A common property of all oscillatory systems is the emergence of force. Free vibrations
fluctuations are a very common form of movement. You must have seen oscillatory movements at least once in your life in a swinging pendulum of a clock or tree branches in the wind. Chances are you've plucked the strings of a guitar at least once and seen them vibrate. It is obvious that even if you have not seen it with your own eyes, you can at least imagine how a needle moves in a sewing machine or a piston in an engine.
In all these cases, we have a body that periodically performs repetitive motions. It is precisely such movements that are called in physics oscillations or oscillatory movements. Fluctuations occur in our lives very, very often.
Soundare fluctuations in air density and pressure,
radio waves– periodic changes in the strength of the electric and magnetic fields,
visible light- too electromagnetic oscillations, only with slightly different wavelength and frequency.
earthquakes- ground vibrations,
ebbs and flows- change in the level of the seas and oceans, caused by the attraction of the moon and reaching in some areas 18 meters,
heartbeat- periodic contractions of the human heart muscle, etc.
The change of wakefulness and sleep, work and rest, winter and summer... Even our daily going to work and returning home falls under the definition of fluctuations, which are interpreted as processes that repeat exactly or approximately at regular intervals.
Vibrations are mechanical, electromagnetic, chemical, thermodynamic and various others. Despite this diversity, they all have much in common and are therefore described by the same equations.
home general characteristics periodically repeating movements - these movements are repeated at regular intervals, called the oscillation period.
Let's summarize:mechanical vibrations - These are body movements that repeat exactly or approximately at the same intervals of time.
A special branch of physics - the theory of oscillations - deals with the study of the laws of these phenomena. Shipbuilders and aircraft builders, industry and transport specialists, creators of radio engineering and acoustic equipment need to know them.
In the process of making oscillations, the body constantly tends to the equilibrium position. Oscillations also arise due to the fact that someone or something deviated the given body from its equilibrium position, thus giving the body energy, which causes its further oscillations.
Vibrations that occur only due to this primordial energy are called free vibrations. This means that they do not need constant help from the outside to maintain the oscillatory movement. 
Most fluctuations in the reality of life occur with gradual damping due to friction forces, air resistance, and so on. Therefore, free oscillations are often called such oscillations, the gradual damping of which can be neglected for the duration of the observations.
In this case, all bodies connected and directly involved in oscillations are collectively called an oscillatory system. In the general case, it is usually said that an oscillatory system is a system in which oscillations can exist.
In particular, if a freely suspended body oscillates on a thread, then the body itself, the suspension, will enter the oscillatory system, to which the suspension and the Earth are attached with its attraction, which makes the body oscillate, constantly returning to a state of rest. 
Such a body is a pendulum. In physics, several types of pendulums are distinguished: thread, spring, and some others. All systems in which an oscillating body or its suspension can be conditionally represented as a thread are filament systems. If this ball is shifted away from the equilibrium position and released, then it will start hesitate, i.e., to perform repetitive movements, periodically passing through the equilibrium position.
Well, spring pendulums, as you might guess, consist of a body and a certain spring that can oscillate under the action of the elastic force of the spring.
The main model for observing oscillations is the so-called mathematical pendulum. Mathematical pendulum called a body of small size (compared to the length of the thread), suspended on a thin inextensible thread, the mass of which is negligible compared to the mass body. Simply put, in our reasoning, we do not take into account the pendulum thread at all.
What properties should bodies have so that we can safely say that they constitute an oscillatory system, and we can describe it theoretically and mathematically.
Well, think for yourself how the oscillatory movement occurs for a filament pendulum.
As a hint - a picture.
Any oscillatory motion is a motion that occurs with acceleration, therefore forces must act on oscillating bodies that impart these accelerations to them. In particular, if a point body with a mass performs a harmonic oscillation, then, according to the second law of mechanics, a force equal to
where The direction of the force coincides with the direction of acceleration, and the acceleration vector for harmonic oscillations, according to formula (4.5), is always directed towards the equilibrium position. Thus, in order for a body to perform a harmonic oscillatory motion, a force must act on it, always directed towards the equilibrium position, and in magnitude - directly proportional to the displacement from this position. In the study of oscillatory systems, one can easily find the coefficient of proportionality between the force acting on the body and the displacement x of this body from the equilibrium position; then, knowing also the mass of the oscillating body, one can calculate the frequency and period of the oscillation; from the ratio it follows:
Forces that are always directed towards the equilibrium position are called restoring forces. Let's look at a few examples:
1. An oscillatory system consisting of a mass and a spring (see Fig. 1.36, b). The restoring force is the elastic force acting on the body from the deformed spring. This force at small deformations is directly proportional to the change in the length of the spring. By applying external forces to the spring and measuring the elongations caused by them
(or compression) of the spring, you can find the coefficient of elasticity of the spring and, using formula (4.10), calculate the vibration frequency of the bodies attached to the ends of the spring. In this case, the oscillations will be harmonic and constant) only if no other forces act on the oscillating body, except for the restoring one, and the coefficient on which, according to formula (4.10), the oscillation frequency depends, must always remain constant. In particular, if the temperature of the spring changes, then, consequently, the oscillation frequency also changes; vibrations are not harmonic.
2. A system that performs torsional (rotary) vibrations (see Fig. 1.38, b). During torsional vibrations, a restoring moment acts on the body, which stops the deviation of the body from the state of equilibrium and then imparts a reverse movement to it. The restoring moment occurs when the deformation (torsion) of the spring (or rod) to which the oscillating body is attached. At small deflection angles, this moment is directly proportional to the deflection angle.
If the torsional vibrations are harmonic, i.e.
then angular velocity and angular acceleration during rotation also change according to the harmonic law:
We find the restoring moment as the product of the angular acceleration and the moment of inertia of the oscillating body:
where is a constant value (if the moment of inertia of the body does not change during oscillations). This coefficient can be found by applying external torsional moments to the spring (or rod) and measuring the twisting angles a:
then the frequency and period of oscillations are determined by the formulas:
According to expression (4.13), with harmonic torsional vibrations, the restoring moment must be exactly proportional to the deflection angle; if this proportionality is not observed (for example, at very large angles of rotation), then the oscillations will not be harmonic (although in the absence of friction they will be undamped).
3. Physical pendulum (Fig. 1.40). The restoring moment is the moment of gravity, which has a sign,
opposite to the sign of the deflection angle a and equal to
where is the distance from the fulcrum to the center of gravity of the body.
At small deflection angles (angle a - in radians); then the returning moment
is proportional to the angle of deflection and the pendulum's oscillations will be harmonic.
Comparing with expression (4.13), we obtain, therefore,
At large deflection angles, as well as when the body is deformed during oscillations (variable oscillations turn out to be non-harmonic, although they can be undamped in the absence or compensation of friction.
4. Mathematical pendulum represents a point body with a mass suspended from a weightless and inextensible thread of length I (Fig. 1.41). The restoring force is the projection of gravity on the direction of motion of the body; we have:
in radians). We note that the condition of proportionality between the restoring force and the displacement from the equilibrium position x is also not observed here, therefore the oscillations of this pendulum are not harmonic. But if the angles a are small, then
since this force is always directed towards the equilibrium position and therefore has a sign opposite to that
In this case, the oscillations can be considered harmonic; comparing with expression (4.9), we get:
i.e., the frequency and period of oscillations do not depend on the mass of the oscillating body, but are determined only by the length of the thread and the acceleration of gravity (oscillations of pendulums are used to determine For the constant coefficient and, consequently, the frequency of oscillations, constancy is necessary. Meanwhile, the force acting along the thread can cause its elongation, which will be minimal in extreme positions and maximum when the body passes through point O. Therefore, in order for the pendulum to be harmonic, it is necessary, in addition to the smallness of the angles of deflection, to additionally have the condition of inextensibility of the thread.
These examples show that at small amplitudes, the frequency (or period) of oscillations is determined only by the properties of the system. However, for large deviations from the equilibrium position linear dependence the restoring force from the displacement as well as the increasing moment from the angle of rotation is not strictly observed and the oscillation frequency depends to some extent also on the oscillation amplitude or
The earth, the stand and the body suspended from the stand (see Fig. 3) form an oscillatory system called a physical pendulum. Racks, two springs and body m (see Fig. 4) form an oscillatory system, which is usually called a horizontal spring pendulum. All oscillatory systems have a number of common properties. Let's consider the main ones.
1 Each oscillatory system has a state of stable equilibrium. For a physical pendulum, this is the position in which the center of mass of the suspended body is on the same vertical with the suspension point. For a vertical spring pendulum, this is the position in which the force of gravity is balanced by the elastic force of the spring. For a horizontal spring pendulum, this is the position at which both springs are deformed equally.
2 After the oscillatory system is removed from the position of stable equilibrium, a force appears that returns the system to a stable position. The origin of this force may be different. So, for a physical pendulum, this is the resultant f of the gravity G and the elastic force T (Fig. 5), and for spring pendulums, this is the elastic force of the springs (Fig. 6).
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3 Returning to a stable state, the oscillatory system cannot immediately stop. In mechanical oscillatory systems, this is hindered by the inertia of the oscillating body. These properties lead to the fact that if the oscillatory system is brought out of the state of stable equilibrium in one way or another, then in the absence of external forces, oscillations will arise and persist for some time. The oscillations that have arisen could continue indefinitely if there were no friction (resistance) in the oscillatory system. It is these ideal oscillatory systems that we will consider in many cases. An ideal oscillatory system has two defining features:
a) there is no friction (resistance) in it and, therefore, no irreversible transformations of energy occur;
b) the parameters of such an oscillatory system (the length of the thread, the mass of the oscillating body, the stiffness of the spring) are constant.
An example of an ideal oscillatory system is the so-called mathematical pendulum, which is a small weight suspended on a flexible, weightless and inextensible spring. The length of the thread and the mass of the load remain unchanged during the oscillation of the pendulum. If the thread is considered infinitely thin and ideally flexible, and the dimensions of the load are infinitesimal, point-like, then there will be no friction during oscillations of the mathematical pendulum.
In real oscillatory systems, there is friction, and the parameters of the system change slightly during the oscillatory motion. So, a pendulum, which is a load of finite dimensions suspended on a silk thread, cannot be considered in the full sense an ideal oscillatory system, since in the process of its oscillatory movement air resistance and friction at the suspension point act, and the length of the thread changes (albeit very slightly) . But with small oscillations of such a pendulum, the air resistance is small, and the length of the thread changes so insignificantly that, with a certain approximation, this pendulum can be considered an almost ideal oscillatory system. This also applies to the spring pendulum. It can be considered an ideal oscillatory system if the mass of the oscillating body and the stiffness of the spring are constant, and the friction is so small that it can be ignored.
1 Free vibrations. Oscillations that occur in an oscillatory system that is not subject to the action of periodic external forces are called free oscillations. For the occurrence of free oscillations, a short-term impact must be exerted on the oscillatory system from the outside, bringing the system out of equilibrium (deviation from the average position of the pendulum, a steel ruler clamped in a vice, a string, etc.).
2 Oscillogram of oscillations.If the weight of the pendulum is a vessel with ink, in which there is a narrow hole, then when the pendulum oscillates.
General properties all oscillatory systems:
The presence of a position of stable equilibrium.
The presence of a force that returns the system to an equilibrium position.
Characteristics of the oscillatory movement:
Amplitude - the largest (in absolute value) deviation of the body from the equilibrium position.
Period - the time interval during which the body makes one complete oscillation.
Frequency - the number of oscillations per unit time.
Phase (phase difference)
Disturbances that propagate in space, moving away from their place of origin, are called waves.
A necessary condition for the occurrence of a wave is the appearance at the moment of the occurrence of a perturbation of forces preventing it, for example, elastic forces.
Wave types:
Longitudinal - a wave in which oscillations occur along the direction of wave propagation
Transverse - a wave in which oscillations occur perpendicular to the direction of their propagation.
Wave characteristics:
Wavelength - the distance between points closest to each other, oscillating in the same phases.
Wave speed is a value numerically equal to the distance that any point of the wave travels per unit time.
Sound waves - These are longitudinal elastic waves. The human ear perceives in the form of sound vibrations with a frequency of 20 Hz to 20,000 Hz.
The source of sound is a body vibrating at a sound frequency.
Sound receiver - a body capable of receiving sound vibrations.
The speed of sound is the distance a sound wave travels in 1 second.
The speed of sound depends on:
Temperatures.
Sound characteristics:
Pitch
Amplitude
Volume. Depends on the amplitude of the oscillations: the greater the amplitude of the oscillations, the louder the sound.
Ticket number 9. Models of the structure of gases, liquids and solids. Thermal motion of atoms and molecules. Brownian motion and diffusion. Interaction of particles of matter
Gas molecules, moving in all directions, are almost not attracted to each other and fill the entire vessel. In gases, the distance between molecules is much greater than the size of the molecules themselves. Since, on average, the distances between molecules are tens of times greater than the size of the molecules, they are weakly attracted to each other. Therefore, gases do not have their own shape and constant volume.
Molecules of a liquid do not diverge over long distances, and the liquid under normal conditions retains its volume. Liquid molecules are located close to each other. The distances between each two molecules are smaller than the size of the molecules, so the attraction between them becomes significant.
IN solids ah, the attraction between molecules (atoms) is even greater than that of liquids. Therefore, under normal conditions, solids retain their shape and volume. In solids, molecules (atoms) are arranged in a certain order. These are ice, salt, metals, etc. Such bodies are called crystals. Molecules or atoms of solids oscillate around a certain point and cannot move far from it. A solid body therefore retains not only volume, but also shape.
Because its t is associated with the speed of movement of molecules, then the chaotic movement of the molecules that make up the body is called thermal motion. Thermal motion differs from mechanical motion in that many molecules participate in it, and each one moves randomly.
Brownian motion - this is a random movement of small particles suspended in a liquid or gas, which occurs under the influence of impacts of the molecules of the environment. Discovered and first studied in 1827 by the English botanist R. Brown like the movement of pollen in water, seen at high magnification. Brownian motion does not stop.
The phenomenon in which there is a mutual penetration of molecules of one substance between the molecules of another is called diffusion.
There is mutual attraction between the molecules of a substance. At the same time, repulsion exists between the molecules of a substance.
At distances comparable to the size of the molecules themselves, attraction is more noticeable, and with further approach, repulsion.
Ticket No. 10. Thermal equilibrium. Temperature. Temperature measurement. Connection of temperature with the speed of chaotic motion of particles
Two systems are in a state of thermal equilibrium if, upon contact through a diathermic partition, the state parameters of both systems do not change. The diathermic partition does not interfere with the thermal interaction of the systems at all. During thermal contact, the two systems come to a state of thermal equilibrium.
Temperature is a physical quantity that approximately characterizes the average kinetic energy of particles of a macroscopic system per one degree of freedom, which is in a state of thermodynamic equilibrium.
Temperature is a physical quantity that characterizes the degree of heating of a body.
The temperature is measured with thermometers. The main temperature units are Celsius, Fahrenheit and Kelvin
Thermometer - a device used to measure the temperature of a given body by comparison with reference values, conditionally selected as reference points and allowing you to set the measurement scale. At the same time, different thermometers use different relationships between temperature and some observable property of the device, which can be considered linearly dependent on temperature.
With increasing temperature average speed particle motion is increased.
As the temperature decreases, the average particle velocity decreases.
Ticket number 11. Internal energy. Work and heat transfer as ways of changing the internal energy of the body. The law of conservation of energy in thermal processes
The energy of motion and interaction of the particles that make up the body is called internal energy of the body.
The internal energy of a body does not depend on the mechanical movement of the body, nor on the position of this body relative to other bodies.
The internal energy of a body can be changed in two ways: by mechanical work or by heat transfer.
heat transfer.
As the temperature rises, the internal energy of the body increases. As the temperature decreases, the internal energy of the body decreases. The internal energy of a body increases when work is done on it.
Mechanical and internal energy can pass from one body to another.
This conclusion is valid for all thermal processes. In heat transfer, for example, a hotter body gives off energy, and a less heated body receives energy.
When energy is transferred from one body to another, or when one type of energy is transformed into another, energy preserved .
If heat exchange occurs between bodies, then the internal energy of all heating bodies increases as much as the internal energy of cooling bodies decreases.
TicketNo. 12. Types of heat transfer: thermal conductivity, convection, radiation. Examples of heat transfer in nature and technology
The process of changing internal energy without doing work on the body or the body itself is called heat transfer.
The transfer of energy from more heated parts of the body to less heated as a result of thermal motion and the interaction of particles is called thermal conductivity.
At convection energy is carried by the jets of gas or liquid themselves.
Radiation - heat transfer process by radiation.
Energy transfer by radiation differs from other types of heat transfer in that it can be carried out in a complete vacuum.
Examples of heat transfer in nature and technology:
winds. All winds in the atmosphere are convection currents on a huge scale.
Convection explains, for example, winds and breezes that arise on the shores of the seas. On summer days, the land warms up by the sun faster than water, so the air over land heats up more than over water, its density decreases and the pressure becomes less than the pressure of colder air over the sea. As a result, as in communicating vessels, cold air moves downstream from the sea to the shore - the wind blows. This is the daytime breeze. At night, water cools more slowly than land, and over land the air becomes colder than over water. A night breeze is formed - the movement of cold air from land to sea.
Thrust. We know that without an influx of fresh air, fuel combustion is impossible. If air does not enter the furnace, furnace, or samovar pipe, the combustion of fuel will stop. Usually use a natural influx of air - draft. To create traction above the furnace, for example, in boiler plants of factories, factories, power plants, a pipe is installed. When the fuel burns, the air in it heats up. This means that the pressure of the air in the furnace and the pipe becomes less than the pressure of the outside air. Due to the pressure difference, cold air enters the furnace, and warm air rises - draft is formed.
The higher the pipe built above the furnace, the more difference pressure of outside air and air in a pipe. Therefore, the thrust increases with increasing pipe height.
Heating and cooling of residential premises. Residents of countries located in the temperate and cold zones of the Earth are forced to heat their homes. In countries located in tropical and subtropical zones, the air temperature even in January reaches + 20 and + 30 ° C. Devices that cool the air in the premises are used here. Both heating and cooling of indoor air is based on convection.
It is advisable to place cooling devices at the top, closer to the ceiling, so that natural convection occurs. After all, cold air has a greater density than warm air, and therefore will sink.
Heating devices are located below. Many modern large houses are equipped with water heating. The circulation of water in it and the heating of the air in the room occur due to convection.
If the installation for heating the building is located in it, then a boiler is installed in the basement, in which water is heated. Hot water rises through a vertical pipe from the boiler into a tank, which is usually placed in the attic of the house. A system of distribution pipes is carried out from the tank, through which water passes to the radiators installed on all floors, it gives them its heat and returns to the boiler, where it is heated again. So there is a natural circulation of water - convection.
