Periodic mechanical oscillations. Free oscillations
Characteristic of oscillations
Phase Determines the state of the system, namely the coordinate, speed, acceleration, energy, etc.
Cyclic frequency characterizes the rate of changing the oscillation phase.
The initial state of the oscillatory system characterizes primary phase
Oscillation amplitude A. - It is the greatest offset from the equilibrium position.
T. - This is a period of time during which the point performs one complete oscillation.
Frequency of oscillations - This is the number of full fluctuations per unit time t.
Frequency, cyclic frequency and period of oscillations correlate as
Types of oscillations
Oscillations that occur in closed systems are called free or own oscillations. Oscillations that occur under the action of external forces are called forced. There are also found autocalbania (forced automatically).
If we consider oscillations according to the changing characteristics (amplitude, frequency, period, etc.), they can be divided into harmonic, flowing, increments (and also sawn, rectangular, complex).
With free oscillations in real systems, energy loss always occur. Mechanical energy is consumed, for example, to perform work to overcome the air resistance forces. Under the influence of friction force, a decrease in the amplitude of oscillations occurs, and after a while, the oscillations stop. Obviously, the greater the power of resistance to movement, the faster the oscillations stop.
Forced oscillations. Resonance
Forced oscillations are unsuccessful. Therefore, it is necessary to fill energy losses for each period of oscillations. To do this, it is necessary to effect on the oscillating body by periodically changing force. Forced oscillations are performed with a frequency equal to the frequency of change of external force.
Forced oscillations
The amplitude of forced mechanical oscillations reaches the greatest value if the frequency of the forcing force coincides with the frequency of the oscillating system. This phenomenon is called resonance.
For example, if you periodically pull the cord into the tact of its own oscillations, then we note the increase in the amplitude of its oscillations.
If a wet finger moving along the edge of the glade, then the glass will make ringing sounds. Although it is imperceptibly, the finger moves intermittently and transfers the glass to the energy with short portions, forcing a glass of vibrate
The walls of the gland also begin to vibrate if it is to send a sound wave with a frequency equal to its own. If the amplitude becomes very big, then the glass can even break. Due to the resonance with the singing of F.I.Schalyapin trembled (resonated) crystal chandeliers. The emergence of resonance can be traced in the bathroom. If you are quietly rushing the sounds of different frequency, then the resonance will arise on one of the frequencies.
In musical instruments, the role of resonators perform parts of their buildings. A person also has its own resonator - this is the oral cavity, reinforcing the sounds of the sounds.
The phenomenon of resonance must be taken into account in practice. In some phenomena, it can be useful, in others - harmful. Resonance phenomena may cause irreversible destruction in various mechanical systems, for example, incorrectly designed bridges. So, in 1905, the Egyptian bridge collapsed in St. Petersburg collapsed when an equestrian squadron was held on him, and in 1940 the Tajic Bridge collapsed in the United States.
The resonance phenomenon is used when with the help of a small force it is necessary to obtain a large increase in the amplitude of oscillations. For example, a heavy tongue of a large bell can be sought, acting a relatively small force with a frequency equal to its own frequency of bell oscillations.
(or own oscillations) - These are oscillations of the oscillatory system, performed only due to the initially reported energy (potential or kinetie) in the absence of external influences.
Potential or kinetic energy can be reported, for example, in mechanical systems through the initial displacement or initial speed.
Free fluid fluctuating bodies always interact with other bodies and together with them type the system of bodies, which is called oscillatory system.
For example, a spring, a ball and a vertical stand, to which the upper end of the spring is attached (see fig. Below) are included in the oscillatory system. Here the ball freely slides in the string (friction force is negligible). If you take the ball to the right and give it yourself, it will make free oscillations near the position of the equilibrium (points ABOUT) Due to the action of the strength of the spring, aimed at the position of equilibrium.
Another classic example of a mechanical oscillatory system is a mathematical pendulum (see Fig. Below). In this case, the ball performs free fluctuations under the action of two forces: the gravity and the strength of the elasticity of the thread (the Earth is also included in the oscillatory system). Their referring is aimed at the position of equilibrium.
Forces acting between the bodies of the oscillatory system are called internal forces. External forces Called the forces acting on the system from the side of 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 the internal forces after the system is derived from the equilibrium position.
The conditions for the emergence of free oscillations are:
1) the emergence of force in them returning the system to the position of a stable equilibrium, after it was derived from this state;
2) No friction in the system.
Dynamics of free oscillations.
Body fluctuations under the action of elasticity. The equation of the oscillatory movement of the body under the action of the force of elasticity F. () can be obtained taking into account the Second Law of Newton ( F \u003d MA) and the law of the throat ( F UPR \u003d -KX), where m. - the mass of the ball, and - the acceleration acquired by the ball under the action of the force of elasticity, k. - Spring rigidity coefficient, h. - Body displacement from the equilibrium position (both equations are recorded in the projection on the horizontal axis Oh). Equating the right parts of these equations and considering the acceleration but - This is the second derivative of the coordinate h. (displacements), we get:
.
Similar to acceleration expression but We get differentiating ( v \u003d -V M SIN ω 0 T \u003d -V M x M cos (ω 0 t + π / 2)):
a \u003d -a m cos ω 0 t,
where a m \u003d ω 2 0 x m - Acceleration amplitude. Thus, the amplitude of the speed of harmonic cola is proportional to the frequency, and the amplitude of the acceleration is the square of the oscillation frequency.
Oscillations- These are movements or processes that are definitely or approximately repeated at certain time intervals.
Mechanical oscillationsoscillations of mechanical values \u200b\u200b(displacement, speed, acceleration, pressure, etc.).
Mechanical oscillations (depending on the nature of the forces) are:
free;
forced;
self-oscillations.
Freecall oscillations arising from a single effect of external force (initial energy report) and in the absence of external influences on the oscillating system.
Free (or Own) - These are fluctuations in the system under the influence of the inner forces, after the system is derived from the state of equilibrium (in real conditions, free fluctuations are always decaying).
The conditions for the emergence of free oscillations
1. The oscillatory system must have a stable equilibrium position.
2. When the system is removed from the equilibrium position, an automatic force must occur, which returns the system to its original position.
3. Friction forces (resistance) are very small.
Forced oscillations - oscillations occurring under the influence of external forces varying in time.
Autocalbania- Unlucky fluctuations in the system supported by internal sources of energy in the absence of an external variable force.
The frequency and amplitude of self-oscillation is determined by the properties of the oscillating system itself.
From free oscillations, self-oscillations are distinguished by the independence of the amplitude from time and from the initial impact that excites the process of oscillations.
The auto-oscillating system consists of: oscillatory system; source of energy; feedback devices that regulate the flow of energy from the internal source of energy into the oscillatory system.
The energy coming from the source for the period is equal to the energy lost by the oscillatory system during the same time.
Mechanical oscillations are divided into:
fading;
unlucky.
Flowing oscillations - oscillations whose energy decreases over time.
Characteristics of the oscillatory movement:
permanent:
amplitude (a)
period (t)
frequency ()
The largest (module) deviation of the oscillating body from the equilibrium position is called the amplitude of oscillations.Usually the amplitude is denoted by the letter A.
The period of time during which the body makes one complete oscillation, called period of oscillations.
The oscillation period is typically denoted by the letter T and in Xi is measured in seconds (C).
The number of oscillations per unit of time is called frequency of oscillations.
Denotes the frequency of the letter V ("nu"). Per unit of frequency accepted one oscillation per second. This unit in honor of the German scientist Herin Hertz is named Hertz (Hz).
the period of oscillation t and the frequency of oscillations V is associated with the following dependence:
T \u003d 1 / or \u003d 1 / t.
Cyclic (circular) frequency Ω - the number of oscillations for 2π seconds
Harmonic oscillations - Mechanical oscillations that occur under the action of force proportional to the displacement and directed opposite to it. Harmonic oscillations are performed by the law of sinus or cosine.
Let the material point makes harmonic oscillations.
The harmonic oscillation equation is:
a - Acceleration V- speed Q - Charge A - amplitude T -
- These are movements or processes that are characterized by a certain repeatability in time.
Period of oscillations T. - The time interval during which one complete oscillation occurs.
Oscillation frequency ν. - The number of full fluctuations per unit of time. In the SI system, it is expressed in Hertz (Hz).
The period and frequency of oscillations are associated with the relation:
Harmonic oscillations - These are fluctuations in which the oscillating value, for example, the shift of cargo on the spring from the equilibrium position is changed by the law of sine or cosine:
 |
Acceleration with harmonic oscillations is always directed to the side opposite to the displacement; Maximum acceleration is equal to the module 
Spring and mathematical pendulums can be brought as examples of free oscillations. Spring (harmonic ) pendulum - Mass Mass Mass, attached to the rigidity k, the second end of which is fixed motionless. The cyclic frequency of cargo oscillations is:
Autocalbania - It is an unlucky free oscillations supported by periodic energy swap from a source of external force. An example of an auto-oscillating system can serve mechanical clock.
1. oscillations. Periodic oscillations. Harmonic oscillations.
2. Free oscillations. Non-mindy and fading oscillations.
3. Forced oscillations. Resonance.
4. Comparison of vibrational processes. The energy of unlucky harmonic oscillations.
5. Autocalbania.
6. Human body fluctuations and their registration.
7. Basic concepts and formulas.
8. Tasks.
1.1. Oscillations. Periodic oscillations.
Harmonic oscillations
Oscillationscall processes that differ in one or another degree of repeatability.
Repeatablethe processes continuously occur inside any living organism, for example: heart cuts, lungs; we tremble when we are cold; We hear and speak thanks to the fluctuations of the drummers and voice ligaments; When walking, our legs make oscillatory movements. I fluctuate atoms from which we are. The world in which we live is surprisingly inclined to vibrations.
Depending on the physical nature of the recurring process, fluctuations are distinguished: mechanical, electric, etc. In this lecture are considered mechanical oscillations.
Periodic oscillations
Periodicthese oscillations are called, in which all the motion characteristics are repeated after a certain period of time.
For periodic oscillations use the following characteristics:
period of oscillationsT, equal to the time during which one complete oscillation is performed;
frequency of oscillationsν, equal to the number of oscillations performed in one second (ν \u003d 1 / t);
oscillation amplitudeA equal to the maximum displacement from the equilibrium position.
Harmonic oscillations
Special place among periodic oscillations occupy harmonicoscillations. Their significance is due to the following reasons. Firstly, fluctuations in nature and the technique often have a character, very close to harmonic, and, secondly, the periodic processes of another form (with a different time dependence) can be represented as the imposition of several harmonic oscillations.
Harmonic oscillations- These are oscillations in which the observed value varies in time according to the law of sine or cosine:
In mathematics, the function of this species is called harmonictherefore, the oscillations described by such functions are also called harmonic.
The position of the body performing the oscillatory movement is characterized displacementregarding the equilibrium position. In this case, the values \u200b\u200bincluded in formula (1.1) have the following meaning:
h.- biasbodies at time t;
BUT - amplitudeoscillations equal to the maximum displacement;
ω - circular frequencyoscillations (the number of oscillations committed in 2 π seconds) associated with frequency oscillation by relation
φ = (ωt. +φ 0) - phaseoscillations (at time t); φ 0 - primary phaseoscillations (at t \u003d 0).
Fig. 1.1.Graphs of the dependence of the displacement from time for x (0) \u003d a and x (0) \u003d 0
1.2. Free oscillations. Difficult and fading oscillations
Freeor ownthey are called such oscillations that occur in the system granted to themselves after it was removed from the equilibrium position.
An example is the oscillations of the ball suspended on the thread. In order to cause oscillations, you need to either push the ball, or, recalling, let go. With a push, the ball is reported kineticenergy, and with deviation - potential.
Free oscillations are made due to the initial stock of energy.
Loose unlucky oscillations
Free oscillations can be unsuccessful only in the absence of friction force. Otherwise, the initial stock of energy will be spent on its overcoming, and the swing of oscillations will decrease.
As an example, consider fluctuations in the body suspended on the weightless spring, arising after the body is rejected down and then released (Fig. 1.2).
Fig. 1.2.Body fluctuations on spring
From the side of the stretched spring on the body acts elastic strengthF, proportional to the magnitude of the displacement x:
Permanent multiplier K called spring rigidityand depends on its size and material. The sign "-" indicates that the force of elasticity is always directed towards the opposite direction of the displacement, i.e. To the position of equilibrium.
In the absence of friction, elastic strength (1.4) is the only force acting on the body. According to Newton's second law (Ma \u003d f):
After the transfer of all the components to the left and division on the body (M), we obtain a differential equation of free oscillations in the absence of friction:
The value of ω 0 (1.6) was equal to the cyclic frequency. This frequency is called own.
Thus, free oscillations in the absence of friction are harmonic, if the deviation from the equilibrium position occurs elastic strength(1.4).
Own circularthe frequency is the main characteristic of free harmonic oscillations. This value depends only on the properties of the oscillating system (in the case under consideration - from the body weight and spring rigidity). In the future, the symbol ω 0 will always be used to designate own circular frequency(i.e. frequencies with whose fluctuations in the absence of friction force).
Amplitude free oscillationsdetermined by the properties of the oscillatory system (M, K) and the energy reported to it at the initial moment of time.
In the absence of friction, free oscillations close to harmonic, also arise in other systems: mathematical and physical pendulum (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 rejected from the equilibrium position to a small (up to 5 °) angle α and release, the body will perform oscillations with a period determined by the formula
where L is the length of the thread, G is the acceleration of the free fall.
Fig. 1.3.Mathematical pendulum (a), physical pendulum (b)
Physical pendulum- A solid body that performs vibrations under the action of gravity around the fixed horizontal axis. Figure 1.3 B shows schematically the physical pendulum in the form of a body of an arbitrary shape deflected on the equilibrium position to the angle α. The period of oscillations of the physical pendulum is described by the formula
where j is the moment of inertia of the body relative to the axis, M - 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 the value depending on the mass of the body, its size and position relative to the axis of rotation. The moment of inertia is calculated by special formulas.
Loose floating oscillations
The friction forces acting in real systems substantially change the nature of the movement: the energy of the oscillatory system is constantly decreasing, and fluctuations or fadeither do not arise at all.
The resistance force is directed to the side opposite to the movement of the body, and with not very high speeds are proportional to the speed:
The schedule of such oscillations is shown in Fig. 1.4.
As a characteristic of the degree of attenuation, a dimensionless value called logarithmic decrement of attenuationλ.
Fig. 1.4.The dependence of the displacement of time with fading oscillations
Logarithmic decrement attenuationit is equal to natural logarithm for the amplitude of the previous oscillation to the amplitude of the subsequent oscillation.
where i is the sequence number of the oscillation.
It is easy to see that the logarithmic decrement of attenuation is in the formula
Strong attenuation.For
performing the condition β ≥ ω 0 The system returns to the equilibrium position without performing oscillations. Such a movement is called aperiodic.Figure 1.5 shows two possible ways to return to the equilibrium position in aperiodic motion.
Fig. 1.5.Aperiodic movement
1.3. Forced oscillations, resonance
Free oscillations in the presence of friction forces are fading. Unlucky oscillations can be created using a periodic external influence.
Forcedsuch oscillations are called, in the process of which the fluctuating system is exposed to an external periodic force (it is called forgoing force).
Let the generating force varies on the harmonic law
The schedule of forced oscillations is shown in Fig. 1.6.
Fig. 1.6.Schedule of the displacement of time with forced oscillations
It can be seen that the amplitude of the forced oscillations reaches the steady value gradually. The established forced oscillations are harmonious, and their frequency is equal to the frequency of the forcing force:
The amplitude (a) of the established forced oscillations is by the formula:
Resonanceit is called achieving the maximum amplitude of the forced oscillations at a certain value of the frequency of the forced force.
If condition (1.18) is not fulfilled, then the resonance does not occur. In this case, with an increase in the frequency of the forced strength of the amplitude of the forced oscillations, monotonously decreases, striving for zero.
The graphic dependence of the amplitude of the forced oscillations from the circular frequency of the forcing force at different values \u200b\u200bof the attenuation coefficient (β 1\u003e β 2\u003e β 3) is shown in Fig. 1.7. Such a totality of graphs is called resonant curves.
In some cases, severe increase in the amplitude of oscillations during resonance is dangerous for the strength of the system. There are cases when the resonance led to the destruction of structures.
Fig. 1.7.Resonant curves
1.4. Comparison of vibrational processes. Energy of non-teaching harmonic oscillations
Table 1.1 presents the characteristics of the considered oscillatory processes.
Table 1.1.Features of free and forced oscillations
Energy of non-teaching harmonic oscillations
The body that performs harmonic oscillations has two types of energy: the kinetic energy of the E K \u003d MV 2/2 movement and the potential energy E P associated with the action of elastic force. It is known that under the action of elastic force (1.4), the potential energy of the body is determined by the formula e n \u003d КХ 2/2. For unlucky oscillations h.\u003d A cos (ωt), and the body speed is determined by the formula v.\u003d - A ωsin (ωt). From here, expressions are obtained for the energy of the body that performs the unlucky oscillations:
The total energy of the system, in which unsophisticating harmonic oscillations occur, is made up of these energies and remains unchanged:
Here M is the mass of the body, ω and a - circular frequency and amplitude of oscillations, K is the coefficient of elasticity.
1.5. Autocalbania
There are systems that themselves regulate the periodic replenishment of lost energy and therefore can fluctuate for a long time.
Autocalbania- Unlucky oscillations supported by an external source of energy, the arrival of which is regulated by the oscillating system itself.
Systems in which such oscillations arise are called self-oscillatory.Amplitude and frequency of self-oscillations depend on the properties of the self-oscillating system itself. The auto-oscillating system can be submitted to the following scheme:
In this case, the oscillating system of feedback channel itself affects the energy regulator, informing it about the system status.
Feedbackit is called the impact of the results of some kind of process on its flow.
If such an impact leads to an increase in the intensity of the process, the feedback is called positive.If the impact leads to a decrease in the intensity of the process, then the feedback is called negative.
The auto-oscillating system may be present both positive and negative feedback.
An example of an auto-oscillatory system is the clock in which the pendulum gets shocks due to the energy raised weights or twisted spring, and these shocks occur in those moments when the pendulum passes through the middle position.
An example of biological auto-oscillatory systems are organs such as heart, lungs.
1.6. Human body fluctuations and their registration
Analysis of oscillations created by the human body or its individual parts is widely used in medical practice.
The oscillatory movements of the human body when walking
Walking is a complex periodic locomotor process resulting from the coordinated activity of skeletal muscles of the body and limbs. Analysis of the walking process gives a lot of diagnostic signs.
A characteristic feature of walking is the frequency of the reference position by one foot (a period of a single support) or two legs (dual support period). 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 5 cm) and the deviation to the side (normally 2.5 cm). At the same time, the CM makes movement along the curve, which can be approximately a harmonic function (Fig. 1.8).
Fig. 1.8.Vertical displacement of the CM of the human body during walking
Complex vibrational movements while maintaining the vertical position of the body.
The person standing vertically, the complex fluctuations in the general center of mass (OCS) and the pressure center (CD) stop on the plane of the support. On the analysis of these oscillations is based stocianesimetria- The method of assessing a person's ability to maintain a vertical posture. Through the retention of the projection by the BCM within the coordinates of the border 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 the vertical posture. The fluctuations made by the Test Test when maintaining vertical postures are transmitted by stabiloplatform and are recorded by special strain gauges. Tensifold signals are transmitted to the recording device. At the same time recorded stocinesigram -the trajectory of the displacement of the CD subject on the horizontal plane in the two-dimensional coordinate system. By harmonic spectrum stocinesigrammasit can be judged on the peculiarization features in the norm and with deviations from it. This method allows you to analyze the indicators of the static stability (s) of a person.
Mechanical oscillations of the heart
There are various methods of heart research, which are based on mechanical periodic processes.
Ballergartiography(BKG) - Method of studying mechanical manifestations of cardiac activity, based on the registration of pulse microswits of the body due to the throwing of blood from the ventricles of the heart into large vessels. At the same time there is a phenomenon return.The human body is placed on a special mobile platform located on a massive stationary table. The platform as a result of the return comes into a complex oscillatory movement. The dependence of the displacement of the platform with a body from time is called balleriogram (Fig. 1.9), the analysis of which allows to judge the flow of blood and the state of cardiac activity.
APECKSKARDIY(AKG) - the method of graphic registration of low-frequency chest oscillations in the region of the top of the shock caused by the work of the heart. Registration of the apexcardiogram is carried out, as a rule, on multichannel electrocardials
Fig. 1.9.Record ballerokardiogram
robbery with the help of a piezocrystalline sensor, which is a transducer of mechanical oscillations to electrical. Before recording on the front wall of the chest palpatorially, determine the maximum ripple point (the top push), in which the sensor fixes. Agreement is automatically built by the sensor signals. An amplitude analysis of AKG is carried out - compare the amplitudes of the curve at different phases of the heart of the heart with a maximum deviation from the zero line - the EO segment taken for 100%. Figure 1.10 shows a apexcardiogram.
Fig. 1.10.Recording apexcardiogram
Kintocardiography(KKG) - a method for registering low-frequency vibrations of the wall of the chest, due to cardiac activity. The kinetocardiogram differs from the apexcardiogram: the first fixes the recording of absolute movements of the chest wall in space, the second registers the oscillations of the intercreation relative to the ribs. In this method, the movement (KKG X) is determined, the movement rate (KKG V) as well as acceleration (KKG A) for chest oscillations. Figure 1.11 presents a comparison of various kinetocardiograms.
Fig. 1.11.Record the displacement (x), speed (V), speed, acceleration (s)
Dynamocardiography(DCG) is a method for assessing the movement of the center of gravity of the chest. The dynamocardiograph allows you to register forces acting on the side of the human chest. To record the dynamocardiogram, the patient is located on the table lying on the back. Under the chest is a perceiving device, which consists of two rigid metal plates with a size of 30x30 cm, between which elastic elements with strain gauges are located on them. Periodically changing the magnitude and place of the application, the load acting on the perceiving device is composed of three components: 1) the constant component is the mass of the chest; 2) the variable - the mechanical effect of respiratory movements; 3) variable - mechanical processes accompanying the heart abbreviation.
The record of the dynamocardiogram is carried out with the delay in breathing under investigators in two directions: relative to the longitudinal and transverse axis of the perceive device. A comparison of various dynamocardiograms is shown in Fig. 1.12.
Seismocardiographybased on the registration of mechanical fluctuations in human body caused by the work of the heart. In this method, with the help of sensors installed in the field of the base of the sword-shaped process, a heart impetus is recorded due to the mechanical activity of the heart during the reduction period. At the same time, processes related to the activities of tissue mechanoreceptors of the vascular channel, activating when a decrease in the volume of circulating blood are occurring. Seismocardius forms the shape of sternum oscillations.
Fig. 1.12.Record normal longitudinal (a) and transverse (b) dynamocardiograms
Vibration
The wide introduction of various machines and mechanisms to human life increases 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 it.
Vibration- Forced fluctuations in the body, at which either the whole body fluctuates as a whole, or its individual parts with different amplitudes and frequencies fluctuate.
A person is constantly experiencing various kinds of vibration effects in transport, in production, in everyday life. Oscillations that arose in any place of the body (for example, a working hand holding a jackhammer), spread throughout the body in the form of elastic waves. These waves are caused in the tissues of the body variables of deformation of various types (compression, stretching, shift, bending). The effect of vibrations per person is due to many factors characterizing vibration: frequency (frequency spectrum, main frequency), amplitude, speed and acceleration of the oscillating point, the energy of the oscillatory processes.
The prolonged impact of vibrations causes persistent violations of normal physiological functions in the body. A "vibrational disease" may occur. This disease leads to a number of serious disorders in the human body.
The influence that vibrations are on the body depends on the intensity, frequency, duration of vibrations, the locations of their application and direction towards the body, position, as well as from the state of the person and its individual characteristics.
Oscillations with a frequency of 3-5 Hz cause the vestibular apparatus reaction, vascular disorders. At frequencies of 3-15 Hz, disorders are observed associated with resonant oscillations of individual organs (liver, stomach, head) and body as a whole. The oscillations with frequencies of 11-45 Hz cause impairment, nausea, vomiting. At frequencies exceeding 45 Hz, there are damage to the vessels of the brain, a violation of blood circulation, etc. Figure 1.13 shows the fields of vibration frequencies that have a harmful effect on the person and the system of its organs.
Fig. 1.13.Frequency areas of the harmful effects of vibration per person
At the same time, in some cases, vibrations are used in medicine. For example, with the help of a special vibrator, the dentist is preparing amalgam. The use of high-frequency vibration devices allows drilled in the teeth a hole of a complex shape.
Vibration is used and with massage. With manual massage, massageable fabrics are given in an oscillatory movement with the hands of the masseur. With hardware massage, vibrators are used, in which the tips of various shapes are used to transmit the body of oscillatory movements. Vibration devices are divided into apparatuses for general vibration, causing the shaking of the entire body (vibration "chair", "bed", "platform", etc.), and local vibrational impact devices for individual parts of the body.
Mechanotherapy
In therapeutic physical education (LFC), simulators are used, on which the oscillatory movements of various parts of the human body are carried out. They are used in mechanotherapy -the form of the exercise, one of the tasks of which is the implementation of dosage, rhythmically repeated physical exercises in order to train or restoring mobility in the joints on the pendulum type devices. The basis of these devices is balancing (from FR. balancer.- Swing, balancing) The pendulum, which is a biscuit lever, performing oscillatory (swinging) movements near the stationary axis.
1.7. Basic concepts and formulas
Table continuation
Table continuation
Ending table
1.8. Tasks
1. Create examples of human oscillatory systems.
2. In an adult, the heart makes 70 cuts per minute. Determine: a) the frequency of abbreviations; b) number of reductions for 50 years
Answer:a) 1,17 Hz; b) 1.84x10 9.
3. What length should the mathematical pendulum, so that his oscillations period be equal to 1 second?
4.
The thin direct homogeneous rod 1 m long is suspended for the end on the axis. Determine: a) what is the period of its oscillations (small)? b) What is the length of a mathematical pendulum having the same period of oscillations?
5.
The body weighing 1 kg makes oscillations by law x \u003d 0.42 cos (7.40t), where T is measured in seconds, and x - in meters. Find: a) amplitude; b) frequency; c) full energy; d) kinetic and potential energy at x \u003d 0.16 m.
6.
Evaluate the speed with which a person goes with a step length l.\u003d 0.65 m. Leg length L \u003d 0.8 m; The center of gravity is at a distance of H \u003d 0.5 m from the foot. For the moment of inertia, the legs relative to the hip joint use the formula i \u003d 0.2ML 2.
7.
How can you determine the mass of a small body on board the space station, if you have a clock, a spring and a set of weights?
8.
The amplitude of the fading oscillations decreases for 10 oscillations by 1/10 part of its initial value. The period of oscillations T \u003d 0.4 s. Determine the logarithmic decrement and attenuation coefficient.
