Mechanical definition vibrations. Mechanical vibrations
Fluctuations Are movements or processes that repeat exactly or approximately at certain intervals.
Mechanical vibrations fluctuations of mechanical values (displacement, speed, acceleration, pressure, etc.).
Mechanical vibrations (depending on the nature of the forces) are:
free;
forced;
self-oscillation.
Free called the vibrations that arise with a single action of an external force (initial energy transfer) and in the absence of external influences on the oscillatory system.
Free (or own)- these are oscillations in the system under the influence internal forces, after the system is taken out of equilibrium (in real conditions, free oscillations are always damped).
Conditions of occurrence free vibrations
1. The oscillatory system must have a stable equilibrium position.
2. When removing the system from the equilibrium position, a resultant force should arise that returns the system to its original position
3. The forces of friction (resistance) are very small.
Forced vibrations- vibrations occurring under the influence of external forces that change over time.
Self-oscillations- undamped oscillations in the system, supported by internal sources of energy 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 by the independence of the amplitude from time and from the initial impact that excites the oscillation process.
The self-oscillating system consists of: an oscillating system; energy source; feedback devices that regulate the flow of energy from an internal energy source into the oscillatory system.
The energy coming from the source during the period is equal to the energy lost by the oscillatory system during the same time.
Mechanical vibrations are divided into:
fading;
undamped.
Damped Oscillations- vibrations, the energy of which decreases over time.
Oscillatory motion characteristics:
permanent:
amplitude (A)
period (T)
frequency ()
The greatest (in modulus) deviation of the oscillating body from the equilibrium position is called amplitude of oscillations. Usually, the amplitude is indicated by the letter A.
The period of time during which the body makes one complete vibration is called period of fluctuations.
The period of oscillation is usually denoted by the letter T and in SI it is measured in seconds (s).
The number of vibrations per unit of time is called vibration frequency.
The frequency is indicated by the letter v (“nu”). One vibration per second is taken as a unit of frequency. 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- 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 oscillations are performed according to the sine or cosine law.
Let the material point perform harmonic vibrations.
The harmonic vibration equation has the form:
a - acceleration V - speed q - charge A - amplitude t - time
1. Oscillations. Periodic fluctuations. Harmonic vibrations.
2. Free vibrations. Continuous and damped oscillations.
3. Forced vibrations. Resonance.
4. Comparison of oscillatory processes. Energy of sustained harmonic vibrations.
5. Self-oscillations.
6. Oscillations of the human body and their registration.
7. Basic concepts and formulas.
8. Tasks.
1.1. Fluctuations. Periodic fluctuations.
Harmonic vibrations
Fluctuations are called processes that differ in varying degrees of repeatability.
Recurring processes continuously occur inside any living organism, for example: heart contractions, lung function; we shiver when we are cold; we hear and speak due to vibrations of the eardrums and vocal cords; when we walk, our legs oscillate. The atoms of which we are made vibrate. The world we live in is surprisingly prone to hesitation.
Depending on the physical nature of the repeating process, oscillations are distinguished: mechanical, electrical, etc. This lecture discusses mechanical vibrations.
Periodic fluctuations
Periodic called such fluctuations in which all the characteristics of the movement are repeated after a certain period of time.
For periodic oscillations, the following characteristics are used:
oscillation period T, equal to the time during which one complete oscillation occurs;
vibration frequencyν, equal to the number of oscillations performed in one second (ν = 1 / T);
vibration amplitude A, equal to the maximum displacement from the equilibrium position.
Harmonic vibrations
A special place among periodic oscillations is occupied by harmonic fluctuations. Their importance is due to the following reasons. Firstly, oscillations in nature and in technology often have a character very close to harmonic, and, secondly, periodic processes of a different form (with a different dependence on time) can be represented as the superposition of several harmonic oscillations.
Harmonic vibrations- these are fluctuations in which the observed value changes over time according to the law of sine or cosine:
In mathematics, functions of this kind are called harmonic, therefore, oscillations described by such functions are also called harmonic.
The position of the body performing the oscillatory motion is characterized by displacement relative to the equilibrium position. In this case, the quantities included in formula (1.1) have the following meaning:
NS- bias bodies at time t;
A - amplitude fluctuations equal to the maximum displacement;
ω - circular frequency oscillations (the number of oscillations made in 2 π seconds) associated with the vibration frequency by the ratio
φ = (ωt +φ 0) - phase fluctuations (at time t); φ 0 - initial phase oscillations (at t = 0).
Rice. 1.1. Time displacement plots for x (0) = A and x (0) = 0
1.2. Free vibrations. Continuous and damped oscillations
Free or own are called such vibrations that occur in the system, left to itself, after it has been removed from the equilibrium position.
An example is the vibrations of a ball suspended from a thread. In order to cause vibrations, you need to either push the ball, or, taking it to the side, release it. When pushing, the ball is told kinetic energy, and in case of deviation - potential.
Free vibrations are performed due to the initial supply of energy.
Free undamped vibrations
Free vibrations can be continuous only in the absence of friction force. Otherwise, the initial supply of energy will be spent on overcoming it, and the range of fluctuations will decrease.
As an example, consider the vibrations of a body suspended on a weightless spring that occur after the body is deflected down and then released (Fig. 1.2).
Rice. 1.2. Body vibrations on a spring
From the side of the stretched spring, the body acts elastic force F proportional to the amount of displacement NS:
The constant factor k is called spring rate and depends on its size and material. The sign "-" indicates that the elastic force is always directed in the direction opposite to the direction of displacement, i.e. to the equilibrium position.
In the absence of friction, the elastic force (1.4) is the only force acting on the body. According to Newton's second law (ma = F):
After transferring all the terms to the left side and dividing by the body mass (m), we obtain the differential equation of free vibrations in the absence of friction:
The value ω 0 (1.6) turned out to be equal to the cyclic frequency. This frequency is called own.
Thus, free vibrations in the absence of friction are harmonic if, upon deviation from the equilibrium position, elastic force(1.4).
Own circular frequency is the main characteristic of free harmonic oscillations. This value depends only on the properties of the oscillatory system (in the case under consideration, on the body mass and spring stiffness). In what follows, the symbol ω 0 will always be used to denote natural circular frequency(i.e. the frequency with which the oscillations would occur in the absence of frictional force).
Amplitude of free vibrations is determined by the properties of the oscillatory system (m, k) and the energy imparted to it at the initial moment of time.
In the absence of friction, free oscillations close to harmonic ones also arise in other systems: mathematical and physical pendulums (the theory of these issues is not considered) (Fig. 1.3).
Mathematical pendulum- a small body (material point), suspended on a weightless thread (Fig. 1.3 a). If the thread is deflected from the equilibrium position by a small (up to 5 °) angle α and released, then the body will oscillate with a period determined by the formula
where L is the length of the thread, g is the acceleration of gravity.
Rice. 1.3. Mathematical pendulum (a), physical pendulum (b)
Physical pendulum- solid oscillating under the action of gravity around a fixed horizontal axis. Figure 1.3 b schematically shows a physical pendulum in the form of a body of arbitrary shape, deflected from the equilibrium position by an angle α. The oscillation period of a physical pendulum is described by the formula
where J is the moment of inertia of the body about the axis, m is the mass, h is the distance between the center of gravity (point C) and the axis of the suspension (point O).
The moment of inertia is a quantity that depends on the mass of the body, its size and position relative to the axis of rotation. The moment of inertia is calculated using special formulas.
Free damped oscillations
Friction forces acting in real systems significantly change the nature of motion: the energy of the oscillatory system is constantly decreasing, and the oscillations either fade out or do not arise at all.
The force of resistance is directed to the side opposite movement body, and at not very high speeds is proportional to the magnitude of the speed:
The graph of such fluctuations is shown in Fig. 1.4.
As a characteristic of the degree of attenuation, a dimensionless quantity called logarithmic damping decrementλ.
Rice. 1.4. Displacement versus time for damped oscillations
Logarithmic damping decrement is equal to natural logarithm the ratio of the amplitude of the previous oscillation to the amplitude of the subsequent oscillation.
where i is the ordinal number of the vibration.
It is easy to see that the logarithmic damping decrement is found by the formula
Strong attenuation. At
if the condition β ≥ ω 0 is satisfied, the system returns to the equilibrium position without vibrating. This movement is called aperiodic. Figure 1.5 shows two possible ways to return to the equilibrium position during aperiodic movement.
Rice. 1.5. Aperiodic movement
1.3. Forced vibrations, resonance
Free vibrations in the presence of friction forces are damped. Continuous oscillations can be created using periodic external influences.
Forced such oscillations are called, during which the oscillating system is exposed to an external periodic force (it is called a driving force).
Let the driving force change according to the harmonic law
The forced oscillation graph is shown in Fig. 1.6.
Rice. 1.6. Plot of displacement versus time for forced oscillations
It is seen that the amplitude of the forced oscillations reaches the steady-state value gradually. The steady-state forced vibrations are harmonic, and their frequency is equal to the frequency of the driving force:
The amplitude (A) of steady-state forced oscillations is found by the formula:
Resonance is the achievement of the maximum amplitude of forced vibrations at a certain value of the frequency of the driving force.
If condition (1.18) is not satisfied, then the resonance does not arise. In this case, with an increase in the frequency of the driving force, the amplitude of the forced oscillations decreases monotonically, tending to zero.
The graphical dependence of the amplitude A of forced vibrations on the circular frequency of the driving force at different values of the damping coefficient (β 1> β 2> β 3) is shown in Fig. 1.7. This set of graphs is called resonance curves.
In some cases, a strong increase in the vibration amplitude at resonance is dangerous for the strength of the system. There are cases when resonance has led to the destruction of structures.
Rice. 1.7. Resonance curves
1.4. Comparison of oscillatory processes. Energy of sustained harmonic vibrations
Table 1.1 shows the characteristics of the considered oscillatory processes.
Table 1.1. Characteristics of free and forced vibrations
Energy of sustained harmonic vibrations
A body performing harmonic vibrations has two types of energy: kinetic energy of motion E k = mv 2/2 and potential energy E p associated with the action of an elastic force. It is known that under the action of an elastic force (1.4), the potential energy of a body is determined by the formula E n = kx 2/2. For sustained vibrations NS= A cos (ωt), and the speed of the body is determined by the formula v= - А ωsin (ωt). From this, expressions are obtained for the energies of a body performing continuous oscillations:
The total energy of the system, in which undamped harmonic oscillations occur, is made up of these energies and remains unchanged:
Here m is the body mass, ω and A are the circular frequency and vibration amplitude, k is the coefficient of elasticity.
1.5. Self-oscillations
There are such systems that themselves regulate the periodic replenishment of lost energy and therefore can fluctuate for a long time.
Self-oscillations- undamped oscillations, supported by an external source of energy, the flow of which is regulated by the oscillating system itself.
Systems in which such oscillations occur are called self-oscillating. The amplitude and frequency of self-oscillations depend on the properties of the self-oscillating system itself. A self-oscillating system can be represented by the following diagram:
V this case the oscillatory system itself acts on the energy regulator by a feedback channel, informing it about the state of the system.
Feedback the impact of the results of any process on its course is called.
If such an impact leads to an increase in the intensity of the process, then the feedback is called positive. If the impact leads to a decrease in the intensity of the process, then the feedback is called negative.
In a self-oscillating system, both positive and negative feedback can be present.
An example of a self-oscillating system is a clock in which the pendulum receives shocks due to the energy of a raised weight or a twisted spring, and these shocks occur at those moments when the pendulum passes through the middle position.
An example of biological self-oscillating systems are organs such as the heart and lungs.
1.6. Human body vibrations and their registration
The analysis of vibrations created by the human body or its individual parts is widely used in medical practice.
Oscillatory movements of the human body when walking
Walking is a complex periodic locomotor process resulting from the coordinated activity of the skeletal muscles of the trunk and limbs. Analysis of the walking process provides many diagnostic features.
A characteristic feature of walking is the frequency of the supporting position with one leg (period of single support) or two legs (period of double support). Normally, the ratio of these periods is 4: 1. When walking, there is a periodic displacement of the center of mass (CM) along the vertical axis (normally by 5 cm) and a deviation to the side (normally by 2.5 cm). In this case, the CM moves along a curve, which can be approximately represented by a harmonic function (Fig. 1.8).
Rice. 1.8. Vertical displacement of the CM of the human body during walking
Complex oscillatory movements while maintaining an upright position of the body.
A person standing upright has complex oscillations of the general center of mass (GCM) and the center of pressure (CP) of the feet on the plane of support. The analysis of these fluctuations is based on statokinesimetry- a method for assessing a person's ability to maintain an upright posture. By keeping the projection of the GCM within the coordinates of the boundary of the support area. This method is implemented using a stabilometric analyzer, the main part of which is a stabiloplatform, on which the subject is in a vertical position. Oscillations made by the subject's CP while maintaining an upright posture are transmitted to the stabiloplatform and recorded by special strain gauges. The load cell signals are transmitted to the recording device. In this case, it is written statokinesigram - trajectory of movement of the test subject's CP on the horizontal plane in two-dimensional system coordinates. Harmonic spectrum statokinesigrams it is possible to judge about the features of verticalization in the norm and in case of deviations from it. This method allows you to analyze the indicators of statokinetic stability (SKU) of a person.
Mechanical vibrations of the heart
Exists different methods heart studies, which are based on mechanical periodic processes.
Ballistocardiography(BCG) is a method for studying the mechanical manifestations of cardiac activity, based on the registration of pulse micromovements of the body, caused by the ejection of a push of blood from the ventricles of the heart into large vessels. In this case, the phenomenon arises recoil. The human body is placed on a special movable platform located on a massive stationary table. As a result of the recoil, the platform comes into a complex oscillatory motion. The dependence of the displacement of the platform with the body on time is called a ballistocardiogram (Fig. 1.9), the analysis of which makes it possible to judge the movement of blood and the state of cardiac activity.
Apexcardiography(AKG) is a method of graphical registration of low-frequency oscillations of the chest in the area of the apical impulse caused by the work of the heart. Registration of an apexcardiogram is performed, as a rule, on a multichannel electrocardiogram.
Rice. 1.9. Ballistocardiogram recording
ograph using a piezocrystalline sensor, which is a converter of mechanical vibrations into electrical ones. Before recording on the anterior chest wall, palpation determines the point of maximum pulsation (apical impulse), in which the sensor is fixed. According to the sensor signals, an apexcardiogram is automatically built. An amplitude analysis of ACG is carried out - the amplitudes of the curve are compared at different phases of the heart with a maximum deviation from the zero line - the EO segment, taken as 100%. Figure 1.10 shows an apexcardiogram.
Rice. 1.10. Apexcardiogram recording
Kinetocardiography(CCG) is a method of recording low-frequency vibrations of the chest wall caused by cardiac activity. The kinetocardiogram differs from the apexcardiogram: the first records the absolute movements of the chest wall in space, the second records the vibrations of the intercostal space relative to the ribs. V this method displacement (KKG x), speed of movement (KKG v) and acceleration (KKG a) for chest oscillations are determined. Figure 1.11 shows a comparison of different kinetocardiograms.
Rice. 1.11. Recording of kinetocardiograms of displacement (x), speed (v), acceleration (a)
Dynamocardiography(DCG) - a method for assessing the movement of the center of gravity of the chest. The dynamocardiograph allows you to register the forces acting from the side of the human chest. To record a dynamocardiogram, the patient is placed on a table lying on his back. Under the chest there is a sensing device, which consists of two rigid metal plates measuring 30x30 cm, between which there are elastic elements with strain gauges fixed on them. Periodically varying in size and place of application, the load acting on the sensing device is composed of three components: 1) constant component - chest mass; 2) variable - the mechanical effect of respiratory movements; 3) variable - mechanical processes accompanying heart contraction.
The dynamocardiogram is recorded while holding the patient's breath in two directions: relative to the longitudinal and transverse axes of the receiving device. Comparison of various dynamocardiograms is shown in Fig. 1.12.
Seismocardiography based on the registration of mechanical vibrations of the human body caused by the work of the heart. In this method, with the help of sensors installed in the region of the base of the xiphoid process, a cardiac impulse is recorded due to the mechanical activity of the heart during the period of contraction. In this case, there are processes associated with the activity of tissue mechanoreceptors of the vascular bed, which are activated when the volume of circulating blood decreases. The seismic cardiac signal forms the form of oscillations of the sternum.
Rice. 1.12. Recording of normal longitudinal (a) and transverse (b) dynamocardiograms
Vibration
The widespread introduction of various machines and mechanisms into human life increases labor productivity. However, the work of many mechanisms is associated with the occurrence of vibrations that are transmitted to a person and have a harmful effect on him.
Vibration- forced vibrations of the body, in which either the whole body vibrates as a whole, or its separate parts vibrate with different amplitudes and frequencies.
A person constantly experiences various kinds of vibrational influences in transport, in production, in everyday life. Vibrations that have arisen in any part of the body (for example, the hand of a worker holding a jackhammer) propagate throughout the body in the form of elastic waves. These waves cause variable deformations of various types (compression, stretching, shear, bending) in the tissues of the body. The effect of vibrations on a person is due to many factors characterizing vibrations: frequency (frequency spectrum, fundamental frequency), amplitude, speed and acceleration of an oscillating point, energy of oscillatory processes.
Prolonged exposure to vibrations causes permanent disturbances in normal physiological functions in the body. Vibration sickness may occur. This disease leads to a number of serious disorders in the human body.
The effect that vibrations have on the body depends on the intensity, frequency, duration of vibrations, the place of their application and direction in relation to the body, posture, as well as on the state of the person and his individual characteristics.
Oscillations with a frequency of 3-5 Hz cause reactions of the vestibular apparatus, vascular disorders. At frequencies of 3-15 Hz, disorders associated with resonant vibrations of individual organs (liver, stomach, head) and the body as a whole are observed. Fluctuations with frequencies of 11-45 Hz cause visual impairment, nausea, and vomiting. At frequencies exceeding 45 Hz, damage to the vessels of the brain occurs, impaired blood circulation, etc. Figure 1.13 shows the areas of vibration frequencies that have a harmful effect on a person and systems of his organs.
Rice. 1.13. Frequency ranges of harmful effects of vibration on humans
At the same time, in a number of cases, vibrations are used in medicine. For example, using a special vibrator, the dentist prepares the amalgam. The use of high-frequency vibrating devices makes it possible to drill a hole with a complex shape in the tooth.
Vibration is also used in massage. During manual massage, the massaged tissues are set in vibrational motion with the help of the masseur's hands. During hardware massage, vibrators are used, in which handpieces are used to transmit vibrational movements to the body. of various shapes... Vibration apparatuses are subdivided into apparatuses for general vibration, which cause shaking of the whole body (vibrating "chair", "bed", "platform", etc.), and apparatuses of local vibration impact on certain parts of the body.
Mechanotherapy
In physiotherapy exercises (exercise therapy), simulators are used, on which oscillatory movements of various parts of the human body are carried out. They are used in mechanotherapy - form of exercise therapy, one of the tasks of which is the implementation of dosed, rhythmically repetitive physical exercises in order to train or restore mobility in the joints on pendulum-type apparatus. The basis of these devices is a balancing one (from fr. balancer- swing, balance) a pendulum, which is a two-arm lever that performs oscillatory (swinging) movements about a fixed axis.
1.7. Basic concepts and formulas
Table continuation
Table continuation
End of the table
1.8. Tasks
1. Give examples of human vibrational systems.
2. In an adult, the heart beats 70 per minute. Determine: a) the frequency of contractions; b) the number of reductions in 50 years
Answer: a) 1.17 Hz; b) 1.84x10 9.
3. How long must a mathematical pendulum have for its oscillation period to be equal to 1 second?
4.
A thin, straight, homogeneous rod 1 m long is suspended by the end on an axis. Determine: a) what is the period of its oscillations (small)? b) what is the length of a mathematical pendulum with the same oscillation period?
5.
A body weighing 1 kg vibrates according to the law x = 0.42 cos (7.40t), where t is measured in seconds, and x is in meters. Find: a) the amplitude; b) frequency; c) full energy; d) kinetic and potential energies at x = 0.16 m.
6.
Estimate the speed at which a person walks with a stride length l= 0.65 m. Leg length L = 0.8 m; the center of gravity is at a distance H = 0.5 m from the foot. For the moment of inertia of the leg relative to the hip joint, use the formula I = 0.2mL 2.
7.
How can you determine the mass of a small body aboard a space station if you have a clock, a spring, and a set of weights at your disposal?
8.
The amplitude of the damped oscillations decreases in 10 oscillations by 1/10 of its original value. The oscillation period is T = 0.4 s. Determine the logarithmic decrement and damping factor.
(or natural vibrations) - these are oscillations of the oscillatory system, performed only due to the initially communicated 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, which is called oscillatory system.
For example, the spring, ball and upright, to which the upper end of the spring is attached (see figure below), are included in the oscillation 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 vibrate freely around the equilibrium position (points O) due to the action of the elastic force of the spring directed towards the equilibrium position.
Others classic example a mechanical oscillatory system is a mathematical pendulum (see figure below). In this case, the ball performs free vibrations under the action of two forces: the force of gravity and the elastic force of the thread (the Earth also enters 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. External forces the forces acting on the system from the side of bodies that are not included in it are called. From this point of view, free vibrations can be defined as vibrations in the system under the influence of internal forces after the system is taken out of the equilibrium position.
The conditions for the occurrence of free vibrations 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) lack of friction in the system.
The dynamics of free vibrations.
Vibrations of the body under the influence of elastic forces... The equation of vibrational motion of a body under the influence of elastic force F() can be obtained taking into account Newton's second law ( F = mа) and Hooke's law ( F ctrl = -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, NS- 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 NS(displacement), we get:
.
Similarly, the 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.
There are different types of oscillations in physics, characterized by certain parameters. Let's consider their main differences, classification according to different factors.
Basic definitions
By oscillation is meant a process in which, at regular intervals, the basic characteristics of movement have the same values.
Periodic fluctuations are those in which the values of the basic quantities are repeated at regular intervals (period of fluctuations).
Varieties of oscillatory processes
Consider the main modes of vibration that exist in fundamental physics.
Free vibrations are those that arise in a system that is not subject to external variable influences after the initial shock.
An example of free vibrations is a mathematical pendulum.
Those types of mechanical vibrations that arise in the system under the influence 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 variant of interaction with the environment
Types of vibrations by interaction with environment there are several groups.
Forced oscillations appear in the system under the action of an external periodic action. As examples of this type of vibration, we can consider the movement of hands, leaves on trees.
For forced harmonic oscillations, the appearance of resonance is possible, in which, with equal values of the frequency of the external influence and the oscillator, with a sharp increase in the amplitude.
These are natural oscillations 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 weight that is suspended by a thread or attached to a spring.
Self-oscillations are the types in which the system has a certain reserve of potential energy, which goes to make oscillations. Distinctive feature their is the fact that the amplitude is characterized by the properties of the system itself, and not by the initial conditions.
For random vibrations, the external load has a random value.
Basic parameters of oscillatory movements
All modes of vibration have certain characteristics, which should be mentioned separately.
The amplitude is called the maximum deviation from the equilibrium position, the deviation of the fluctuating value, it is measured in meters.
The period is the time of one full oscillation through 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 oscillation period.
The oscillation phase characterizes the state of the system.
Harmonic characteristic
These types of oscillations occur according to the cosine or sine law. Fourier was able 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 with certain period and cyclic frequency.
What are these types of vibrations characterized by? Physics considers an idealized system that consists of material point, which is suspended on a weightless inextensible thread, vibrates under the influence of gravity.
These types of vibrations have a certain amount of energy, they are common in nature and technology.
With prolonged oscillatory motion, the coordinate of its center of mass changes, and with alternating current, the value of the current and voltage in the circuit changes.
There are different types of harmonic vibrations according to their physical nature: electromagnetic, mechanical, etc.
Shaking acts as forced vibrations vehicle driving on a rough road.
The main differences between forced and free oscillations
These types of electromagnetic waves differ in physical characteristics... The presence of resistance of the medium and the friction force lead to damping of free vibrations. In the case of forced oscillations, energy losses are compensated for by its additional input from an external source.
The period of a spring pendulum connects body mass and spring stiffness. In the case of a mathematical pendulum, it depends on the length of the thread.
With a known period, you can calculate the natural frequency of the oscillatory system.
In technology and nature, there are vibrations with different meanings frequencies. For example, a 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, 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. Vibrating hammer is a shock-vibration machine, which is intended for driving pipes, piles and other metal structures into the ground.
Electromagnetic vibrations
The characteristic of the modes of vibration involves the analysis of the main physical parameters: charge, voltage, current. As an elementary system, which is used to observe electromagnetic oscillations, there is an oscillatory circuit. It is formed when a coil and a capacitor are connected 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 during their execution 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 possesses.
That is why damped oscillations occur in a real circuit. A decrease in the charge on the capacitor leads to a decrease in the energy value in comparison with its original indicator. 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 end.
The importance of fluctuations in science and technology
Any movement that has a certain degree of repeatability is wobble. For example, a mathematical pendulum is characterized by a systematic deviation in both directions from the initial vertical position.
For a spring pendulum, one full swing 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 capacitor plates. What is the reason for the oscillatory movements? The pendulum functions because gravity forces 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 middle state.
Electrical vibrations 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, vibrations are used that differ significantly in their nature, degree of repetition, character, and also the "mechanism" of their appearance.
Mechanical vibrations are made by strings musical instruments, sea waves, pendulum. Chemical fluctuations associated with a change in the concentration of reactants are taken into account when carrying out various interactions.
Electromagnetic vibrations make it possible to create various technical devices, for example, a telephone, ultrasonic medical devices.
Brightness fluctuations of Cepheids are of particular interest in astrophysics; scientists from different countries are studying them.
Conclusion
All types of vibrations are closely related to a huge number of technical processes and physical phenomena. They are great practical significance in aircraft construction, ship building, construction of residential complexes, electrical engineering, radio electronics, medicine, fundamental science. An example of a typical oscillatory process in physiology is the movement of the heart muscle. Mechanical vibrations occur in organic and inorganic chemistry, meteorology, as well as in many other natural science fields.
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. 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, Rayleigh. He managed to find practical use electromagnetic waves, use them to transmit a radio signal over a long distance.
Academician P. N. Lebedev for many years carried out experiments related to obtaining high-frequency electromagnetic oscillations using alternating electric fields. Through numerous experiments related to different kinds fluctuations, scientists managed to find areas of their optimal use in modern science and technology.
