One of the most interesting topics in physics is oscillations. The study of mechanics is closely connected with them, with how bodies behave, which are affected by certain forces. So, studying oscillations, we can observe pendulums, see the dependence of the oscillation amplitude on the length of the thread on which the body hangs, on the stiffness of the spring, and the weight of the load. Despite the apparent simplicity, this topic is far from being given to everyone as easily as we would like. Therefore, we decided to collect the most well-known information about oscillations, their types and properties, and compile for you a brief summary on this topic. Perhaps it will be useful to you.

Concept definition

Before talking about such concepts as mechanical, electromagnetic, free, forced vibrations, about their nature, characteristics and types, conditions of occurrence, this concept should be defined. So, in physics, oscillation is a constantly repeating process of changing the state around one point in space. The simplest example is a pendulum. Each time it oscillates, it deviates from a certain vertical point, first in one direction, then in the other direction. Engaged in the study of the phenomenon of the theory of oscillations and waves.

Causes and conditions of occurrence

Like any other phenomenon, fluctuations occur only if certain conditions are met. Mechanical forced vibrations, as well as free vibrations, arise when the following conditions are met:

1. The presence of a force that brings the body out of a state of stable equilibrium. For example, the push of a mathematical pendulum, at which the movement begins.

2. The presence of a minimum friction force in the system. As you know, friction slows down certain physical processes. The greater the friction force, the less likely the oscillations to occur.

3. One of the forces must depend on the coordinates. That is, the body changes its position in a certain coordinate system relative to a certain point.

Types of vibrations

Having dealt with what oscillation is, we will analyze their classification. There are two most famous classifications - by physical nature and by the nature of interaction with the environment. So, according to the first sign, mechanical and electromagnetic are distinguished, and according to the second - free and forced vibrations. There are also self-oscillations, damped oscillations. But we will only talk about the first four types. Let's take a closer look at each of them, find out their features, and also give a very brief description of their main characteristics.

Mechanical

It is with mechanical that the study of oscillations in the school course of physics begins. Students begin their acquaintance with them in such a branch of physics as mechanics. Note that these physical processes occur in the environment, and we can observe them with the naked eye. With such vibrations, the body repeatedly performs the same movement, passing through a certain position in space. Examples of such oscillations are the same pendulums, the vibration of a tuning fork or a guitar string, the movement of leaves and branches on a tree, a swing.

electromagnetic

After such a concept as mechanical oscillations is firmly mastered, the study of electromagnetic oscillations begins, which are more complex in structure, since this type occurs in various electrical circuits. In this process, oscillations are observed in electric as well as magnetic fields. Despite the fact that electromagnetic oscillations have a slightly different nature of occurrence, the laws for them are the same as for mechanical ones. With electromagnetic oscillations, not only the strength of the electromagnetic field can change, but also such characteristics as the strength of the charge and current. It is also important to note that there are free and forced electromagnetic oscillations.

Free vibrations

This type of oscillation occurs under the influence of internal forces when the system is taken out of a state of stable equilibrium or rest. Free oscillations are always damped, which means that their amplitude and frequency decrease with time. A striking example of this type of rocking is the movement of a load suspended on a thread and oscillating from one side to the other; a load attached to a spring, then falling down under the action of gravity, then rising up under the action of the spring. By the way, it is precisely this kind of oscillations that is paid attention to in the study of physics. Yes, and most of the tasks are devoted just to free vibrations, and not to forced ones.

Forced

Despite the fact that this kind of process is not studied in such detail by schoolchildren, it is forced oscillations that are most often encountered in nature. A rather striking example of this physical phenomenon can be the movement of branches on trees in windy weather. Such fluctuations always occur under the influence of external factors and forces, and they arise at any moment.

Oscillation characteristics

Like any other process, oscillations have their own characteristics. There are six main parameters of the oscillatory process: amplitude, period, frequency, phase, displacement and cyclic frequency. Naturally, each of them has its own designations, as well as units of measurement. Let's analyze them in a little more detail, dwelling on a brief description. At the same time, we will not describe the formulas that are used to calculate a particular value, so as not to confuse the reader.

Bias

The first one is displacement. This characteristic shows the deviation of the body from the equilibrium point at a given time. It is measured in meters (m), the common designation is x.

Oscillation amplitude

This value denotes the greatest displacement of the body from the equilibrium point. In the presence of undamped oscillation is a constant value. It is measured in meters, the generally accepted designation is x m.

Oscillation period

Another value that denotes the time for which one complete oscillation takes place. The generally accepted designation is T, measured in seconds (s).

Frequency

The last characteristic we will talk about is the oscillation frequency. This value indicates the number of oscillations in a certain period of time. It is measured in hertz (Hz) and is denoted as ν.

Types of pendulums

So, we have analyzed forced oscillations, talked about free ones, which means that we should also mention the types of pendulums that are used to create and study free oscillations (in school conditions). There are two types - mathematical and harmonic (spring). The first is a body suspended from an inextensible thread, the size of which is equal to l (the main significant value). The second is a weight attached to a spring. Here it is important to know the mass of the load (m) and the stiffness of the spring (k).

findings

So, we figured out that there are mechanical and electromagnetic oscillations, gave their brief description, described the causes and conditions for the occurrence of these types of oscillations. We said a few words about the main characteristics of these physical phenomena. We also figured out that there are forced vibrations and free ones. Determine how they differ from each other. In addition, we said a few words about pendulums used in the study of mechanical oscillations. We hope this information was useful to you.

There are different types of oscillations in physics, characterized by certain parameters. Consider their main differences, classification according to various factors.

Basic definitions

Oscillation is understood as a process in which, at regular intervals, the main characteristics of the movement have the same values.

Such oscillations are called periodic, in which the values ​​of the basic quantities are repeated at regular intervals (period of oscillations).

Varieties of oscillatory processes

Let us consider the main types of oscillations that exist in fundamental physics.

Free vibrations are those that occur in a system that is not subjected to external variable influences after the initial shock.

An example of free oscillations is a mathematical pendulum.

Those types of mechanical vibrations that occur in the system under the action of an external variable force.

Features of the classification

According to the physical nature, the following types of oscillatory movements are distinguished:

• mechanical;
• thermal;
• electromagnetic;
• mixed.

According to the option of interaction with the environment

Types of oscillations in interaction with the environment are divided into several groups.

Forced oscillations appear in the system under the action of an external periodic action. As examples of this type of oscillation, we can consider the movement of hands, leaves on trees.

For forced harmonic oscillations, a resonance may appear, in which, with equal values ​​of the frequency of the external action and the oscillator, with a sharp increase in amplitude.

Natural vibrations in the system under the influence of internal forces after it is taken out of equilibrium. The simplest variant of free vibrations is the movement of a load that is suspended on a thread or attached to a spring.

Self-oscillations are called types in which the system has a certain amount of potential energy used to make oscillations. Their distinctive feature is the fact that the amplitude is characterized by the properties of the system itself, and not by the initial conditions.

For random oscillations, the external load has a random value.

Basic parameters of oscillatory movements

All types of oscillations have certain characteristics, which should be mentioned separately.

Amplitude is the maximum deviation from the equilibrium position, the deviation of a fluctuating value, it is measured in meters.

The period is the time of one complete oscillation, after which the characteristics of the system are repeated, calculated in seconds.

The frequency is determined by the number of oscillations per unit of time, it is inversely proportional to the period of oscillation.

The oscillation phase characterizes the state of the system.

Characteristic of harmonic vibrations

Such types of oscillations occur according to the law of cosine or sine. Fourier managed to establish that any periodic oscillation can be represented as a sum of harmonic changes by expanding a certain function in

As an example, consider a pendulum having a certain period and cyclic frequency.

What characterizes these types of oscillations? Physics considers an idealized system, which consists of a material point, which is suspended on a weightless inextensible thread, oscillates under the influence of gravity.

Such types of vibrations have a certain amount of energy, they are common in nature and technology.

With prolonged oscillatory motion, the coordinates of its center of mass change, and with alternating current, the value of current and voltage in the circuit changes.

There are different types of harmonic oscillations according to their physical nature: electromagnetic, mechanical, etc.

The shaking of the vehicle, which moves on a rough road, acts as a forced oscillation.

The main differences between forced and free vibrations

These types of electromagnetic oscillations differ in physical characteristics. The presence of medium resistance and friction forces lead to damping of free oscillations. In the case of forced oscillations, energy losses are compensated by its additional supply from an external source.

The period of a spring pendulum relates the mass of the body and the stiffness of the spring. In the case of a mathematical pendulum, it depends on the length of the thread.

With a known period, it is possible to calculate the natural frequency of the oscillatory system.

In technology and nature, there are vibrations with different frequency values. For example, the pendulum that oscillates in St. Isaac's Cathedral in St. Petersburg has a frequency of 0.05 Hz, while for atoms it is several million megahertz.

After a certain period of time, the damping of free oscillations is observed. That is why forced oscillations are used in real practice. They are in demand in a variety of vibration machines. The vibratory hammer is a shock-vibration machine, which is intended for driving pipes, piles, and other metal structures into the ground.

Electromagnetic vibrations

Characteristics of vibration modes involves the analysis of the main physical parameters: charge, voltage, current strength. As an elementary system, which is used to observe electromagnetic oscillations, is an oscillatory circuit. It is formed by connecting a coil and a capacitor in series.

When the circuit is closed, free electromagnetic oscillations arise in it, associated with periodic changes in the electric charge on the capacitor and the current in the coil.

They are free due to the fact that when they are performed there is no external influence, but only the energy that is stored in the circuit itself is used.

In the absence of external influence, after a certain period of time, attenuation of the electromagnetic oscillation is observed. The reason for this phenomenon will be the gradual discharge of the capacitor, as well as the resistance that the coil actually has.

That is why damped oscillations occur in a real circuit. Reducing the charge on the capacitor leads to a decrease in the energy value in comparison with its original value. Gradually, it will be released in the form of heat on the connecting wires and the coil, the capacitor will be completely discharged, and the electromagnetic oscillation will be completed.

The Significance of Fluctuations in Science and Technology

Any movements that have a certain degree of repetition are oscillations. For example, a mathematical pendulum is characterized by a systematic deviation in both directions from the original vertical position.

For a spring pendulum, one complete oscillation corresponds to its movement up and down from the initial position.

In an electrical circuit that has capacitance and inductance, there is a repetition of charge on the plates of the capacitor. What is the cause of oscillatory movements? The pendulum functions due to the fact that gravity causes it to return to its original position. In the case of a spring model, a similar function is performed by the elastic force of the spring. Passing the equilibrium position, the load has a certain speed, therefore, by inertia, it moves past the average state.

Electrical oscillations can be explained by the potential difference that exists between the plates of a charged capacitor. Even when it is completely discharged, the current does not disappear, it is recharged.

In modern technology, oscillations are used, which differ significantly in their nature, degree of repetition, character, and also the "mechanism" of occurrence.

Mechanical vibrations are made by the strings of musical instruments, sea waves, and a pendulum. Chemical fluctuations associated with a change in the concentration of reactants are taken into account when conducting various interactions.

Electromagnetic oscillations make it possible to create various technical devices, for example, a telephone, ultrasonic medical devices.

Cepheid brightness fluctuations are of particular interest in astrophysics, and scientists from different countries are studying them.

Conclusion

All types of oscillations are closely related to a huge number of technical processes and physical phenomena. Their practical importance is great in aircraft construction, shipbuilding, the construction of residential complexes, electrical engineering, radio electronics, medicine, and fundamental science. An example of a typical oscillatory process in physiology is the movement of the heart muscle. Mechanical vibrations are found in organic and inorganic chemistry, meteorology, and also in many other natural sciences.

The first studies of the mathematical pendulum were carried out in the seventeenth century, and by the end of the nineteenth century, scientists were able to establish the nature of electromagnetic oscillations. The Russian scientist Alexander Popov, who is considered the "father" of radio communications, conducted his experiments precisely on the basis of the theory of electromagnetic oscillations, the results of research by Thomson, Huygens, and Rayleigh. He managed to find a practical application for electromagnetic oscillations, to use them to transmit a radio signal over a long distance.

Academician P. N. Lebedev for many years conducted experiments related to the production of high-frequency electromagnetic oscillations using alternating electric fields. Thanks to numerous experiments related to various types of oscillations, scientists have managed to find areas for their optimal use in modern science and technology.

Periodic fluctuations

"... periodic fluctuations - fluctuations in which each value of a fluctuating quantity is repeated at regular intervals ..."

Source:

"GOST 24346-80 (ST SEV 1926-79). State Union of the SSR. Terms and definitions"

(approved and put into effect by the Decree of the State Standard of the USSR of 31.07.1980 N 3942)

Official terminology. Akademik.ru. 2012 .

See what "Periodic Oscillations" is in other dictionaries:

periodic oscillations (vibration)- Oscillations (vibration), in which each value of the oscillating quantity (characterizing vibration) is repeated at regular intervals. Explanations Terms and definitions for related concepts that differ only in individual words are combined, ... ...

VASCULATION- movements or processes that have a certain degree of repetition in time. Radiation is characteristic of all natural phenomena: the radiation of stars pulsates, inside which cyclic reactions occur. I. reactions; planets rotate with a high degree of periodicity ... ... Physical Encyclopedia

SEVERAL VIBRATIONS- periodic and long-period fluctuations: ur. m., land (as a result of epeirogenic movements), climate, ur. lakes, ends of glaciers. The term is outdated, since periodic fluctuations in the intensity of the manifestation of certain processes can be ... ... Geological Encyclopedia

periodic fluctuations- Mechanical vibrations, in which the state of the mechanical system is repeated at regular intervals. [Collection of recommended terms. Issue 106. Mechanical vibrations. USSR Academy of Sciences. Committee of Scientific and Technical Terminology. 1987... Technical Translator's Handbook

CLIMATE VARIATIONS- are installed as periodic with decomp. vibrational rhythms. Basically, they are synchronous, as they can be traced over large spaces, only deviating in places, depending on both general (geographical, etc.) and local (peculiarities of geol ... Geological Encyclopedia

SEA LEVEL VARIATIONS PERIODICAL- 1. Fluctuations ur. m. in the form of ebbs and flows. 2. Seasonal declines and increases lvl. m., as well as annual, perennial and secular, due to climatic reasons. The amplitude of seasonal fluctuations does not exceed 28 cm. In inland seas, it ... ... Geological Encyclopedia

Periodic oscillations (vibration)- - fluctuations (vibration), in which each value of the oscillating quantity (characterizing vibration) is repeated at regular intervals. [GOST 24346 80] Heading of the term: Types of vibration Encyclopedia headings: Abrasive equipment, ... ... Encyclopedia of terms, definitions and explanations of building materials

Periodic level fluctuations- changes in the water level depending on the tidal phenomena, precipitation, changes in atmospheric pressure and the direction of the winds in the area. The frequency of changes, as a rule, is semi-daily, seasonal, annual. ... ... Marine Dictionary

fluctuations- Movements or processes that have a varying degree of repeatability in time [Terminological dictionary for construction in 12 languages ​​(VNIIIS Gosstroy of the USSR)] fluctuations An element of the time series that reflects the periodic events occurring in the economy ... Technical Translator's Handbook

fluctuations- an element of the time series, reflecting the periodic changes occurring in the economy, for example, ups and downs in production and consumption of certain goods. In economic and mathematical models for an approximate ... ... Economic and Mathematical Dictionary

Books

• Nonlinear Oscillations and Waves, P. S. Landa. This book presents the current state of the theory of nonlinear oscillations and waves. From a unified point of view, oscillatory and wave processes are considered, both periodic and ...

General oscillation characteristic

Rhythmic processes of any nature, characterized by repetition in time, are called oscillations.

Oscillation is a process characterized by the repeatability in time of the parameters that describe it. The unity of the regularities of rhythmic processes made it possible to develop a single mathematical apparatus for their description - the theory of oscillations. There are many features by which fluctuations can be classified.

By physical nature oscillating system distinguish between mechanical and electromagnetic oscillations.

The fluctuations are called periodic, if the value characterizing the state of the system is repeated at regular intervals - the period of oscillation.

Period (T) - the minimum time after which the state of the oscillatory system is repeated, i.e. the time of one complete oscillation.

For such fluctuations

x(t)=x(t+T);(3. 1)

Periodic are the oscillations of the pendulum of the clock, alternating current, the beating of the heart, and the oscillations of trees under a gust of wind, foreign exchange rates are not periodic.

In addition to the period, in the case of periodic oscillations, their frequency is determined.

Frequency()those. number of oscillations per unit of time.

Frequency is the reciprocal of the oscillation period,

The frequency unit is Hertz: 1 Hz \u003d 1 s -1, the frequency corresponding to one oscillation per second. When describing periodic oscillations, one also uses cyclic frequency– number of oscillations for 2 π seconds:

With periodic oscillations, these parameters are constant, while with other oscillations they can change.

The law of oscillations - the dependence of a fluctuating quantity on time x(t)- may be different. The simplest are harmonic fluctuations (Fig. 3.1), for which the fluctuating value changes according to the sine or cosine law, which allows using one function to describe the process in time:

Here: x(t) - the value of the fluctuating value at a given time t, BUT – amplitude- the largest deviation of the oscillating value from the average value., ω - cyclic frequency, ( ωt+φ) – oscillation phase, φ - initial phase.

Many well-known oscillatory processes obey the harmonic law. including mentioned above, but most importantly, with the help of Fourier method any periodic function decomposing into harmonic components ( harmonics) with multiple frequencies:

f(t)= BUT + BUT 1 cos( t + )+ BUT cos(2t+ )+…; (3.5)

Here the main frequency is determined by the period of the process: .

Each harmonic is characterized by frequency () and amplitude ( BUT). The set of harmonics is called spectrum. The spectra of periodic oscillations are discrete (linear) (Fig. 3.1a), and not periodic continuous (Fig. 3.1b).

Rice. 3.1 Discrete (a) and continuous (b) spectra of complex vibrational

Types of vibrations

The oscillatory system has a certain energy, due to which vibrations are made. The energy depends on the amplitude and frequency of oscillations.

Oscillations are divided into the following types: free or natural, damped, forced, self-oscillations.

Free oscillations occur in a system that is once taken out of equilibrium and subsequently left to itself. In this case, oscillations occur with own frequency (), which does not depend on their amplitude, i.e. determined by the properties of the system itself.

In real conditions, fluctuations are always fading, i.e. energy decreases over time due to its dissipation and as a result, the amplitude of oscillations decreases. Dissipation is an irreversible transition of a part of the energy of ordered processes (“order energy”) into the energy of disordered processes (“chaos energy”). Dissipation occurs in any oscillating open system.

To create undamped oscillations in real systems, a periodic external action is necessary - a periodic replenishment of the energy lost due to dissipation. Harmonic oscillations occurring due to external periodic influences ("driving force") are called forced. Their frequency coincides with the frequency of the driving force (), and the amplitude depends on the ratio between the frequency of the force and the natural frequency of the system. The most important effect that occurs during forced oscillations is resonance– a sharp increase in the amplitude when the frequency of forced oscillations approaches the natural frequency of the oscillatory system. The resonant frequency is the closer to its own, and the maximum amplitude is the greater, the less dissipation.

Self-oscillations are undamped oscillations that occur due to an energy source, the type and operation of which is determined by the oscillatory system itself. With self-oscillations, the main characteristics - amplitude, frequency - are determined by the system itself. This distinguishes these oscillations from both forced ones, in which these parameters depend on external influences, and from natural ones, in which the external influence sets the oscillation amplitude. The simplest self-oscillating system includes:

oscillatory system (with damping),

oscillation amplifier (energy source),

non-linear limiter (valve),

feedback link

With self-oscillations, for their establishment, nonlinearity is important, which controls the input and output of source energy, and allows you to set oscillations of a certain amplitude. Examples of self-oscillating systems are: mechanical - pendulum clock, thermodynamic - heat engine, electromagnetic - tube generator, optical - laser (optical quantum generator). The laser scheme is shown in Fig. 4.5. Here the oscillatory system is an optically active medium that fills the optical resonator, there is an external energy source that provides the "pumping" process, a valve and feedback - a translucent mirror at the output of the optical resonator, the nonlinearity is determined by the conditions of stimulated emission.

In all self-oscillatory systems, feedback regulates the inclusion of an external source and the energy supply to the oscillatory system: as long as the energy input (contribution) is higher than the loss, self-excitation (buildup) occurs, oscillations in the system increase; when the energy loss equals the energy gain, the valve closes. The system oscillates in a stationary mode with a constant amplitude; as the loss increases, the amplitude decreases and the valve opens again, the contribution increases, the amplitude is restored, and the valve closes.

Mechanical vibrations. Oscillation parameters. Harmonic vibrations.

hesitation A process is called exactly or approximately repeating at certain intervals.

A feature of oscillations is the obligatory presence of a stable equilibrium position on the trajectory, in which the sum of all forces acting on the body is equal to zero is called the equilibrium position.

A mathematical pendulum is a material point suspended on a thin, weightless and inextensible thread.

Parameters of oscillatory motion.

1. Offset or coordinate (x) - deviation from the equilibrium position in a given

moment of time.	[x ]=m

2. Amplitude ( xm) is the maximum deviation from the equilibrium position.

[ X m ]=m

3. Oscillation period ( T) is the time it takes for one complete oscillation.

[T ]=c.

0 "style="margin-left:31.0pt;border-collapse:collapse">

Mathematical pendulum

Spring pendulum

m

https://pandia.ru/text/79/117/images/image006_26.gif" width="134" height="57 src="> Frequency (linear) ( n ) – the number of complete oscillations in 1 s.

[n]= Hz

5. Cyclic frequency ( w ) – the number of complete oscillations in 2p seconds, i.e., approximately 6.28 s.

w = 2pn ; [w]=0" style="margin-left:116.0pt;border-collapse:collapse">

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The shadow on the screen fluctuates.

Equation and graph of harmonic oscillations.

Harmonic vibrations - these are oscillations in which the coordinate changes over time according to the law of sine or cosine.

https://pandia.ru/text/79/117/images/image014_7.jpg" width="254" height="430 src="> x=Xmsin(w t+ j 0 )

x=Xmcos(w t+ j 0 )

x - coordinate,

Xm is the oscillation amplitude,

w is the cyclic frequency,

wt+j 0 = j is the oscillation phase,

j 0 is the initial phase of oscillations.

https://pandia.ru/text/79/117/images/image016_4.jpg" width="247" height="335 src=">

Graphs are different only amplitude

Graphs differ only in period (frequency)

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If the amplitude of the oscillations does not change over time, the oscillations are called undamped.

Natural vibrations do not take into account friction, the total mechanical energy of the system remains constant: E to + E n = E fur = const.

Natural oscillations are undamped.

With forced oscillations, the energy supplied continuously or periodically from an external source compensates for the losses arising due to the work of the friction force, and the oscillations can be undamped.

The kinetic and potential energy of the body during vibrations pass into each other. When the deviation of the system from the equilibrium position is maximum, the potential energy is maximum, and the kinetic energy is zero. When passing through the equilibrium position, vice versa.

The frequency of free oscillations is determined by the parameters of the oscillatory system.

The frequency of forced oscillations is determined by the frequency of the external force. The amplitude of forced oscillations also depends on the external force.

Resonan c

Resonance called a sharp increase in the amplitude of forced oscillations when the frequency of the action of an external force coincides with the frequency of natural oscillations of the system.

When the frequency w of the change in the force coincides with the natural frequency w0 of the oscillations of the system, the force does positive work throughout the entire period, increasing the amplitude of the body's oscillations. At any other frequency, during one part of the period, the force does positive work, and during the other part of the period, it does negative work.

At resonance, an increase in the oscillation amplitude can lead to the destruction of the system.

In 1905, under the hooves of a squadron of guards cavalry, the Egyptian bridge across the Fontanka River in St. Petersburg collapsed.

Self-oscillations.

Self-oscillations are called undamped oscillations in the system, supported by internal energy sources in the absence of external force change.

Unlike forced oscillations, the frequency and amplitude of self-oscillations are determined by the properties of the oscillatory system itself.

Self-oscillations differ from free oscillations by the independence of the amplitude from time and from the initial short-term impact that excites the process of oscillations. A self-oscillating system can usually be divided into three elements:

1) oscillatory system;

2) energy source;

3) a feedback device that regulates the flow of energy from a source into an oscillatory system.

The energy coming from the source over a period is equal to the energy lost in the oscillatory system over the same time.