Consider vibrations heavy on a string or heavy on a spring. In the examples given, the system oscillated around a stable equilibrium position. Why do oscillations occur precisely near this position of the system? The fact is that when the system deviates from a stable equilibrium position,

the resultant of all forces applied to the body tends to return the system to an equilibrium position. This resultant is called reciprocal force. However, having returned to a state of equilibrium, the system, due to inertia, “overshoots” it. After this, a reciprocal force arises again, now directed in the opposite direction. This is how fluctuations arise. In order for oscillations to continue for a long time, it is necessary that the friction or resistance forces be very small.

So, in order for free oscillations to occur in the system, two conditions must be met:

The system must be near a stable equilibrium position;

Frictional or drag forces must be sufficiently small

Oscillation amplitude

During oscillations, the displacement of the body from the equilibrium position changes periodically.

The amplitude of oscillations is a physical quantity that characterizes oscillatory motion and is equal to the maximum distance by which the oscillating body deviates from its equilibrium position.

The amplitude of oscillations is denoted by the symbol A. The SI unit of amplitude of oscillations is meter (m).

The amplitude of free oscillations is determined by the initial conditions, i.e. by the initial deflection or push with which the weights on the thread or on the spring were set in motion.

If the load on the thread (or on the spring) is left alone, then after some time the amplitude of the oscillations will noticeably decrease. Oscillations whose amplitude decreases over time are called damped. Oscillations whose amplitude does not change over time are called undamped.

Question for students while presenting new material

1. What bodies form a system during oscillations of a load hanging on a thread? What is the nature of the forces in the case of interaction of these bodies?

2. What bodies form a system during oscillations of a load that is on a spring? What is the nature of the forces in the case of interaction of these bodies?

3. The resultant of which forces plays the role of a reciprocal force during oscillations of a hanging load:

a) on a thread?

b) on a spring?

4. Can the amplitude of oscillations be taken as amplitude?

Reinforcing the material learned

1. We train to solve problems

1. We can call free vibrations:

a) a float on the waves?

b) violin strings?

c) does the truck go over potholes?

d) sewing machine needles?

e) sections of the tuning fork?

2. Which of the following oscillations are free:

a) vibrations of a person suspended on a spring are severe after an accidental shock;

b) vibrations of the surface of the switched on speaker;

c) the oscillations of a person suspended on a thread are heavy (the thread was taken out of the equilibrium position and released)?

3. The body performed 50 oscillations in 10 s. What is the period of oscillation?

4. During oscillations, a weight suspended on a thread passes through the equilibrium position at intervals of 0.5 s. What is the period of oscillation?

5. The float oscillates on the surface of the water, floats up and dives into the water six times in 3 seconds. Calculate the period and frequency of the oscillations.

2. Test questions

1. Give examples of free and forced vibrations.

2. In what cases is oscillation impossible?

3. Name the properties of an oscillatory system.

4. What is the fundamental difference between oscillatory motion and circular motion?

5. What quantities characterizing oscillatory motion change periodically?

6. In what units are period, frequency and cyclic frequency of oscillations measured?

What did we learn in class?

Oscillations are physical processes that repeat exactly or approximately at regular intervals.

Mechanical vibrations are those movements of bodies during which, at equal intervals of time, the coordinates of the body in motion - speed and acceleration - acquire their original values.
Free vibrations are vibrations that occur in a mechanical system under the influence of internal forces of the system after a short-term influence of some external force.

Oscillations that arise under the influence of external forces and change over time in magnitude and direction are called forced.

Conditions for the existence of free oscillations:

The system must be near a stable equilibrium position;

The frictional or drag forces must be sufficiently small;

The amplitude of oscillations is a physical quantity that characterizes oscillatory motion and is equal to the maximum distance by which the oscillating body deviates from its equilibrium position.

>> Conditions for the occurrence of free oscillations

§ 19 CONDITIONS FOR THE APPEARANCE OF FREE VIBRATIONS

Let us find out what properties a system must have in order for free oscillations to occur in it. It is most convenient to first consider the vibrations of a ball strung on a smooth horizontal rod under the action of the elastic force of a spring 1.

If you move the ball slightly from the equilibrium position (Fig. 3.3, a) to the right, then the length of the spring will increase by (Fig. 3.3, b), and the elastic force from the spring will begin to act on the ball. This force, according to Hooke's law, is proportional to the deformation of the spring and the direction of the foam to the left. If you release the ball, then under the action of elastic force it will begin to move with acceleration to the left, increasing its speed. In this case, the elastic force will decrease, since the deformation of the spring decreases. At the moment when the ball reaches the equilibrium position, the elastic force of the spring becomes equal to zero. Consequently, according to Newton’s second law, the acceleration of the ball will also become zero.

At this point, the speed of the ball will reach its maximum value. Without stopping in the equilibrium position, it will continue to move to the left by inertia. The spring is compressed. As a result, an elastic force appears, directed to the right and inhibiting the movement of the ball (Fig. 3.3, c). This force, and therefore the acceleration directed to the right, increases in magnitude in direct proportion to the modulus of the displacement x of the ball relative to the equilibrium position.

1 Analysis of the vibrations of a ball suspended on a vertical spring is somewhat more complicated. In this case, the variable elastic force of the spring and the constant force of gravity act simultaneously. But the nature of the oscillations in both cases is completely the same.

The speed will decrease until, in the extreme left position of the ball, it becomes zero. After this, the ball will begin to accelerate to the right. With decreasing displacement modulus x force F control decreases in absolute value and in the equilibrium position again goes to zero. But by this moment the ball has already acquired speed and, therefore, by inertia continues to move to the right. This movement leads to stretching of the spring and the appearance of a force directed to the left. The movement of the ball is slowed down until it comes to a complete stop in the extreme right position, after which the whole process is repeated all over again.

If there were no friction, the movement of the ball would never cease. However, friction and air resistance prevent the ball from moving. The direction of the resistance force both when the ball moves to the right and when it moves to the left is always opposite to the direction of speed. The scope of its oscillations will gradually decrease until the movement stops. With low friction, damping becomes noticeable only after the ball has oscillated a lot. If you observe the movement of the ball over a not very large time interval, then the damping of oscillations can be neglected. In this case, the influence of the resistance force on the voltage can be ignored.

If the resistance force is large, then its action cannot be neglected even over short time intervals.

Place a ball on a spring into a glass with a viscous liquid, for example glycerin (Fig. 3.4). If the spring stiffness is small, then the ball removed from its equilibrium position will not oscillate at all. Under the action of elastic force, it will simply return to its equilibrium position (dashed line in Figure 3.4). Due to the action of the drag force, its speed in the equilibrium position will be practically zero.

In order for free oscillations to occur in a system, two conditions must be met. Firstly, when moving a body from an equilibrium position, a force must arise in the system directed towards the equilibrium position and, therefore, tending to return the body to the equilibrium position. This is exactly how a spring acts in the system we considered (see Fig. 3.3): when the ball moves both to the left and to the right, the elastic force is directed towards the equilibrium position. Secondly, the friction in the system should be quite low. Otherwise, the vibrations will quickly die out. Undamped oscillations are possible only in the absence of friction.

1. What vibrations are called free!
2. Under what conditions do free oscillations occur in the system?
3. What oscillations are called forced! Give examples of forced oscillations.

Let us find out under what conditions oscillatory motion arises and is maintained for some time.

The first condition necessary for the occurrence of oscillations is the presence of excess energy (kinetic or potential) at a material point compared to its energy in a stable equilibrium position (§ 24.1).

The second condition can be established by following the movement of load 3 in Fig. 24.1. In position b, load 3 is acted upon by an elastic force directed towards the equilibrium position of the load (see Fig. 24.1, b). under the action of this force, the load is shifted to the equilibrium position with a gradually increasing speed of movement V, and the force decreases and disappears when the load reaches this position (Fig. 24.1, c). The speed of the load at this moment is maximum in value, and the load, jumping through the equilibrium position, continues to move to the right. In this case, an elastic force arises which slows down the movement of load 3 and stops it (Fig. 24.1, d). The force in this position is at its maximum; under the influence of this force, load 3 begins to move to the left. In the equilibrium position (Fig. 24.1, 5), the force disappears, and the speed of the load reaches its greatest value, so the load continues to move to the left until it reaches the position in Fig. 24.1. Next, the entire described process is repeated again in the same order.

Thus, oscillations of load 3 occur due to the action of force and the presence of inertia in the load. The force applied to

material point, always directed towards the position of stable equilibrium of the point, is called the restoring force. At a stable equilibrium position, the restoring force is zero and increases as the point moves away from this position.

So, the second condition necessary for the occurrence and continuation of oscillations of a material point is the action of a restoring force on the material point. Let us remind you that. this force always arises when any body is removed from a position of stable equilibrium.

In an ideal case, in the absence of friction and resistance of the medium, the total mechanical energy of the oscillating point remains constant, since during such oscillations only the transition of kinetic energy into potential energy and vice versa occurs. This oscillation must continue indefinitely.

If oscillations of a material point occur in the presence of friction and resistance of the medium, then the total mechanical energy of the material point gradually decreases, the range of oscillations decreases, and after some time the point stops in a position of stable equilibrium.

There are cases when the loss of energy by a material point is so great that if an external force deflects this point from its equilibrium position, then it loses all its excess energy when returning to the equilibrium position. In this case, there will be no oscillations. So, the third condition necessary for the occurrence and continuation of oscillations is the following: the excess energy received by a material point when displaced from a stable equilibrium position should not be completely spent on overcoming resistance when returning to this position.

One of the most interesting topics in physics is oscillations. The study of mechanics is closely connected with them, with how bodies behave when they are affected by certain forces. Thus, when studying oscillations, we can observe pendulums, see the dependence of the amplitude of oscillation on the length of the thread on which the body hangs, on the stiffness of the spring, and the weight of the load. Despite its apparent simplicity, this topic is not as easy for everyone as we would like. Therefore, we decided to collect the most well-known information about vibrations, their types and properties, and compile for you a brief summary on this topic. Perhaps it will be useful to you.

Definition of the concept

Before talking about concepts such as mechanical, electromagnetic, free, forced vibrations, their nature, characteristics and types, conditions of occurrence, it is necessary to define this concept. Thus, in physics, an oscillation is a constantly repeating process of changing 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. The theory of oscillations and waves studies the phenomenon.

Causes and conditions of occurrence

Like any other phenomenon, oscillations only occur if certain conditions are met. Mechanical forced vibrations, like free ones, arise when the following conditions are met:

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

2. The presence of minimal friction force in the system. As you know, friction slows down certain physical processes. The greater the friction force, the less likely it is for vibrations 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 understood what an oscillation is, let’s analyze their classification. There are two most well-known classifications - by physical nature and by the nature of interaction with the environment. Thus, according to the first criterion, mechanical and electromagnetic vibrations are distinguished, and according to the second, free and forced vibrations. There are also self-oscillations and 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 vibrations that the study of vibrations in a school physics course 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 oscillations, the body repeatedly makes the same movement, passing a certain position in space. Examples of such oscillations are the same pendulums, the vibration of a tuning fork or guitar string, the movement of leaves and branches on a tree, a swing.

Electromagnetic

After the concept of mechanical vibrations has been firmly grasped, the study of electromagnetic vibrations, which are more complex in structure, begins, since this type occurs in various electrical circuits. During this process, oscillations in electric as well as magnetic fields are observed. 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 characteristics such as charge and current strength. 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 removed from a state of stable equilibrium or rest. Free oscillations are always damped, which means their amplitude and frequency decrease over time. A striking example of this type of swing is the movement of a load suspended on a thread and oscillating from one side to the other; a load attached to a spring, either falling down under the influence of gravity, or rising up under the action of the spring. By the way, it is precisely this kind of oscillations that is paid attention to when studying physics. And most of the problems are devoted to free vibrations, and not 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 found in nature. A fairly 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 look at them in a little more detail, focusing on a brief description. At the same time, we will not describe the formulas that are used to calculate this or that value, so as not to confuse the reader.

Bias

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

Oscillation amplitude

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

Oscillation period

Another quantity that indicates the time it takes to complete one complete oscillation. 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 oscillations, which means we should also mention the types of pendulums that are used to create and study free oscillations (in school conditions). Here we can distinguish two types - mathematical and harmonic (spring). The first is a certain body suspended from an inextensible thread, the size of which is equal to l (the main significant quantity). The second is a weight attached to a spring. Here it is important to know the mass of the load (m) and the spring stiffness (k).

conclusions

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

“Physical and mathematical pendulum” - It is customary to distinguish: Presentation on the topic: “Pendulum”. Mathematical pendulum. Performed by Tatyana Yunchenko. Mathematical pendulum physical pendulum. Pendulum.

“Sound resonance” - The same thing happens with two equally tuned strings. By passing the bow along one string, we will cause vibrations on the other. Having set one tuning fork in vibration, you will notice that the other tuning fork will sound by itself. Concept. Prepared by: Velikaya Yulia Checked by: Sergeeva Elena Evgenievna Municipal Educational Institution “Secondary School No. 36” 2011.

“Oscillating movement” - Extreme left position. Swing. Examples of oscillatory movements. Conditions for the occurrence of oscillations. Amplitude shift. V=max a=0 m/s?. Sewing machine needle. Oscillatory movement. Balance position. Tree branches. V=0 m/s a=max. Far right position. Car springs. Clock pendulum. Feature of oscillatory movement.

“Lesson on mechanical vibrations” - Types of pendulums. Towards a position of equilibrium. Free vibrations. G. Klin, Moscow region 2012. Example: pendulum. Types of oscillatory systems 3. The main property of oscillatory systems 4. Free vibrations. Presentation for a physics lesson. Completed by: physics teacher Lyudmila Antonevna Demashova. 6. An oscillatory system is a system of bodies capable of performing oscillatory movements.

“Pendulum swings” - Cosine. “The world we live in is surprisingly prone to fluctuations” R. Bishop. Types of vibrations. Basic characteristics of the oscillatory process (motion). Mathematical and spring pendulum tests. 7. A weight suspended on a spring was brought out of its equilibrium position and released. Unit of measurement (second s).

“Physics of mechanical vibrations” - Let's talk about vibrations... Parameters of mechanical vibrations. Shows the maximum displacement of the body from the equilibrium position. Oscillatory systems. “There was a merry ball in the castle, the musicians were singing. Period. Video task. Bazhina G.G. – physics teacher at Municipal Educational Institution “GYMNASIA No. 11” in Krasnoyarsk. The breeze in the garden rocked the light swing" Konstantin Balmont.

There are a total of 14 presentations in the topic