Vibrations: mechanical and electromagnetic. Free and forced vibrations. Characteristic. Natural oscillations What is characteristic of oscillations

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).

conclusions

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.

Depending on the reasons that excite the oscillatory process, the following types of oscillations are distinguished:

free vibrations

forced oscillations,

self-oscillations

parametric fluctuations.

Free vibrations occur in systems that at the initial moment of time are removed from the state of equilibrium, after which the causes of excitation are eliminated and the system continues to move in the absence of external influences. Oscillations occur due to the energy reserve that the system received during the initial excitation.

Forced vibrations characterized by the fact that the system is under constant action of external dynamic loads. The energy necessary to maintain the oscillation process comes from the work of external influences.

Parametric vibrations also arise under external influences, however, they do not occur from the impact of dynamic loads, but are predetermined by the change in time of the parameters of the system itself - masses or stiffnesses.

Self-oscillations arise in the absence of external influences due to an internal source of energy and have a periodic character.

All real oscillatory systems have internal friction, as a result of which the energy that supports the oscillatory process is gradually dissipated. There is a so-called energy dissipation. A similar effect is exerted by the resistance of the medium in which oscillations occur. Therefore, to maintain the process of oscillations, it is necessary to have a constant influx of energy, without which they will gradually stop, fade. In many cases, however, the attenuation has a small value, which allows solving problems without taking into account energy dissipation. Accordingly, oscillations are distinguished with and without taking into account the forces of resistance. For free vibrations, the concept is used fading And undamped fluctuations.

Distinguish linear And non-linear oscillations. The first of these are characteristic of the so-called linear oscillatory systems, which are described by linear

differential equations. Such oscillations are also called small, or elastic, since linear deformability is preserved only for small elastic displacements of the system. For linear oscillations, the principle of independence of the action of forces (the principle of superposition) is valid: the overall effect of the action of several dynamic loads can be represented as the sum of the actions of each of them separately.

Finally, vibrations can be classified depending on the nature of the deformations that occur in the system. From this point of view, it is possible to distinguish longitudinal, transverse, torsional, flexural-torsional vibrations, etc.

Purpose of dynamic analysis

The main purpose of the dynamic analysis of the structure is to ensure the bearing capacity and allowable movement of elements during vibrations. In accordance with this, the task of dynamic calculation of a structure is to determine the dynamic forces and displacements caused by dynamic deformations of its elements. The direct solution of this problem is usually preceded by an analysis of the frequencies and forms of free oscillations of the structure. Thanks to this analysis, it is possible to reliably predict the development of dynamic processes under various external influences, as well as to form effective design dynamic models of a structure, with the help of which calculations are performed to estimate the amplitude values ​​of internal forces and displacements. The level of permissible internal forces is determined by the conditions of dynamic strength, and the permissible swings of structural vibrations are set by the conditions of normal operation. At the same time, along with the possible disruption of the normal course of the production process due to large amplitudes of vibrations of the structure, the harmful effects on people of high levels of vibration are also taken into account.

As a rule, performing a dynamic calculation, one directly determines the nature of the change in the displacements of the structure, which corresponds to the considered oscillation mode. And then, knowing the displacements, they find the internal forces in the structural elements.

It is considered that the problem of dynamic calculation is solved if, as a result of the analysis, it is established that for the types of external actions under consideration, the bearing capacity of the structure is ensured, and the calculated values ​​of the vibration amplitudes do not exceed the allowable ones. If at least one of these conditions is not satisfied, the problem arises of determining an effective way to reduce the level of vibration. In modern engineering practice, there are many approaches that can significantly reduce the intensity of oscillations. It should be noted that such problems arise not only at the design stage of a structure, but also during operation, if it turns out that dangerous dynamic processes develop in an existing structure under certain conditions.

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

Potential or kinetic energy can be communicated, for example, in mechanical systems through an initial displacement or an 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 an oscillatory system. Here the ball slides freely along the string (friction forces are negligible). If you take 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 the mathematical pendulum (see figure below). In this case, the ball performs free oscillations under the action of two forces: gravity and the elastic force of the thread (the Earth also enters the oscillatory system). Their resultant is directed to the equilibrium position.

The forces acting between the bodies of an oscillatory system are called internal forces. Outside forces are called the forces acting on the system from the bodies that are not included in it. From this point of view, free oscillations can be defined as oscillations in the system under the action of internal forces after the system is taken out of equilibrium.

The conditions for the occurrence of free oscillations are:

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

2) no friction in the system.

Dynamics of free oscillations.

Vibrations of a body under the action of elastic forces. The equation of oscillatory motion of a body under the action of an 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 the elastic force, k- coefficient of spring stiffness, X is the displacement of the body from the equilibrium position (both equations are written in projection onto the horizontal axis Oh). Equating the right sides of these equations and taking into account that the acceleration A is the second derivative of the coordinate X(offsets), we get:

.

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

a \u003d -a m cos ω 0 t,

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

fluctuations- These are movements or processes that repeat exactly or approximately at certain intervals of time.

Mechanical oscillations - fluctuations in mechanical quantities (displacement, speed, acceleration, pressure, etc.).

Mechanical vibrations (depending on the nature of the forces) are:

free;

forced;

self-oscillations.

free called vibrations that occur when a single action of an external force (the initial message of energy) and in the absence of external influences on the oscillatory system.

Free (or own)- these are oscillations in the system under the action of internal forces, after the system is taken out of equilibrium (in real conditions, free oscillations are always damped).

Conditions for the occurrence of free oscillations

1. The oscillatory system must have a position of stable equilibrium.

2. When the system is taken out of equilibrium, a resultant force must arise that returns the system to its original position

3. Forces of friction (resistance) are very small.

Forced vibrations- fluctuations occurring under the influence of external forces that change over time.

Self-oscillations- undamped oscillations in the system, supported by internal energy sources in the absence of an external variable force.

The frequency and amplitude of self-oscillations is determined by the properties of the oscillatory system itself.

Self-oscillations differ from free oscillations in that the amplitude is independent of time and of the initial action that excites the process of oscillations.

Self-oscillating system consists of: oscillatory system; energy source; feedback device that regulates the flow of energy from an internal energy source into an oscillatory system.

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

Mechanical vibrations are divided into:

fading;

undamped.

damped vibrations- fluctuations, the energy of which decreases with time.

Characteristics of the oscillatory movement:

permanent:

amplitude (A)

period (T)

frequency()

The greatest (in absolute value) deviation of an oscillating body from the equilibrium position is called vibration amplitude. Typically, the amplitude is denoted by the letter A.

The time interval during which the body completes one complete oscillation is called period of oscillation.

The period of oscillation is usually denoted by the letter T and in SI is measured in seconds (s).

The number of oscillations per unit time is called oscillation frequency.

The frequency is denoted by the letter v (“nu”). The unit of frequency is one oscillation per second. This unit is named hertz (Hz) in honor of the German scientist Heinrich Hertz.

the oscillation period T and the oscillation frequency v are related by the following relationship:

T=1/ or =1/T.

Cyclic (circular) frequency ω is the number of oscillations in 2π seconds

Harmonic vibrations- mechanical vibrations that occur under the action of a force proportional to the displacement and directed opposite to it. Harmonic vibrations are made according to the law of sine or cosine.

Let the material point perform harmonic oscillations.

The equation of harmonic oscillations has the form:

a - acceleration V - speed q - charge A - amplitude t - time

>>Physics: Types of vibrations

The oscillations of the spring and thread pendulums, which were discussed in the previous paragraphs, are called free. Free oscillations occur "by themselves", without the influence of external periodically changing forces. In the presence of such forces, oscillations are called forced.

The shaking of a car moving on a rough road, the vibrations of the stern of the vessel associated with the operation of the propeller, the movement of the swing, which someone periodically pushes - all these are forced vibrations.

To study forced hesitation you can use the installation shown in Figure 36. A spring pendulum is fixed on a crank with a handle. With uniform rotation of the handle on the load, the action of a periodically changing force will be transmitted through the spring. Changing with a frequency equal to the frequency of rotation of the handle, this force will cause the load to make forced oscillations.

Despite the external similarity, there are significant differences between free and forced oscillations.

Due to the presence of friction and resistance of the medium, free oscillations damp out: their energy and amplitude decrease with time. Forced oscillations are undamped: energy losses in the process of these oscillations are compensated by the energy supply from the external force source.

The frequency and period of forced oscillations can be anything; they coincide with the frequency and period of changes in the external force (for example, the rotational speed of the handle in Figure 36). Free oscillations can occur only with quite definite frequencies and periods, depending on the characteristics of the oscillatory system. So, for example, a spring pendulum is characterized by mass m and spring stiffness k; they determine the period of free oscillations of the load on the spring:

The period of free oscillations of the thread pendulum depends on the length of the thread l and free fall acceleration g:

The period of oscillation of the thread pendulum does not depend on the mass of the body.

Knowing the period, you can find the frequency of free oscillations. They call her natural frequency oscillatory system. This name is due to the fact that each oscillatory system has its own and it is impossible to change it (without changing the parameters of the system itself).

In nature and technology, vibrations of various frequencies occur. So, for example, the natural frequency of a pendulum oscillating in St. Isaac's Cathedral in St. Petersburg is 0.05 Hz; the oscillation frequency of a railway car on the springs is about 1 Hz; tuning forks oscillate with frequencies from tens of hertz to several kilohertz, and the frequency of vibrations of atoms in molecules can reach millions of megahertz!

Free vibrations decay with time. Therefore, in practice, not free, but forced oscillations are more often used. They are most widely used in various vibration machines. One of them - a jackhammer - has already been described in a textbook for grade VII. In vibration machines of another type, forced oscillations arise as a result of periodic influences from unbalanced rotating rotors (the so-called unbalances). An example of a machine of this type is a vibratory hammer.

vibrohammer- this is a shock-vibration machine designed for driving various piles, pipes, etc. into the ground. The diagram of this machine is shown in Figure 37. The vibratory hammer is connected to pile 2 with the help of a spring suspension 1. When the unbalances 3 rotate, forced vibrations occur, accompanied by shock pulses of the striker 4 on the anvil 5 of the immersed pile. The soil under the pile is loosened, and under the action of gravity, the pile falls down.

1. What oscillations are called free? Give examples. 2. What oscillations are called forced? Give examples. 3. Which oscillations - free or forced - include the following phenomena: piston movement in an internal combustion engine; table vibration caused by a heavy object falling on it; moving the needle in a running sewing machine; vertical movement of the float on the waves; vibrations of the string that arose after a single impact? 4. Why do free vibrations decay over time, but forced vibrations do not? 5. What determines the frequency of free oscillations? Why is it called the natural frequency of an oscillatory system? 6. What formulas are used to find the period of free oscillations of a spring and thread pendulums? 7. Which machines use forced vibrations?

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