increase in the discharge current.

When the discharge current reaches its maximum value, the energy of the magnetic field is maximum and is equal to:

and the energy of the capacitor at this moment is zero. Thus, through t=T/4 the energy of the electric field has completely passed into the energy of the magnetic field.

(Let's observe the process of discharging a capacitor on a dynamic model. I draw your attention to the fact that this way of representing the processes of charging and discharging a capacitor in the form of a flow of running particles is conditional and is chosen for ease of perception. You know perfectly well that the speed of electrons is very small ( of the order of several centimeters per second). So, you see how, with a decrease in the charge on the capacitor, the current strength in the circuit changes, how the energies of the magnetic and electric fields change, what relationship exists between these changes. Since the circuit is ideal, there is no energy loss , so the total energy of the circuit remains constant).

With the start of recharging the capacitor, the discharge current will decrease to zero not immediately, but gradually. This is again due to the occurrence of counter-e. d.s. and inductive current of opposite direction. This current counteracts the decrease in the discharge current, as it previously counteracted its increase. Now it will support the main current. The energy of the magnetic field will decrease, the energy of the electric field will increase, the capacitor will be recharged.

Thus, the total energy of the oscillatory circuit at any time is equal to the sum of the energies of the magnetic and electric fields

The oscillations at which the energy of the electric field of the capacitor is periodically converted into the energy of the magnetic field of the coil are called ELECTROMAGNETIC oscillations. Since these oscillations occur due to the initial energy supply and without external influences, they are FREE.

Lesson topic: Analogy between mechanical and electromagnetic oscillations.

Explanation of new material.

The purpose of the lesson: to explain the essence and prove the analogy between electromagnetic oscillations and oscillations of a spring pendulum using the dynamic oscillation model “Analogy between mechanical and electromagnetic oscillations” and PowerPoint presentations.

Material to repeat:

the concept of an oscillatory circuit;

the concept of an ideal oscillatory circuit;

conditions for the occurrence of fluctuations in c / c;

concepts of magnetic and electric fields;

fluctuations as a process of periodic energy change;

the energy of the circuit at an arbitrary point in time;

the concept of (free) electromagnetic oscillations.

(For repetition and consolidation, students are once again shown a dynamic model of an ideal oscillatory circuit).

In this lesson, we will look at the analogy between mechanical and electromagnetic oscillations. We will consider a spring pendulum as a mechanical oscillatory system.

(On the screen you see a dynamic model that demonstrates the analogy between mechanical and electromagnetic oscillations. It will help us understand oscillatory processes, both in a mechanical system and in an electromagnetic one).

So, in a spring pendulum, an elastically deformed spring imparts velocity to the load attached to it. A deformed spring has the potential energy of an elastically deformed body

a moving object has kinetic energy

The transformation of the potential energy of a spring into the kinetic energy of an oscillating body is a mechanical analogy of the transformation of the energy of the electric field of a capacitor into the energy of the magnetic field of a coil. In this case, the analog of the mechanical potential energy of the spring is the energy of the electric field of the capacitor, and the analog of the mechanical kinetic energy of the load is the energy of the magnetic field, which is associated with the movement of charges. Charging the capacitor from the battery corresponds to the message to the spring of potential energy (for example, displacement by hand).

Let's compare the formulas and derive general patterns for electromagnetic and mechanical vibrations.

From a comparison of the formulas, it follows that the analog of the inductance L is the mass m, and the analog of the displacement x is the charge q, the analog of the coefficient k is the reciprocal of the electrical capacity, i.e. 1/C.

The moment when the capacitor is discharged and the current strength reaches its maximum corresponds to the passage of the equilibrium position by the body at maximum speed (pay attention to the screens: you can observe this correspondence there).

As already mentioned in the last lesson, the movement of electrons along a conductor is conditional, because for them the main type of movement is oscillatory movement around the equilibrium position. Therefore, sometimes electromagnetic oscillations are compared with oscillations of water in communicating vessels (look at the screen, you can see that such an oscillatory system is located in the upper right corner), where each particle oscillates around the equilibrium position.

So, we found out that the analogy of inductance is mass, and the analogy of displacement is charge. But you know very well that a change in charge per unit of time is nothing more than a current strength, and a change in coordinates per unit of time is a speed, that is, q "= I, and x" = v. Thus, we have found another correspondence between mechanical and electrical quantities.

Let's make a table that will help us systematize the relationships between mechanical and electrical quantities in oscillatory processes.

Correspondence table between mechanical and electrical quantities in oscillatory processes.

Lesson topic: The equation of free harmonic oscillations in the circuit.

Explanation of new material.

The purpose of the lesson: the derivation of the basic equation of electromagnetic oscillations, the laws of change in charge and current strength, obtaining the Thomson formula and the expression for the natural frequency of the oscillation of the circuit using PowerPoint presentations.

Material to repeat:

the concept of electromagnetic oscillations;

the concept of the energy of an oscillatory circuit;

correspondence of electrical quantities to mechanical quantities during oscillatory processes.

(For repetition and consolidation, it is necessary to once again demonstrate the model of the analogy of mechanical and electromagnetic oscillations).

In the past lessons, we found out that electromagnetic oscillations, firstly, are free, and secondly, they represent a periodic change in the energies of the magnetic and electric fields. But in addition to energy, during electromagnetic oscillations, the charge also changes, and hence the current strength in the circuit and the voltage. In this lesson, we must find out the laws by which the charge changes, which means the current strength and voltage.

So, we found out that the total energy of the oscillatory circuit at any time is equal to the sum of the energies of the magnetic and electric fields: . We believe that the energy does not change with time, that is, the contour is ideal. This means that the time derivative of the total energy is equal to zero, therefore, the sum of the time derivatives of the energies of the magnetic and electric fields is equal to zero:

That is.

The minus sign in this expression means that when the energy of the magnetic field increases, the energy of the electric field decreases and vice versa. And the physical meaning of this expression is such that the rate of change in the energy of the magnetic field is equal in absolute value and opposite in direction to the rate of change in the electric field.

Calculating the derivatives, we get

But, therefore, and - we got an equation describing free electromagnetic oscillations in the circuit. If we now replace q with x, x""=a x with q"", k with 1/C, m with L, we get the equation

describing the vibrations of a load on a spring. Thus, the equation of electromagnetic oscillations has the same mathematical form as the equation of oscillations of a spring pendulum.

As you saw in the demo model, the charge on the capacitor changes periodically. It is necessary to find the dependence of the charge on time.

From the ninth grade, you are familiar with the periodic functions sine and cosine. These functions have the following property: the second derivative of the sine and cosine is proportional to the functions themselves, taken with the opposite sign. Apart from these two, no other functions have this property. Now back to electric charge. We can safely say that the electric charge, and hence the current strength, during free oscillations change over time according to the law of cosine or sine, i.e. make harmonic vibrations. The spring pendulum also perform harmonic oscillations (acceleration is proportional to the displacement, taken with a minus sign).

So, in order to find the explicit dependence of the charge, current and voltage on time, it is necessary to solve the equation

taking into account the harmonic nature of the change in these quantities.

If we take an expression like q = q m cos t as a solution, then, when substituting this solution into the original equation, we get q""=-q m cos t=-q.

Therefore, as a solution, it is necessary to take an expression of the form

q=q m cossh o t,

where q m is the amplitude of the charge oscillations (modulus of the largest value of the oscillating value),

w o = - cyclic or circular frequency. Its physical meaning is

the number of oscillations in one period, i.e., for 2p s.

The period of electromagnetic oscillations is the period of time during which the current in the oscillatory circuit and the voltage on the capacitor plates make one complete oscillation. For harmonic oscillations T=2p s (smallest cosine period).

The oscillation frequency - the number of oscillations per unit time - is determined as follows: n = .

The frequency of free oscillations is called the natural frequency of the oscillatory system.

Since w o \u003d 2p n \u003d 2p / T, then T \u003d.

We defined the cyclic frequency as w o = , which means that for the period we can write

Т= = - Thomson's formula for the period of electromagnetic oscillations.

Then the expression for the natural oscillation frequency takes the form

It remains for us to obtain the equations for the oscillations of the current strength in the circuit and the voltage across the capacitor.

Since, then at q = q m cos u o t we get U=U m cos o t. This means that the voltage also changes according to the harmonic law. Let us now find the law according to which the current strength in the circuit changes.

By definition, but q=q m cosшt, so

where p/2 is the phase shift between current and charge (voltage). So, we found out that the current strength during electromagnetic oscillations also changes according to the harmonic law.

We considered an ideal oscillatory circuit in which there are no energy losses and free oscillations can continue indefinitely due to the energy once received from an external source. In a real circuit, part of the energy goes to heating the connecting wires and heating the coil. Therefore, free oscillations in the oscillatory circuit are damped.

Own undamped electromagnetic oscillations

Electromagnetic vibrations are called oscillations of electric charges, currents and physical quantities that characterize electric and magnetic fields.

Oscillations are called periodic if the values ​​of physical quantities that change in the process of oscillations are repeated at regular intervals.

The simplest type of periodic oscillations are harmonic oscillations. Harmonic oscillations are described by the equations

Or .

There are fluctuations of charges, currents and fields, inextricably linked with each other, and fluctuations of fields that exist in isolation from charges and currents. The former take place in electrical circuits, the latter in electromagnetic waves.

Oscillatory circuit called an electrical circuit in which electromagnetic oscillations can occur.

An oscillatory circuit is any closed electrical circuit consisting of a capacitor with a capacitance C, an inductor with an inductance L and a resistor with a resistance R, in which electromagnetic oscillations occur.

The simplest (ideal) oscillatory circuit is a capacitor and an inductor connected to each other. In such a circuit, the capacitance is concentrated only in the capacitor, the inductance is concentrated only in the coil, and, in addition, the ohmic resistance of the circuit is zero, i.e. no heat loss.

In order for electromagnetic oscillations to occur in the circuit, the circuit must be brought out of equilibrium. To do this, it is enough to charge the capacitor or excite the current in the inductor and leave it to itself.

We will inform one of the capacitor plates a charge + q m. Due to the phenomenon of electrostatic induction, the second capacitor plate will be charged with a negative charge - q m. An electric field with energy will appear in the capacitor .

Since the inductor is connected to a capacitor, the voltage at the ends of the coil will be equal to the voltage between the capacitor plates. This will lead to the directed movement of free charges in the circuit. As a result, in the electrical circuit of the circuit, it is observed simultaneously: neutralization of charges on the capacitor plates (capacitor discharge) and the ordered movement of charges in the inductor. The ordered movement of charges in the circuit of the oscillatory circuit is called the discharge current.

Due to the phenomenon of self-induction, the discharge current will begin to increase gradually. The greater the inductance of the coil, the slower the discharge current increases.

Thus, the potential difference applied to the coil accelerates the movement of charges, and the self-induction emf, on the contrary, slows them down. Joint action potential difference and emf self-induction leads to a gradual increase discharge current . At the moment when the capacitor is completely discharged, the current in the circuit will reach its maximum value I m.

This completes the first quarter of the period of the oscillatory process.

In the process of discharging the capacitor, the potential difference on its plates, the charge of the plates and the electric field strength decrease, while the current through the inductor and the magnetic field increase. The energy of the electric field of the capacitor is gradually converted into the energy of the magnetic field of the coil.

At the moment of completion of the discharge of the capacitor, the energy of the electric field will be equal to zero, and the energy of the magnetic field will reach its maximum

,

where L is the inductance of the coil, I m is the maximum current in the coil.

Presence in the circuit capacitor leads to the fact that the discharge current on its plates is interrupted, the charges here are decelerated and accumulated.

On the plate in the direction to which the current flows, positive charges accumulate, on the other plate - negative. An electrostatic field reappears in the capacitor, but now in the opposite direction. This field slows down the movement of coil charges. Consequently, the current and its magnetic field begin to decrease. A decrease in the magnetic field is accompanied by the appearance of a self-induction emf, which prevents the current from decreasing and maintains its original direction. Due to the combined action of the newly arisen potential difference and the self-induction emf, the current decreases to zero gradually. The energy of the magnetic field is again converted into the energy of the electric field. This completes half of the period of the oscillatory process. In the third and fourth parts, the described processes are repeated, as in the first and second parts of the period, but in the opposite direction. After passing all these four stages, the circuit will return to its original state. Subsequent cycles of the oscillatory process will be exactly repeated.

In the oscillatory circuit, the following physical quantities periodically change:

q - charge on the capacitor plates;

U is the potential difference across the capacitor and, consequently, at the ends of the coil;

I - discharge current in the coil;

Electric field strength;

Magnetic field induction;

W E - energy of the electric field;

W B - energy of the magnetic field.

Let's find dependences q , I , , W E , W B on time t .

To find the law of charge change q = q(t), it is necessary to compose a differential equation for it and find a solution to this equation.

Since the circuit is ideal (that is, it does not radiate electromagnetic waves and does not generate heat), its energy, consisting of the sum of the magnetic field energy W B and the electric field energy W E , remains unchanged at any time.

where I(t) and q(t) are the instantaneous values ​​of the current and charge on the capacitor plates.

Denoting , we obtain a differential equation for the charge

The solution of the equation describes the change in the charge on the capacitor plates over time.

,

where is the amplitude value of the charge; - initial phase; - cyclic oscillation frequency, - oscillation phase.

Oscillations of any physical quantity describing the equation are called natural undamped oscillations. The value is called the natural cyclic oscillation frequency. The oscillation period T is the smallest period of time after which the physical quantity takes the same value and has the same speed.

The period and frequency of natural oscillations of the circuit are calculated by the formulas:

Expression called the Thomson formula.

Changes in the potential difference (voltage) between the capacitor plates over time

, where - voltage amplitude.

The dependence of the current strength on time is determined by the relation -

where - current amplitude.

The dependence of the self-induction emf on time is determined by the relation -

where - self-induction emf amplitude.

The dependence of the electric field energy on time is determined by the relation

where - the amplitude of the energy of the electric field.

The dependence of the magnetic field energy on time is determined by the relation

where - the amplitude of the energy of the magnetic field.

The expressions for the amplitudes of all changing quantities include the amplitude of the charge q m . This value, as well as the initial phase of oscillations φ 0 are determined by the initial conditions - the charge of the capacitor and the current in contour at the initial time t = 0.

Dependencies
from time t are shown in fig.

In this case, the oscillations of the charge and the potential difference occur in the same phases, the current lags behind the potential difference in phase by , the frequency of oscillations of the energies of the electric and magnetic fields is twice the frequency of oscillations of all other quantities.

ELECTROMAGNETIC OSCILLATIONS. FREE AND FORCED ELECTRIC OSCILLATIONS IN THE OSCILLATION CIRCUIT.

1. Electromagnetic vibrations- interconnected fluctuations of electric and magnetic fields.

Electromagnetic oscillations appear in various electrical circuits. In this case, the charge value, voltage, current strength, electric field strength, magnetic field induction and other electrodynamic quantities fluctuate.

Free electromagnetic oscillationsarise in the electromagnetic system after removing it from the state of equilibrium, for example, by imparting a charge to the capacitor or by changing the current in the circuit section.

These are damped vibrations, since the energy communicated to the system is spent on heating and other processes.

Forced electromagnetic oscillations- undamped oscillations in the circuit caused by an external periodically changing sinusoidal EMF.

Electromagnetic oscillations are described by the same laws as mechanical ones, although the physical nature of these oscillations is completely different.

Electrical oscillations are a special case of electromagnetic ones, when oscillations of only electrical quantities are considered. In this case, they talk about alternating current, voltage, power, etc.

1. OSCILLATORY CIRCUIT

An oscillatory circuit is an electrical circuit consisting of a series-connected capacitor with a capacitance C, an inductor with an inductance Land a resistor with resistance R. Ideal circuit - if the resistance can be neglected, that is, only the capacitor C and the ideal coil L.

The state of stable equilibrium of the oscillatory circuit is characterized by the minimum energy of the electric field (the capacitor is not charged) and the magnetic field (there is no current through the coil).

1. CHARACTERISTICS OF ELECTROMAGNETIC OSCILLATIONS

Analogy of mechanical and electromagnetic oscillations

where q" is the second derivative of charge with respect to time.

Value is the cyclic frequency. The same equations describe fluctuations in current, voltage, and other electrical and magnetic quantities.

One of the solutions to equation (1) is the harmonic function

This is an integral equation of harmonic oscillations.

Oscillation period in the circuit (Thomson formula):

The value φ = ώt + φ 0 , standing under the sign of sine or cosine, is the phase of the oscillation.

The current in the circuit is equal to the derivative of the charge with respect to time, it can be expressed

The voltage on the capacitor plates varies according to the law:

Where I max \u003d ωq poppy is the amplitude of the current (A),

Umax=qmax /C - voltage amplitude (V)

Exercise: for each state of the oscillatory circuit, write down the values ​​of the charge on the capacitor, the current in the coil, the electric field strength, the magnetic field induction, the electric and magnetic energy.

Although mechanical and electromagnetic oscillations have a different nature, many analogies can be drawn between them. For example, consider electromagnetic oscillations in an oscillatory circuit and the oscillation of a load on a spring.

Swinging load on a spring

With mechanical oscillations of a body on a spring, the coordinate of the body will periodically change. In this case, we will change the projection of the body velocity on the Ox axis. In electromagnetic oscillations, over time, according to a periodic law, the charge q of the capacitor will change, and the current strength in the circuit of the oscillatory circuit.

The values ​​will have the same pattern of change. This is because there is an analogy between the conditions under which oscillations occur. When we remove the load on the spring from the equilibrium position, an elastic force F control arises in the spring, which tends to return the load back to the equilibrium position. The coefficient of proportionality of this force will be the stiffness of the spring k.

When the capacitor is discharged, a current appears in the oscillating circuit circuit. The discharge is due to the fact that there is a voltage u on the capacitor plates. This voltage will be proportional to the charge q of any of the plates. The proportionality factor will be the value 1/C, Where C is the capacitance of the capacitor.

When a load moves on a spring, when we release it, the speed of the body increases gradually, due to inertia. And after the termination of the force, the speed of the body does not immediately become equal to zero, it also gradually decreases.

Oscillatory circuit

The same is true in the oscillatory circuit. The electric current in the coil under the influence of voltage does not increase immediately, but gradually, due to the phenomenon of self-induction. And when the voltage ceases to act, the current strength does not immediately become equal to zero.

That is, in the oscillatory circuit, the inductance of the coil L will be similar to the mass of the body m, when the load oscillates on the spring. Consequently, the kinetic energy of the body (m * V ^ 2) / 2, will be similar to the energy of the magnetic field of the current (L * i ^ 2) / 2.

When we remove the load from the equilibrium position, we inform the mind of some potential energy (k * (Xm) ^ 2) / 2, where Xm is the displacement from the equilibrium position.

In the oscillatory circuit, the role of potential energy is performed by the charge energy of the capacitor q ^ 2 / (2 * C). We can conclude that the stiffness of the spring in mechanical vibrations will be similar to the value 1/C, where C is the capacitance of the capacitor in electromagnetic vibrations. And the coordinate of the body will be similar to the charge of the capacitor.

Let us consider in more detail the processes of oscillations, in the following figure.

picture

(a) We inform the body of potential energy. By analogy, we charge the capacitor.

(b) We release the ball, the potential energy begins to decrease, and the speed of the ball increases. By analogy, the charge on the capacitor plate begins to decrease, and a current appears in the circuit.

(c) Equilibrium position. There is no potential energy, the speed of the body is maximum. The capacitor is discharged, the current in the circuit is maximum.

(e) The body deviated in the extreme position, its velocity became equal to zero, and the potential energy reached its maximum. The capacitor charged again, the current in the circuit began to equal zero.

Lesson topic.

Analogy between mechanical and electromagnetic oscillations.

Lesson Objectives:

Didactic – draw a complete analogy between mechanical and electromagnetic oscillations, revealing the similarities and differences between them;

educational – to show the universal nature of the theory of mechanical and electromagnetic oscillations;

Educational - to develop the cognitive processes of students, based on the application of the scientific method of cognition: similarity and modeling;

Educational - to continue the formation of ideas about the relationship between natural phenomena and a single physical picture of the world, to teach to find and perceive beauty in nature, art and educational activities.

Type of lesson :

combined lesson

Work form:

individual, group

Methodological support :

computer, multimedia projector, screen, reference notes, self-study texts.

Intersubject communications :

physics

During the classes

Organizing time.

In today's lesson, we will draw an analogy between mechanical and electromagnetic oscillations.

II. Checking homework.

Physical dictation.

What is an oscillatory circuit made of?

The concept of (free) electromagnetic oscillations.

3. What needs to be done in order for electromagnetic oscillations to occur in the oscillatory circuit?

4. What device allows you to detect the presence of oscillations in the oscillatory circuit?

Knowledge update.

Guys, write down the topic of the lesson.

And now we will carry out comparative characteristics of the two types of oscillations.

Frontal work with the class (checking is carried out through the projector).

(Slide 1)

Question for students: What do the definitions of mechanical and electromagnetic oscillations have in common and how do they differ!

General: in both types of oscillations, a periodic change in physical quantities occurs.

Difference: In mechanical vibrations - this is the coordinate, speed and acceleration In electromagnetic - charge, current and voltage.

(Slide 2)

Question for students: What do the methods of obtaining have in common and how do they differ?

General: both mechanical and electromagnetic oscillations can be obtained using oscillatory systems

Difference: various oscillatory systems - for mechanical ones - these are pendulums,and for electromagnetic - an oscillatory circuit.

(Slide3)

Question to students : "What do the demos shown have in common and how do they differ?"

General: the oscillatory system was removed from the equilibrium position and received a supply of energy.

Difference: the pendulums received a reserve of potential energy, and the oscillatory system received a reserve of energy of the electric field of the capacitor.

Question to students : Why electromagnetic oscillations cannot be observed as well as mechanical ones (visually)

Answer: since we cannot see how the capacitor is charging and recharging, how the current flows in the circuit and in what direction, how the voltage between the capacitor plates changes

Independent work

(Slide3)

Students are asked to complete the table on their own.Correspondence between mechanical and electrical quantities in oscillatory processes

III. Fixing the material

Reinforcing test on this topic:

1. The period of free oscillations of a thread pendulum depends on...
A. From the mass of the cargo. B. From the length of the thread. B. From the frequency of oscillations.

2. The maximum deviation of the body from the equilibrium position is called ...
A. Amplitude. B. Offset. During the period.

3. The oscillation period is 2 ms. The frequency of these oscillations isA. 0.5 Hz B. 20 Hz C. 500 Hz

(Answer:Given:
mswith Find:
Solution: Hz
Answer: 20 Hz)

4. Oscillation frequency 2 kHz. The period of these oscillations is
A. 0.5 s B. 500 µs C. 2 s(Answer:T= 1\n= 1\2000Hz = 0.0005)

5. The oscillatory circuit capacitor is charged so that the charge on one of the capacitor plates is + q. After what is the minimum time after the capacitor is closed to the coil, the charge on the same capacitor plate becomes equal to - q, if the period of free oscillations in the circuit is T?
A. T/2 B. T V. T/4

(Answer:A) Т/2because even after T/2 the charge becomes +q again)

6. How many complete oscillations will a material point make in 5 s if the oscillation frequency is 440 Hz?
A. 2200 B. 220 V. 88

(Answer:U=n\t hence n=U*t ; n=5 s * 440 Hz=2200 vibrations)

7. In an oscillatory circuit consisting of a coil, a capacitor and a key, the capacitor is charged, the key is open. After what time after the switch is closed, the current in the coil will increase to a maximum value if the period of free oscillations in the circuit is equal to T?
A. T/4 B. T/2 W. T

(Answer:Answer T/4at t=0 the capacitance is charged, the current is zerothrough T / 4 the capacity is discharged, the current is maximumthrough T / 2, the capacitance is charged with the opposite voltage, the current is zerothrough 3T / 4 the capacity is discharged, the current is maximum, opposite to that at T / 4through T the capacitance is charged, the current is zero (the process is repeated)

8. The oscillatory circuit consists
A. Capacitor and resistor B. Capacitor and bulb C. Capacitor and inductor

IV . Homework

G. Ya. Myakishev§18, pp.77-79

Answer the questions:

1. In what system do electromagnetic oscillations occur?

2. How is the transformation of energies carried out in the circuit?

3. Write down the energy formula at any time.

4. Explain the analogy between mechanical and electromagnetic oscillations.

V . Reflection

Today I found out...

it was interesting to know...

it was hard to do...

now I can decide..

I have learned (learned)...

I managed…

I could)…

I will try myself...

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