What system of bodies can be considered oscillatory? The main property of oscillatory systems. Velocity and acceleration during harmonic vibrations

(or natural vibrations) are oscillations of an oscillatory system that occur only due to the initially imparted energy (potential or kinetic) in the absence of external influences.

Potential or kinetic energy can be imparted, for example, in mechanical systems through initial displacement or initial velocity.

Freely oscillating bodies always interact with other bodies and together with them form a system of bodies called oscillatory system.

For example, a spring, a ball and a vertical post to which the upper end of the spring is attached (see figure below) are included in the oscillatory system. Here the ball slides freely along the string (friction forces are negligible). If you move the ball to the right and leave it to itself, it will oscillate freely around the equilibrium position (point ABOUT) due to the action of the elastic force of the spring directed towards the equilibrium position.

Another classic example of a mechanical oscillatory system is a mathematical pendulum (see figure below). In this case, the ball performs free oscillations under the influence of two forces: gravity and the elastic force of the thread (the Earth is also included in the oscillatory system). Their resultant is directed towards the equilibrium position.

The forces acting between the bodies of the oscillatory system are called internal forces. By external forces are called forces acting on a system from bodies not included in it. From this point of view, free oscillations can be defined as oscillations in a system under the influence of internal forces after the system is removed from its equilibrium position.

The conditions for the occurrence of free oscillations are:

1) the emergence in them of a force that returns the system to a position of stable equilibrium after it has been removed from this state;

2) lack of friction in the system.

Dynamics of free vibrations.

Body vibrations under the influence of elastic forces. Equation of oscillatory motion of a body under the action of elastic force F() can be obtained taking into account Newton's second law ( F = ma) and Hooke's law ( F control = -kx), Where m is the mass of the ball, and is the acceleration acquired by the ball under the action of elastic force, k— spring stiffness coefficient, X- displacement of the body from the equilibrium position (both equations are written in projection onto the horizontal axis Oh). Equating the right-hand sides of these equations and taking into account that the acceleration A is the second derivative of the coordinate X(displacement), we get:

.

Similar expression for acceleration A we obtain by differentiating ( v = -v m sin ω 0 t = -v m x m cos (ω 0 t + π/2)):

a = -a m cos ω 0 t,

Where a m = ω 2 0 x m— amplitude of acceleration. Thus, the amplitude of the speed of harmonic oscillations is proportional to the frequency, and the amplitude of acceleration is proportional to the square of the oscillation frequency.

Mechanical vibrations – These are movements that are repeated exactly or approximately at certain intervals. (For example, vibration of a branch on a tree, a clock pendulum, a car on springs, and so on)

There are fluctuations free And forced.

Oscillations that occur in a system under the influence of internal forces are calledfree. All free vibrations are damped. (For example: string vibration after impact)

Vibrations made by bodies under the influence of external periodically changing forces are calledforced (For example: vibration of a metal workpiece when a blacksmith works with a hammer).

Conditions for the occurrence of free oscillations :

• When a body is removed from an equilibrium position, a force must arise in the system, tending to return it to the equilibrium position;
• The friction forces in the system must be very small (i.e., tend to zero).

… E kin → E R → E kin →…

Using the example of body oscillations on a thread, we see energy conversion . In position 1, we observe the equilibrium of the oscillatory system. The speed and, therefore, the kinetic energy of the body is maximum. When the pendulum deviates from its equilibrium position, it rises to a height h relative to the zero level, therefore, at point A the pendulum has potential energy E r . When moving to the equilibrium position, to point O, the height decreases to zero, and the speed of the load increases, and at point O all the potential energy E r turns into kinetic energy E kin . At equilibrium, kinetic energy is at its maximum and potential energy is at its minimum. After passing through the equilibrium position by inertia, the kinetic energy is converted into potential energy, the speed of the pendulum decreases and at maximum

General properties of all oscillatory systems:

The presence of a stable equilibrium position.

The presence of a force that returns the system to an equilibrium position.

Characteristics of oscillatory motion:

Amplitude is the largest (in absolute value) deviation of the body from the equilibrium position.

A period is the period of time during which a body makes one complete oscillation.

Frequency is the number of oscillations per unit time.

Phase (phase difference)

Disturbances propagating in space, moving away from the place of their origin, are called waves.

A necessary condition for the occurrence of a wave is the appearance at the moment of the disturbance of forces preventing it, for example elastic forces.

Types of waves:

Longitudinal - a wave in which oscillations occur along the direction of propagation of the wave

Transverse - a wave in which vibrations occur perpendicular to the direction of their propagation.

Wave Characteristics:

Wavelength is the distance between points closest to each other, oscillating in the same phases.

Wave speed is a quantity numerically equal to the distance that any point on the wave travels per unit time.

Sound waves - These are longitudinal elastic waves. The human ear perceives vibrations with a frequency from 20 Hz to 20,000 Hz in the form of sound.

The source of sound is a body vibrating at a sound frequency.

A sound receiver is a body capable of perceiving sound vibrations.

The speed of sound is the distance a sound wave travels in 1 second.

The speed of sound depends on:

1. Temperatures.

Sound characteristics:

1. Pitch

   Amplitude

   Volume. Depends on the amplitude of the vibrations: the greater the amplitude of the vibrations, the louder the sound.

Ticket number 9. Models of the structure of gases, liquids and solids. Thermal movement 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 container. 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.

The molecules of a liquid do not disperse over long distances, and the liquid under normal conditions retains its volume. The molecules of a liquid 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, the attraction between molecules (atoms) is even greater than in 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 vibrate around a certain point and cannot move far from it. Therefore, a solid body retains not only its volume, but also its shape.

Because t is associated with the speed of movement of molecules, then the chaotic movement of the molecules that make up bodies is called thermal movement. Thermal motion differs from mechanical motion in that it involves many molecules and each one moves randomly.

Brownian motion - this is the random movement of small particles suspended in a liquid or gas, occurring under the influence of impacts from environmental molecules. Discovered and first studied in 1827 by the English botanist R. Brown like the movement of pollen in water, visible under high magnification. Brownian motion does not stop.

The phenomenon in which mutual penetration of molecules of one substance between the molecules of another occurs is called diffusion.

There is mutual attraction between the molecules of a substance. At the same time, there is repulsion between the molecules of the substance.

At distances comparable to the size of the molecules themselves, attraction becomes more noticeable, and with further approach, repulsion becomes more noticeable.

Ticket No. 10. Thermal equilibrium. Temperature. Temperature measurement. Relationship between temperature and the speed of chaotic particle motion

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 at all interfere with the thermal interaction of the systems. When thermal contact occurs, the two systems reach 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.

Temperature is measured using thermometers. The basic units of temperature are Celsius, Fahrenheit and Kelvin.

Thermometer is a device used to measure the temperature of a given body by comparison with reference values, conditionally selected as reference points and allowing the measurement scale to be established. Moreover, different thermometers use different relationships between temperature and some observable property of the device, which can be considered linearly dependent on temperature.

As the temperature increases, the average speed of particle movement increases.

As the temperature decreases, the average speed of particle movement decreases.

Ticket number 11. Internal energy. Work and heat transfer as ways to change the internal energy of a body. Law of conservation of energy in thermal processes

The energy of movement and interaction of particles that make up a body is called internal energy of the body.

The internal energy of a body does not depend either on the mechanical motion of the body or on the position of this body relative to other bodies.

The internal energy of a body can be changed in two ways: by performing 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 move from one body to another.

This conclusion is valid for all thermal processes. During heat transfer, for example, a more heated body gives off energy, and a less heated body receives energy.

When energy passes from one body to another or when one type of energy is converted into another, energy saved .

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 ones as a result of thermal movement and interaction of particles is called thermal conductivity.

At convection energy is transferred by the gas or liquid jets themselves.

Radiation - the process of transferring heat 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 of enormous scale.

Convection explains, for example, wind breezes that arise on the shores of the seas. On summer days, land is heated by the sun faster than water, therefore the air above land heats up more than above water, its density decreases and the pressure becomes less than the pressure of colder air above the sea. As a result, as in communicating vessels, cold air from the sea below moves to the shore - the wind blows. This is the daytime breeze. At night, water cools more slowly than land, and the air above land becomes colder than above water. A night breeze is formed - the movement of cold air from land to sea.

Traction. We know that without a supply of fresh air, combustion of fuel is impossible. If no air enters the firebox, the oven, or the pipe of the samovar, then the combustion of the fuel will stop. Usually they use natural air flow - draft. To create draft above the firebox, for example, in boiler installations of factories, plants, power plants, a pipe is installed. When fuel burns, the air in it heats up. This means that the air pressure in the firebox and pipe becomes less than the pressure of the outside air. Due to the pressure difference, cold air enters the firebox, and warm air rises upward - a draft is formed.

The higher the pipe built above the firebox, the greater the difference in pressure between the outside air and the air in the pipe. Therefore, the thrust increases with increasing pipe height.

Residential heating and cooling. Residents of countries located in 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 o C. Here they use devices that cool the air in rooms. Both heating and cooling of indoor air are 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 have 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 the building itself, then a boiler is installed in the basement in which water is heated. A vertical pipe extending from the boiler carries hot water into a tank, which is usually placed in the attic of the house. From the tank, a system of distribution pipes is carried out, through which water passes into radiators installed on all floors, it gives off its heat to them and returns to the boiler, where it is heated again. This is how natural circulation of water occurs - convection.

A motion in which the states of motion of a body are repeated over time, with the body passing through a stable equilibrium position alternately in opposite directions, is called mechanical oscillatory motion.

If the states of motion of a body are repeated at certain intervals, then the oscillations are periodic. A physical system (body), in which oscillations arise and exist when deviating from an equilibrium position, is called an oscillatory system.

The oscillatory process in a system can occur under the influence of both external and internal forces.

Oscillations that occur in a system under the influence of only internal forces are called free.

In order for free oscillations to occur in the system, it is necessary:

1. The presence of a stable equilibrium position of the system. Thus, free oscillations will occur in the system shown in Figure 13.1, a; in cases b and c they will not arise.
2. The presence of excess mechanical energy at a material point compared to its energy in a stable equilibrium position. So, in the system (Fig. 13.1, a) it is necessary, for example, to remove the body from its equilibrium position: i.e. report excess potential energy.
3. The action of a restoring force on a material point, i.e. force always directed towards the equilibrium position. In the system shown in Fig. 13.1, a, the restoring force is the resultant force of gravity and the normal reaction force \(\vec N\) of the support.
4. In ideal oscillatory systems there are no frictional forces, and the resulting oscillations can last a long time. In real conditions, vibrations occur in the presence of resistance forces. In order for an oscillation to arise and continue, the excess energy received by a material point when displaced from a stable equilibrium position must not be completely spent on overcoming resistance when returning to this position.

Literature

Aksenovich L. A. Physics in secondary school: Theory. Tasks. Tests: Textbook. allowance for institutions providing general education. environments, education. - pp. 367-368.

DEFINITION

Oscillatory motion- this is a movement that is repeated exactly or approximately at equal intervals of time, in which the body passes through a position repeatedly and in different directions.

Oscillatory motion, along with translational and rotational motion, is one of the types.

A physical system (or body) in which oscillations occur when deviating from an equilibrium position is called an oscillatory system. Figure 1 shows examples of oscillatory systems: a) thread + ball + Earth; b) load + spring; c) a stretched string.

Fig.1. Examples of oscillatory systems: a) thread + ball + Earth; b) load + spring; c) a stretched string

If there are no losses associated with the action in the oscillatory system, then the oscillations will continue indefinitely. Such oscillatory systems are called ideal. In real oscillatory systems, there are always energy losses caused by resistance forces, as a result of which oscillations cannot continue indefinitely, i.e. are damped.

Free vibrations are vibrations that occur in a system under the influence of internal forces. – oscillations that occur in the system under the influence of an external periodic .

Conditions for the occurrence of free oscillations in the system

• the system must be in a stable position: when the system deviates from the equilibrium position, a force must arise that tends to return the system to the equilibrium position - restoring;
• the presence of excess mechanical energy in the system compared to its energy in the equilibrium position;
• the excess , obtained by the system when it is displaced from the equilibrium position, should not be completely spent on overcoming the friction forces when returning to the equilibrium position, i.e. in the system must be small enough.

Examples of problem solving

EXAMPLE 1

EXAMPLE 2