Mathematical pendulum called material point suspended on a weightless and inextensible thread attached to the suspension and located in the field of gravity (or other force).
Exploring fluctuations mathematical pendulum in an inertial frame of reference, relative to which the point of its suspension is at rest or moves uniformly in a straight line. We will neglect the force of air resistance (an ideal mathematical pendulum). Initially, the pendulum is at rest in the equilibrium position C. In this case, the force of gravity \(\vec F\) and the elastic force \(\vec F_(ynp)\) of the thread acting on it are mutually compensated.
We bring the pendulum out of the equilibrium position (by deflecting it, for example, to position A) and release it without initial speed(Fig. 13.11). In this case, the forces \(\vec F\) and \(\vec F_(ynp)\) do not balance each other. The tangential component of gravity \(\vec F_\tau\), acting on the pendulum, gives it a tangential acceleration \(\vec a_\tau\) (component full acceleration, directed along the tangent to the trajectory of the mathematical pendulum), and the pendulum begins to move towards the equilibrium position with a speed increasing in absolute value. The tangential component of gravity \(\vec F_\tau\) is thus the restoring force. The normal component \(\vec F_n\) of gravity is directed along the thread against the elastic force \(\vec F_(ynp)\). The resultant of the forces \(\vec F_n\) and \(\vec F_(ynp)\) gives the pendulum a normal acceleration \(~a_n\), which changes the direction of the velocity vector, and the pendulum moves along an arc ABCD.
The closer the pendulum approaches the equilibrium position C, the smaller the value of the tangential component \(~F_\tau = F \sin \alpha\) becomes. In the equilibrium position, it is equal to zero, and the speed reaches its maximum value, and the pendulum moves further by inertia, rising upward along the arc. In this case, the component \(\vec F_\tau\) is directed against the speed. With an increase in the angle of deflection a, the modulus of force \(\vec F_\tau\) increases, and the modulus of velocity decreases, and at point D the speed of the pendulum becomes zero. The pendulum stops for a moment and then begins to move in reverse direction to the equilibrium position. Having again passed it by inertia, the pendulum, slowing down, will reach point A (no friction), i.e. makes a full swing. After that, the movement of the pendulum will be repeated in the sequence already described.
We obtain an equation describing the free oscillations of a mathematical pendulum.
Let the pendulum in this moment time is at point B. Its displacement S from the equilibrium position at this moment is equal to the length of the arc SW (i.e. S = |CB|). Denote the length of the suspension thread l, and the mass of the pendulum - m.
Figure 13.11 shows that \(~F_\tau = F \sin \alpha\), where \(\alpha =\frac(S)(l).\) At small angles \(~(\alpha<10^\circ)\) отклонения маятника \(\sin \alpha \approx \alpha,\) поэтому
\(F_\tau = -F\frac(S)(l) = -mg\frac(S)(l).\)
The minus sign in this formula is put because the tangential component of gravity is directed towards the equilibrium position, and the displacement is counted from the equilibrium position.
According to Newton's second law \(m \vec a = m \vec g + F_(ynp).\) We project the vector quantities of this equation onto the direction of the tangent to the trajectory of the mathematical pendulum
\(~F_\tau = ma_\tau .\)
From these equations we get
\(a_\tau = -\frac(g)(l)S\) - dynamic equation of motion of a mathematical pendulum. The tangential acceleration of a mathematical pendulum is proportional to its displacement and is directed towards the equilibrium position. This equation can be written in the form \. Comparing it with the equation of harmonic oscillations \(~a_x + \omega^2x = 0\) (see § 13.3), we can conclude that the mathematical pendulum performs harmonic oscillations. And since the considered oscillations of the pendulum occurred under the action of only internal forces, these were free oscillations of the pendulum. Hence, free oscillations of a mathematical pendulum with small deviations are harmonic.
Denote \(\frac(g)(l) = \omega^2.\) Whence \(\omega = \sqrt \frac(g)(l)\) is the cyclic frequency of the pendulum.
The period of oscillation of the pendulum \(T = \frac(2 \pi)(\omega).\) Therefore,
\(T = 2 \pi \sqrt( \frac(l)(g) )\)
This expression is called Huygens formula. It determines the period of free oscillations of the mathematical pendulum. It follows from the formula that at small angles of deviation from the equilibrium position, the oscillation period of a mathematical pendulum: 1) does not depend on its mass and oscillation amplitude; 2) is proportional to the square root of the length of the pendulum and inversely proportional to the square root of the gravitational acceleration. This is consistent with the experimental laws of small oscillations of a mathematical pendulum, which were discovered by G. Galileo.
We emphasize that this formula can be used to calculate the period if two conditions are met simultaneously: 1) the oscillations of the pendulum must be small; 2) the suspension point of the pendulum must be at rest or move uniformly rectilinearly relative to the inertial frame of reference in which it is located.
If the suspension point of a mathematical pendulum moves with acceleration \(\vec a\), then the tension force of the thread changes, which leads to a change in the restoring force, and, consequently, the frequency and period of oscillation. As calculations show, the period of oscillation of the pendulum in this case can be calculated by the formula
\(T = 2 \pi \sqrt( \frac(l)(g") )\)
where \(~g"\) is the "effective" acceleration of the pendulum in a non-inertial frame of reference. It is equal to the geometric sum of the gravitational acceleration \(\vec g\) and the vector opposite to the vector \(\vec a\), i.e. it can be calculated using the formula
\(\vec g" = \vec g + (- \vec a).\)
Literature
Aksenovich L. A. Physics in high school: Theory. Tasks. Tests: Proc. allowance for institutions providing general. environments, education / L. A. Aksenovich, N. N. Rakina, K. S. Farino; Ed. K. S. Farino. - Mn.: Adukatsia i vykhavanne, 2004. - S. 374-376.
A mechanical system, which consists of a material point (body) hanging on an inextensible weightless thread (its mass is negligible compared to the weight of the body) in a uniform gravity field, is called a mathematical pendulum (another name is an oscillator). There are other types of this device. Instead of a thread, a weightless rod can be used. A mathematical pendulum can clearly reveal the essence of many interesting phenomena. With a small amplitude of oscillation, its movement is called harmonic.
General information about the mechanical system
The formula for the period of oscillation of this pendulum was derived by the Dutch scientist Huygens (1629-1695). This contemporary of I. Newton was very fond of this mechanical system. In 1656 he created the first pendulum clock. They measured time with exceptional accuracy for those times. This invention became the most important stage in the development of physical experiments and practical activities.
If the pendulum is in the equilibrium position (hanging vertically), then it will be balanced by the force of the thread tension. A flat pendulum on an inextensible thread is a system with two degrees of freedom with a connection. When you change just one component, the characteristics of all its parts change. So, if the thread is replaced by a rod, then this mechanical system will have only 1 degree of freedom. What are the properties of a mathematical pendulum? In this simplest system, chaos arises under the influence of a periodic perturbation. In the case when the suspension point does not move, but oscillates, the pendulum has a new equilibrium position. With rapid up and down oscillations, this mechanical system acquires a stable upside down position. She also has her own name. It is called the pendulum of Kapitsa.
pendulum properties
The mathematical pendulum has very interesting properties. All of them are confirmed by known physical laws. The period of oscillation of any other pendulum depends on various circumstances, such as the size and shape of the body, the distance between the point of suspension and the center of gravity, the distribution of mass relative to this point. That is why determining the period of a hanging body is a rather difficult task. It is much easier to calculate the period of a mathematical pendulum, the formula of which will be given below. As a result of observations of similar mechanical systems, the following regularities can be established:
If, while maintaining the same length of the pendulum, different weights are suspended, then the period of their oscillations will turn out to be the same, although their masses will differ greatly. Therefore, the period of such a pendulum does not depend on the mass of the load.
If, when starting the system, the pendulum is deflected by not too large, but different angles, then it will begin to oscillate with the same period, but with different amplitudes. As long as the deviations from the center of equilibrium are not too large, the oscillations in their form will be quite close to harmonic ones. The period of such a pendulum does not depend on the oscillation amplitude in any way. This property of this mechanical system is called isochronism (translated from the Greek "chronos" - time, "isos" - equal).
The period of the mathematical pendulum
This indicator represents the period Despite the complex wording, the process itself is very simple. If the length of the thread of a mathematical pendulum is L, and the free fall acceleration is g, then this value is equal to:
The period of small natural oscillations in no way depends on the mass of the pendulum and the amplitude of oscillations. In this case, the pendulum moves like a mathematical pendulum with a reduced length.
Oscillations of a mathematical pendulum
A mathematical pendulum oscillates, which can be described by a simple differential equation:
x + ω2 sin x = 0,
where x (t) is an unknown function (this is the angle of deviation from the lower equilibrium position at time t, expressed in radians); ω is a positive constant that is determined from the parameters of the pendulum (ω = √g/L, where g is the gravitational acceleration and L is the length of the mathematical pendulum (suspension).
The equation of small oscillations near the equilibrium position (harmonic equation) looks like this:
x + ω2 sin x = 0
Oscillatory movements of the pendulum
A mathematical pendulum that makes small oscillations moves along a sinusoid. The second-order differential equation meets all the requirements and parameters of such a motion. To determine the trajectory, you must specify the speed and coordinate, from which independent constants are then determined:
x \u003d A sin (θ 0 + ωt),
where θ 0 is the initial phase, A is the oscillation amplitude, ω is the cyclic frequency determined from the equation of motion.
Mathematical pendulum (formulas for large amplitudes)
This mechanical system, which makes its oscillations with a significant amplitude, is subject to more complex laws of motion. For such a pendulum, they are calculated by the formula:
sin x/2 = u * sn(ωt/u),
where sn is the Jacobian sine, which for u< 1 является периодической функцией, а при малых u он совпадает с простым тригонометрическим синусом. Значение u определяют следующим выражением:
u = (ε + ω2)/2ω2,
where ε = E/mL2 (mL2 is the energy of the pendulum).
The oscillation period of a non-linear pendulum is determined by the formula:
where Ω = π/2 * ω/2K(u), K is the elliptic integral, π - 3,14.
The movement of the pendulum along the separatrix
A separatrix is a trajectory of a dynamical system that has a two-dimensional phase space. The mathematical pendulum moves along it non-periodically. At an infinitely distant moment of time, it falls from the extreme upper position to the side with zero velocity, then gradually picks it up. It eventually stops, returning to its original position.
If the amplitude of the pendulum's oscillation approaches the number π , this indicates that the motion on the phase plane approaches the separatrix. In this case, under the action of a small driving periodic force, the mechanical system exhibits chaotic behavior.
When the mathematical pendulum deviates from the equilibrium position with a certain angle φ, a tangential force of gravity Fτ = -mg sin φ arises. The minus sign means that this tangential component is directed in the opposite direction from the pendulum deflection. When the displacement of the pendulum along the arc of a circle with radius L is denoted by x, its angular displacement is equal to φ = x/L. The second law, which is for projections and force, will give the desired value:
mg τ = Fτ = -mg sinx/L
Based on this relationship, it can be seen that this pendulum is a non-linear system, since the force that tends to return it to its equilibrium position is always proportional not to the displacement x, but to sin x/L.
Only when the mathematical pendulum makes small oscillations is it a harmonic oscillator. In other words, it becomes a mechanical system capable of performing harmonic vibrations. This approximation is practically valid for angles of 15-20°. Pendulum oscillations with large amplitudes are not harmonic.
Newton's law for small oscillations of a pendulum
If a given mechanical system performs small vibrations, Newton's 2nd law will look like this:
mg τ = Fτ = -m* g/L* x.
Based on this, we can conclude that the mathematical pendulum is proportional to its displacement with a minus sign. This is the condition due to which the system becomes a harmonic oscillator. The modulus of the proportionality factor between displacement and acceleration is equal to the square of the circular frequency:
ω02 = g/L; ω0 = √g/L.
This formula reflects the natural frequency of small oscillations of this type of pendulum. Based on this,
T = 2π/ ω0 = 2π√ g/L.
Calculations based on the law of conservation of energy
The properties of a pendulum can also be described using the law of conservation of energy. In this case, it should be taken into account that the pendulum in the field of gravity is equal to:
E = mg∆h = mgL(1 - cos α) = mgL2sin2 α/2
Total equals kinetic or maximum potential: Epmax = Ekmsx = E
After the law of conservation of energy is written, the derivative of the right and left sides of the equation is taken:
Since the derivative of constants is 0, then (Ep + Ek)" = 0. The derivative of the sum is equal to the sum of the derivatives:
Ep" = (mg/L*x2/2)" = mg/2L*2x*x" = mg/L*v + Ek" = (mv2/2) = m/2(v2)" = m/2* 2v*v" = mv*α,
hence:
Mg/L*xv + mva = v (mg/L*x + mα) = 0.
Based on the last formula, we find: α = - g/L*x.
Practical application of the mathematical pendulum
Acceleration varies with geographic latitude, since the density of the earth's crust is not the same throughout the planet. Where rocks with a higher density occur, it will be somewhat higher. The acceleration of a mathematical pendulum is often used for geological exploration. It is used to search for various minerals. Simply by counting the number of swings of the pendulum, you can find coal or ore in the bowels of the Earth. This is due to the fact that such fossils have a density and mass greater than the loose rocks underlying them.
The mathematical pendulum was used by such prominent scientists as Socrates, Aristotle, Plato, Plutarch, Archimedes. Many of them believed that this mechanical system could influence the fate and life of a person. Archimedes used a mathematical pendulum in his calculations. Nowadays, many occultists and psychics use this mechanical system to fulfill their prophecies or search for missing people.
The famous French astronomer and naturalist C. Flammarion also used a mathematical pendulum for his research. He claimed that with his help he was able to predict the discovery of a new planet, the appearance of the Tunguska meteorite and other important events. During the Second World War in Germany (Berlin) a specialized pendulum institute worked. Today, the Munich Institute of Parapsychology is engaged in similar research. The employees of this institution call their work with the pendulum “radiesthesia”.
Mathematical pendulum called a material point suspended on a weightless and inextensible thread attached to a suspension and located in the field of gravity (or other force).
We study the oscillations of a mathematical pendulum in an inertial frame of reference, relative to which the point of its suspension is at rest or moves uniformly in a straight line. We will neglect the force of air resistance (an ideal mathematical pendulum). Initially, the pendulum is at rest in the equilibrium position C. In this case, the force of gravity acting on it and the force of elasticity F?ynp of the thread are mutually compensated.
We bring the pendulum out of the equilibrium position (deflecting it, for example, to position A) and let it go without initial velocity (Fig. 1). In this case, the forces and do not balance each other. The tangential component of gravity, acting on the pendulum, gives it a tangential acceleration a?? (the component of the total acceleration directed along the tangent to the trajectory of the mathematical pendulum), and the pendulum begins to move towards the equilibrium position with an increasing speed in absolute value. The tangential component of gravity is thus the restoring force. The normal component of gravity is directed along the thread against the elastic force. The resultant force and tells the pendulum normal acceleration, which changes the direction of the velocity vector, and the pendulum moves along the arc ABCD.
The closer the pendulum approaches the equilibrium position C, the smaller the value of the tangential component becomes. In the equilibrium position, it is equal to zero, and the speed reaches its maximum value, and the pendulum moves further by inertia, rising upward along the arc. In this case, the component is directed against the speed. With an increase in the angle of deflection a, the modulus of force increases, and the modulus of velocity decreases, and at point D the speed of the pendulum becomes equal to zero. The pendulum stops for a moment and then begins to move in the opposite direction to the equilibrium position. Having again passed it by inertia, the pendulum, slowing down, will reach point A (no friction), i.e. makes a full swing. After that, the movement of the pendulum will be repeated in the sequence already described.
We obtain an equation describing the free oscillations of a mathematical pendulum.
Let the pendulum at a given moment of time be at point B. Its displacement S from the equilibrium position at this moment is equal to the length of the arc CB (i.e. S = |CB|). Let us denote the length of the suspension thread as l, and the mass of the pendulum as m.
Figure 1 shows that , where . At small angles () pendulum deflection, therefore
The minus sign in this formula is put because the tangential component of gravity is directed towards the equilibrium position, and the displacement is counted from the equilibrium position.
According to Newton's second law. We project the vector quantities of this equation onto the direction of the tangent to the trajectory of the mathematical pendulum
From these equations we get
Dynamic equation of motion of a mathematical pendulum. The tangential acceleration of a mathematical pendulum is proportional to its displacement and is directed towards the equilibrium position. This equation can be written as
Comparing it with the equation of harmonic oscillations 
, we can conclude that the mathematical pendulum makes harmonic oscillations. And since the considered oscillations of the pendulum occurred under the action of only internal forces, these were free oscillations of the pendulum. Consequently, free oscillations of a mathematical pendulum with small deviations are harmonic.
Denote
Cyclic frequency of pendulum oscillations.
The period of oscillation of the pendulum. Hence,
This expression is called the Huygens formula. It determines the period of free oscillations of the mathematical pendulum. It follows from the formula that at small angles of deviation from the equilibrium position, the oscillation period of the mathematical pendulum:
- does not depend on its mass and amplitude of oscillations;
- proportional to the square root of the length of the pendulum and inversely proportional to the square root of the free fall acceleration.
This is consistent with the experimental laws of small oscillations of a mathematical pendulum, which were discovered by G. Galileo.
We emphasize that this formula can be used to calculate the period when two conditions are met simultaneously:
- pendulum oscillations should be small;
- the suspension point of the pendulum must be at rest or move uniformly rectilinearly relative to the inertial reference frame in which it is located.
If the suspension point of a mathematical pendulum moves with acceleration, then the tension force of the thread changes, which leads to a change in the restoring force, and, consequently, the frequency and period of oscillation. As calculations show, the period of oscillation of the pendulum in this case can be calculated by the formula
where is the "effective" acceleration of the pendulum in a non-inertial frame of reference. It is equal to the geometric sum of the gravitational acceleration and the vector opposite to the vector , i.e. it can be calculated using the formula
Pendulum Foucault- a pendulum, which is used to experimentally demonstrate the daily rotation of the Earth.
The Foucault pendulum is a massive weight suspended on a wire or thread, the upper end of which is reinforced (for example, with a cardan joint) so that it allows the pendulum to swing in any vertical plane. If the Foucault pendulum is deflected from the vertical and released without initial velocity, then the forces of gravity and tension of the thread acting on the pendulum's weight will lie all the time in the plane of the pendulum's swings and will not be able to cause its rotation with respect to the stars (to the inertial frame of reference associated with the stars) . An observer who is on the Earth and rotates with it (i.e., located in a non-inertial frame of reference) will see that the swing plane of the Foucault pendulum slowly rotates relative to the earth's surface in the direction opposite to the direction of the Earth's rotation. This confirms the fact of the daily rotation of the Earth.
At the North or South Pole, the swing plane of the Foucault pendulum will rotate 360° per sidereal day (15 o per sidereal hour). At a point on the earth's surface, the geographical latitude of which is φ, the horizon plane rotates around the vertical with an angular velocity of ω 1 = ω sinφ (ω is the Earth's angular velocity modulus) and the pendulum swing plane rotates with the same angular velocity. Therefore, the apparent angular velocity of rotation of the plane of swing of the Foucault pendulum at latitude φ, expressed in degrees per sidereal hour, has the value rotates). In the Southern Hemisphere, the rotation of the rocking plane will be observed in the direction opposite to that observed in the Northern Hemisphere. The refined calculation gives the value
ω m = 15 o sinφ
where a- the amplitude of oscillations of the pendulum weight, l- thread length. The additional term, which reduces the angular velocity, the less, the more l. Therefore, to demonstrate the experience, it is advisable to use the Foucault pendulum with the largest possible length of the thread (several tens of meters).
Story
For the first time this device was designed by the French scientist Jean Bernard Leon Foucault.
This device was a five-kilogram brass ball suspended from the ceiling on a two-meter steel wire.
Foucault's first experience was in the basement of his own house. January 8, 1851. This was recorded in the scientist's scientific diary.
February 3, 1851 Jean Foucault demonstrated his pendulum at the Paris Observatory to academicians who received letters like this: "I invite you to follow the rotation of the Earth."
The first public demonstration of the experience took place at the initiative of Louis Bonaparte in the Paris Panthéon in April of that year. A metal ball was suspended under the dome of the Pantheon. weighing 28 kg with a point fixed on it on a steel wire 1.4 mm in diameter and 67 m long. pendulum allowed him to freely oscillate in all directions. Under the attachment point was made a circular fence with a diameter of 6 meters, along the edge of the fence a sand path was poured in such a way that the pendulum in its movement could draw marks on the sand when crossing it. To avoid a lateral push when starting the pendulum, he was taken aside and tied with a rope, after which the rope burned out. The oscillation period was 16 seconds.
The experiment was a great success and caused a wide response in the scientific and public circles of France and other countries of the world. Only in 1851 were other pendulums created on the model of the first, and Foucault's experiments were carried out at the Paris Observatory, in the Cathedral of Reims, in the church of St. Ignatius in Rome, in Liverpool, in Oxford, Dublin, in Rio de Janeiro, in city of Colombo in Ceylon, New York.
In all these experiments, the dimensions of the ball and the length of the pendulum were different, but they all confirmed the conclusionsJean Bernard Leon Foucault.
Elements of the pendulum, which was demonstrated in the Pantheon, are now kept in the Paris Museum of Arts and Crafts. And Foucault's pendulums are now in many parts of the world: in polytechnic and natural history museums, scientific observatories, planetariums, university laboratories and libraries.
There are three Foucault pendulums in Ukraine. One is kept at the National Technical University of Ukraine “KPI named after I. Igor Sikorsky", the second - at the Kharkiv National University. V.N. Karazin, the third - at the Kharkiv Planetarium.
don't believe your case. Read all of these articles carefully. Then it will become as clear as the shining Sun.
Just as the hand and the brain do not have a mysterious power in all people, the pendulum, too, in the hands of not all people can become mysterious. This power is not acquired, but is born together with a person. In one family, one is born rich and the other poor. No one is able to make the natural rich poor or vice versa. Now you understand with this what I wanted to tell you. If you do not understand, blame yourself, you were born that way.
What is a pendulum? What is it made from? A pendulum is any freely moving body attached to a thread. In the hands of the master, even a simple reed sings like a nightingale. Also, in the hands of a talented biomaster, the pendulum makes incredible impacts in the sphere of being and human existence.
It doesn't always happen that you carry a pendulum with you. So I had to find a lost ring from one family, but I didn’t have a pendulum with me. I looked around and a wine cork caught my eye. From about the middle of the cork, I made a little incision with a knife and attached the thread. The pendulum is ready.
I asked him: “Will you work honestly with me?” He affirmatively strongly spun clockwise, as if responding cheerfully. Mentally let him know: "Let's find the missing ring then." The pendulum swung again in agreement. I started walking around the yard.
Because the daughter-in-law said that she had not yet managed to enter the house when she noticed that she did not have a ring on her finger. She also said that she had long wanted to go to the jeweler, as her fingers had grown thin, and the ring began to fall off. Suddenly, on my hands, the pendulum moved a little, turned back a little, the pendulum fell silent. I walked forward, but the pendulum moved again. I went on, quieted down again, I was amazed. To the left the pendulum is silent, forward is silent. Right go nowhere. There is a small ditch there. Suddenly I enlightened and held the pendulum directly above the water. The pendulum began to spin clockwise intensively. I called my daughter-in-law and showed the location of the ring.
With joy in her eyes, she began to rummage along the canal and quickly found a ring. It turns out that she was washing her hands in the ditch, and at that time the ring fell, but she did not notice. All those present admired the work of the wine cork.
Not all people are born fortune tellers or fortune tellers. Not all fortunetellers or fortune-tellers work successfully. Single predictors work with smaller errors, and many cheat like gypsies. So is the pendulum. It is a good-for-nothing thing for an inept person, although it is made of gold, it has no value. In the hands of a real master, a piece of ordinary stone or a nut does wonders.
I remember like yesterday. At one meeting, I took off my jacket and went out for a while. When he returned, he felt something was wrong with his heart. Mechanically he began to rummage in his pocket. It turned out that someone took my silver pendulum. I kept silent and did not tell anyone about what had happened.
Many days passed, and one day one of those people who sat with us at the gathering where my pendulum was lost came to my house. He apologized deeply and handed me the pendulum. It turns out that he thought that all the power was on my pendulum and thought that this pendulum would work for him as well as for me.
When he realized his mistake, his conscience tormented him for a long time and finally decided to return the pendulum to its owner. I accepted his apology and even treated him to tea and even diagnosed. I found many diseases in him with a pendulum and prepared appropriate medicines for him.
Some people have a natural gift for healing and divination. This talent has not come out for years. Sometimes, on occasion, they come across a connoisseur, and he shows him his destined life path.
Recently, a middle-aged woman came for diagnostics. You can't tell by her appearance that she's sick. She complained about the high warmth in her limbs, both the palms and the soles of the feet were constantly hot, and often felt wild bursting pains in the head in the crown area. First diagnosing it by pulse, noticing an increase in vascular tone, I began to measure blood pressure with a semi-automatic device. The values eventually went off scale both systolic and diastolic. They indicated 135 to 241, and the heart rate was below normal for such hypertension: 62 beats per minute. In front of me, a woman with such high blood pressure sat calmly. As if not feeling discomfort, from his condition of the vessels. Essential (incomprehensible) hypertension did not oppress her.
According to her pulse, I did not notice anything wrong during the pulse diagnostics either. I diagnosed her with rare essential (unexplained cause) hypertension. If an ordinary doctor would measure her blood pressure, he immediately called an ambulance and put her on a stretcher. Wouldn't even let her move. The fact is that a person with such an increase in pressure is considered a hypertensive crisis. It may be followed by a stroke or a heart attack.
According to her, from conventional antihypertensive drugs she feels so bad that after them she even feels sick. At the insistence of her son, she learned to use the pendulum, when her head hurts badly, she asks the pendulum whether or not to drink aspirin or pentalgin. More rarely, with the consent of the pendulum, she takes a decoction of willow leaves or a decoction of quince leaves, which were recommended to her by the healer Mukhiddin four years ago. If her head hurts badly, then she drinks aspirin, in extremely severe cases, she takes pentalgin. Doctors and neighbors of hypertension laugh at her self-medication.
I checked with my pendulum all the medicines she takes for headaches and high blood pressure. All of them proved to be effective.I also asked the pendulum. “Will her health improve if she heals people with her warmth?” The pendulum immediately swung strongly clockwise, in the affirmative. So I prescribed her a treatment from herself, in order to get rid of essential hypertension, she must deal with the treatment of diseases of other people, laying hands or feet on them. Now I myself often refer patients to her, and she successfully treats them. psychic passes. On diseases up to the waist, he directs the warmth of the hand, on diseases below the waist, in a lying position above the patient, he holds the right or left leg, respectively, in the problem area.
Both she and the patients are satisfied with the results. For two years now she has not taken aspirin or pentalgin, and the pendulum sometimes allows her to drink a decoction of willow or quince leaves, with minor headaches.
Who needs her help, write to me, she will help you for a meager fee. I even taught her to treat people who are at great distances in a non-contact way.
A person who truly works with the pendulum during the operation of the pendulum must be in synchronous communication with it and must know and feel in advance to which channel the pendulum’s actions are directed at the moment. With the energy potential of his brain, a person holding the thread of the pendulum should help him subconsciously, and not speculatively, in further actions on this object, but indifferently not look at the action of the pendulum as a spectator.
Almost all famous people in Mesopotamia, Assyria, Urartu, India, China, Japan, ancient Rome, Egypt, Greece, Asia, Africa, America, Europe, in the East and all over the world in many countries have used and still use the pendulum.
Due to the fact that many prominent international institutions, prominent figures in various fields of science have not yet sufficiently appreciated the action and purpose of the pendulum in favor of the coexistence of humanity with the surrounding nature in a symbiotic and harmonious way. The pseudo-scientific views on the universe of the Universal Normal at the level of modern natural science have not completely left humanity yet. There is a stage of erasing the edge of knowledge between religion, esotericism and natural science. Naturally, natural science should become the basis of all fundamental sciences without any side views.
There is hope that the science of the pendulum will also take a worthy place in people's lives along with information science. After all, there was a time when the leaders of our multinational country declared cybernetics a pseudoscience and did not allow not only to study, even to study in educational institutions.
So now, at the level of the highest echelon of modern science, they are looking at the idea of a pendulum as if at a backward industry. It is necessary to systematize the pendulum, the dowsing, the frame under a single section of informatics, and it is necessary to create a computer program module.
With the help of this module, anyone can find missing things, locate objects, and finally, diagnose people, animals, birds, insects, in general, all nature.
To do this, you need to study the ideas of L. G. Puchko on multidimensional medicine and the work of the psychic Geller, as well as the ideas of the Bulgarian healer Kanaliev and the work of many other people who achieved amazing results with the help of the pendulum.