Harmonic vibrations. Period and frequency of oscillations How to find the period and frequency of oscillations formula

37. Harmonic vibrations. Amplitude, period and frequency of oscillations.

Oscillations are processes characterized by a certain repeatability over time. The process of propagation of vibrations in space is called a wave. It is no exaggeration to say that we live in a world of vibrations and waves. Indeed, a living organism exists thanks to the periodic beating of the heart; our lungs vibrate when breathing. A person hears and speaks due to vibrations of his eardrums and vocal cords. Light waves (oscillations of electric and magnetic fields) allow us to see. Modern technology also makes extremely extensive use of oscillatory processes. Suffice it to say that many engines are associated with vibrations: periodic movement of pistons in internal combustion engines, movement of valves, etc. Other important examples are alternating current, electromagnetic oscillations in an oscillating circuit, radio waves, etc. As can be seen from the above examples, the nature of the oscillations is different. However, they come down to two types - mechanical and electromagnetic vibrations. It turned out that, despite the difference in the physical nature of the vibrations, they are described by the same mathematical equations. This allows us to single out the study of oscillations and waves as one of the branches of physics, which implements a unified approach to the study of oscillations of various physical natures.

Any system capable of oscillating or in which oscillations can occur is called oscillatory. Oscillations occurring in an oscillatory system taken out of equilibrium and left to itself are called free oscillations. Free oscillations are damped, since the energy imparted to the oscillatory system constantly decreases.

Harmonic oscillations are those in which any physical quantity describing the process changes over time according to the law of cosine or sine:

Let us find out the physical meaning of the constants A, w, a included in this equation.

The constant A is called the amplitude of the oscillation. Amplitude is the largest value that an oscillating quantity can take. By definition, it is always positive. The expression wt+a under the cosine sign is called the oscillation phase. It allows you to calculate the value of a fluctuating quantity at any time. The constant value a represents the phase value at time t = 0 and is therefore called the initial phase of the oscillation. The value of the initial phase is determined by the choice of the start of the time count. The quantity w is called cyclic frequency, the physical meaning of which is associated with the concepts of period and frequency of oscillations. The period of undamped oscillations is the shortest period of time after which the oscillating quantity takes on its previous value, or in short - the time of one complete oscillation. The number of oscillations performed per unit time is called the oscillation frequency. Frequency v is related to the period T of oscillations by the ratio v=1/T

Oscillation frequency is measured in Hertz (Hz). 1 Hz is the frequency of a periodic process in which one oscillation occurs in 1 s. Let's find the connection between frequency and cyclic frequency of oscillation. Using the formula, we find the values ​​of the oscillating quantity at times t=t 1 and t=t 2 =t 1 +T, where T is the oscillation period.

According to the definition of the oscillation period, This is possible if , since cosine is a periodic function with a period of 2p radians. From here. We get. From this relationship follows the physical meaning of cyclic frequency. It shows how many oscillations occur in 2p seconds.

Free oscillations of the oscillatory system are damped. However, in practice there is a need to create undamped oscillations, when energy losses in the oscillatory system are compensated by external energy sources. In this case, forced oscillations arise in such a system. Oscillations that occur under the influence of a periodically changing influence are called forced, while those of influence are called forcing. Forced oscillations occur with a frequency equal to the frequency of the forcing influences. The amplitude of forced oscillations increases as the frequency of the forcing influences approaches the natural frequency of the oscillatory system. It reaches its maximum value when the indicated frequencies are equal. The phenomenon of a sharp increase in the amplitude of forced oscillations, when the frequency of the forcing influences is equal to the natural frequency of the oscillatory system, is called resonance.

The phenomenon of resonance is widely used in technology. It can be both useful and harmful. For example, the phenomenon of electrical resonance plays a useful role when tuning a radio receiver to the desired radio station. By changing the values ​​of inductance and capacitance, it is possible to ensure that the natural frequency of the oscillatory circuit coincides with the frequency of electromagnetic waves emitted by any radio station. As a result of this, resonant oscillations of a given frequency will appear in the circuit, while the amplitudes of the oscillations created by other stations will be small. This leads to tuning the radio to the desired station.

38. Mathematical pendulum. Period of oscillation of a mathematical pendulum.

39. Oscillation of a load on a spring. Conversion of energy during vibrations.

40. Waves. Transverse and longitudinal waves. Speed ​​and wavelength.

41. Free electromagnetic oscillations in a circuit. Conversion of energy in an oscillatory circuit. Transformation of energy.

Periodic or almost periodic changes in charge, current and voltage are called electrical oscillations.

Producing electrical vibrations is almost as simple as making a body vibrate by hanging it on a spring. But observing electrical vibrations is no longer so easy. After all, we do not directly see either the recharging of the capacitor or the current in the coil. In addition, oscillations usually occur with a very high frequency.

Observe and study electrical vibrations using an electronic oscilloscope. An alternating sweep voltage Up of a “sawtooth” shape is supplied to the horizontal deflection plates of the cathode ray tube of the oscilloscope. The tension increases relatively slowly and then decreases very sharply. The electric field between the plates causes the electron beam to travel horizontally across the screen at a constant speed and then return almost instantly. After this, the whole process is repeated. If we now attach vertical deflection plates to the capacitor, then the voltage fluctuations during its discharge will cause the beam to oscillate in the vertical direction. As a result, a time “sweep” of oscillations is formed on the screen, quite similar to the one drawn by a pendulum with a sandbox on a moving sheet of paper. Vibrations fade over time

These vibrations are free. They arise after a charge is imparted to the capacitor, which takes the system out of equilibrium. Charging the capacitor is equivalent to the deviation of the pendulum from its equilibrium position.

Forced electrical oscillations can also be obtained in an electrical circuit. Such oscillations appear when there is a periodic electromotive force in the circuit. An alternating induced emf arises in a wire frame of several turns when it rotates in a magnetic field (Fig. 19). In this case, the magnetic flux penetrating the frame changes periodically. In accordance with the law of electromagnetic induction, the resulting induced emf also changes periodically. When the circuit is closed, an alternating current will flow through the galvanometer and the needle will begin to oscillate around the equilibrium position.

2. Oscillatory circuit. The simplest system in which free electrical oscillations can occur consists of a capacitor and a coil connected to the capacitor plates (Fig. 20). Such a system is called an oscillatory circuit.

Let's consider why oscillations occur in the circuit. Let's charge the capacitor by connecting it to the battery for a while using a switch. In this case, the capacitor will receive energy:

where qm is the charge of the capacitor, and C is its electrical capacity. A potential difference Um will arise between the plates of the capacitor.

Let's move the switch to position 2. The capacitor will begin to discharge, and an electric current will appear in the circuit. The current does not immediately reach its maximum value, but increases gradually. This is due to the phenomenon of self-induction. When current appears, an alternating magnetic field appears. This alternating magnetic field generates an eddy electric field in the conductor. When the magnetic field increases, the vortex electric field is directed against the current and prevents its instantaneous increase.

As the capacitor discharges, the energy of the electric field decreases, but at the same time the energy of the magnetic field of the current increases, which is determined by the formula: fig.

where i is the current strength. L is the inductance of the coil. At the moment when the capacitor is completely discharged (q = 0), the energy of the electric field becomes zero. The current energy (magnetic field energy), according to the law of conservation of energy, will be maximum. Therefore, at this moment the current will also reach its maximum value

Despite the fact that by this moment the potential difference at the ends of the coil becomes zero, the electric current cannot stop immediately. This is prevented by the phenomenon of self-induction. As soon as the strength of the current and the magnetic field it creates begin to decrease, an eddy electric field appears, which is directed along the current and supports it.

As a result, the capacitor is recharged until the current, gradually decreasing, becomes equal to zero. The energy of the magnetic field at this moment will also be zero, and the energy of the electric field of the capacitor will again become maximum.

After this, the capacitor will be recharged again and the system will return to its original state. If there were no energy losses, this process would continue indefinitely. The oscillations would be undamped. At intervals equal to the period of oscillation, the state of the system would repeat itself.

But in reality, energy losses are inevitable. Thus, in particular, the coil and connecting wires have a resistance R, and this leads to the gradual conversion of the energy of the electromagnetic field into the internal energy of the conductor.

When oscillations occur in the circuit, the transformation of magnetic field energy into electric field energy and vice versa is observed. Therefore, these oscillations are called electromagnetic. The period of the oscillatory circuit is found by the formula.

But what we mean by function is the dependence of a physical quantity that oscillates on time.

This concept in this form is applicable to both harmonic and anharmonic strictly periodic oscillations (and approximately - with varying degrees of success - and non-periodic oscillations, at least those close to periodicity).

In the case when we are talking about oscillations of a harmonic oscillator with damping, the period is understood as the period of its oscillating component (ignoring damping), which coincides with twice the time interval between the nearest passages of the oscillating value through zero. In principle, this definition can be, with greater or less accuracy and usefulness, extended in some generalization to damped oscillations with other properties.

Designations: the usual standard notation for the period of oscillation is: (although others can be used, most often it is , sometimes, etc.).

The period of oscillation is related by the relationship of mutual reciprocity with frequency:

For wave processes, the period is also obviously related to the wavelength

where is the speed of wave propagation (more precisely, the phase speed).

In quantum physics the period of oscillation is directly related to energy (since in quantum physics the energy of an object - for example, a particle - is the frequency of oscillation of its wave function).

Theoretical finding Determining the period of oscillation of a particular physical system comes down, as a rule, to finding a solution to the dynamic equations (equations) that describe this system. For the category of linear systems (and approximately for linearizable systems in the linear approximation, which is often very good), there are standard, relatively simple mathematical methods that allow this to be done (if the physical equations themselves that describe the system are known).

For experimental determination period, clocks, stopwatches, frequency meters, stroboscopes, strobotachometers, and oscilloscopes are used. Also used are beats, heterodyning method in different types, and the principle of resonance is used. For waves, you can measure the period indirectly - through the wavelength, for which interferometers, diffraction gratings, etc. are used. Sometimes sophisticated methods are required, specially developed for a specific difficult case (the difficulty can be both the measurement of time itself, especially if we are talking about extremely short or, conversely, very large times, and the difficulty of observing a fluctuating value).

Periods of oscillations in nature

An idea of ​​the periods of oscillations of various physical processes is given by the article Frequency Intervals (considering that the period in seconds is the reciprocal of the frequency in hertz).

Some idea of ​​the magnitude of the periods of various physical processes can also be given by the frequency scale of electromagnetic oscillations (see Electromagnetic spectrum).

The periods of oscillation of sound audible by humans are in the range

From 5·10 -5 to 0.2

(its clear boundaries are somewhat arbitrary).

Periods of electromagnetic oscillations corresponding to different colors of visible light - in the range

From 1.1·10 -15 to 2.3·10 -15.

Since for extremely large and extremely small periods of oscillation, measurement methods tend to become increasingly indirect (even smoothly flowing into theoretical extrapolations), it is difficult to give clear upper and lower limits for the period of oscillation measured directly. Some estimate for the upper limit can be given by the lifetime of modern science (hundreds of years), and for the lower limit - the period of oscillations of the wave function of the heaviest currently known particle ().

Anyway border below can serve as the Planck time, which is so small that, according to modern concepts, not only can it hardly be physically measured at all, but it is also unlikely that in the more or less foreseeable future it will be possible to get closer to measuring quantities even many orders of magnitude smaller. A border on top- the existence of the Universe is more than ten billion years.

Periods of oscillations of the simplest physical systems

Spring pendulum

Math pendulum

where is the length of the suspension (for example, a thread), is the acceleration of free fall.

The period of oscillation (on Earth) of a mathematical pendulum 1 meter long is, with good accuracy, 2 seconds.

Physical pendulum

where is the moment of inertia of the pendulum relative to the axis of rotation, is the mass of the pendulum, is the distance from the axis of rotation to the center of mass.

Torsion pendulum

where is the moment of inertia of the body, and is the rotational stiffness coefficient of the pendulum.

Electrical Oscillating (LC) Circuit

Oscillation period of the electric oscillatory circuit:

where is the inductance of the coil, is the capacitance of the capacitor.

This formula was derived in 1853 by the English physicist W. Thomson.

Notes

Links

• Oscillation period- article from the Great Soviet Encyclopedia

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See what “Oscillation period” is in other dictionaries:

period of oscillation- period The shortest period of time through which the state of a mechanical system, characterized by the values ​​of generalized coordinates and their derivatives, is repeated. [Collection of recommended terms. Issue 106. Mechanical vibrations. Academy of Sciences... ... Technical Translator's Guide

Period (oscillations)- PERIOD of oscillations, the shortest period of time after which an oscillating system returns to the same state in which it was at the initial moment, chosen arbitrarily. The period is the reciprocal of the oscillation frequency. Concept... ... Illustrated Encyclopedic Dictionary

PERIOD OF OSCILLATIONS- the shortest period of time after which the system oscillating returns again to the same state in which it was at the beginning. moment chosen arbitrarily. Strictly speaking, the concept of “P. To." applicable only when the values ​​of k.l.... ... Physical encyclopedia

PERIOD OF OSCILLATIONS- the shortest period of time after which the oscillating system returns to its original state. The oscillation period is the reciprocal of the oscillation frequency... Big Encyclopedic Dictionary

period of oscillation- period of oscillation; period The shortest period of time through which the state of a mechanical system is repeated, characterized by the values ​​of generalized coordinates and their derivatives... Polytechnic terminological explanatory dictionary

Oscillation period- 16. Oscillation period The shortest time interval through which, during periodic oscillations, each value of the oscillating quantity is repeated Source ... Dictionary-reference book of terms of normative and technical documentation

period of oscillation- the shortest period of time after which the oscillating system returns to its original state. The oscillation period is the reciprocal of the oscillation frequency. * * * PERIOD OF OSCILLATIONS PERIOD OF OSCILLATIONS, the shortest period of time through which... ... encyclopedic Dictionary

period of oscillation- virpesių periodas statusas T sritis automatika atitikmenys: engl. oscillation period; period of oscillations; period of vibrations vok. Schwingungsdauer, m; Schwingungsperiode, f; Schwingungszeit, f rus. period of oscillation, m pranc. période d… … Automatikos terminų žodynas

period of oscillation- virpesių periodas statusas T sritis Standartizacija ir metrologija apibrėžtis Mažiausias laiko tarpas, po kurio pasikartoja periodiškai kintančių dydžių vertės. atitikmenys: engl. vibration period vok. Schwingungsdauer, f; Schwingungsperiode, f… … Penkiakalbis aiškinamasis metrologijos terminų žodynas

period of oscillation- virpesių periodas statusas T sritis chemija apibrėžtis Mažiausias laiko tarpas, po kurio pasikartoja periodiškai kintančių dydžių vertės. atitikmenys: engl. period of oscillation; period of vibration; vibration period rus. period of oscillation... Chemijos terminų aiškinamasis žodynas

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Oscillation characteristics

Phase determines the state of the system, namely coordinate, speed, acceleration, energy, etc.

Cyclic frequency characterizes the rate of change in the phase of oscillations.

The initial state of the oscillatory system is characterized by initial phase

Oscillation amplitude A- this is the largest displacement from the equilibrium position

Period T- this is the period of time during which the point performs one complete oscillation.

Oscillation frequency is the number of complete oscillations per unit time t.

Frequency, cyclic frequency and period of oscillation are related as

Types of vibrations

Oscillations that occur in closed systems are called free or own fluctuations. Oscillations that occur under the influence of external forces are called forced. There are also self-oscillations(forced automatically).

If we consider oscillations according to changing characteristics (amplitude, frequency, period, etc.), then they can be divided into harmonic, fading, growing(as well as sawtooth, rectangular, complex).

During free oscillations in real systems, energy losses always occur. Mechanical energy is spent, for example, on performing work to overcome air resistance forces. Under the influence of friction, the amplitude of oscillations decreases, and after some time the oscillations stop. Obviously, the greater the force of resistance to movement, the faster the oscillations stop.

Forced vibrations. Resonance

Forced oscillations are undamped. Therefore, it is necessary to replenish energy losses for each oscillation period. To do this, it is necessary to influence the oscillating body with a periodically changing force. Forced vibrations occur with a frequency equal to the frequency of changes in the external force.

Forced vibrations

The amplitude of forced mechanical vibrations reaches its greatest value if the frequency of the driving force coincides with the frequency of the oscillatory system. This phenomenon is called resonance.

For example, if we periodically pull the cord in time with its own vibrations, we will notice an increase in the amplitude of its vibrations.

If you move a wet finger along the edge of a glass, the glass will make ringing sounds. Although it is not noticeable, the finger moves intermittently and transfers energy to the glass in short bursts, causing the glass to vibrate

The walls of the glass also begin to vibrate if a sound wave with a frequency equal to its own is directed at it. If the amplitude becomes very large, the glass may even break. Due to resonance, when F.I. Chaliapin sang, the crystal pendants of the chandeliers trembled (resonated). The occurrence of resonance can also be observed in the bathroom. If you softly sing sounds of different frequencies, a resonance will arise at one of the frequencies.

In musical instruments, the role of resonators is performed by parts of their bodies. A person also has his own resonator - this is the oral cavity, which amplifies the sounds produced.

The phenomenon of resonance must be taken into account in practice. In some cases it can be useful, in others it can be harmful. Resonance phenomena can cause irreversible damage in various mechanical systems, such as poorly designed bridges. Thus, in 1905, the Egyptian Bridge in St. Petersburg collapsed while a horse squadron was passing across it, and in 1940, the Tacoma Bridge in the USA collapsed.

The phenomenon of resonance is used when, with the help of a small force, it is necessary to obtain a large increase in the amplitude of vibrations. For example, the heavy tongue of a large bell can be swung by applying a relatively small force with a frequency equal to the natural frequency of the bell.

Everything on the planet has its own frequency. According to one version, it even forms the basis of our world. Alas, the theory is too complex to be presented in one publication, so we will consider exclusively the frequency of oscillations as an independent action. Within the framework of the article, definitions of this physical process, its units of measurement and metrological component will be given. And finally, an example of the importance of ordinary sound in everyday life will be considered. We learn what he is and what his nature is.

What is oscillation frequency called?

By this we mean a physical quantity that is used to characterize a periodic process, which is equal to the number of repetitions or occurrences of certain events in one unit of time. This indicator is calculated as the ratio of the number of these incidents to the period of time during which they occurred. Each element of the world has its own vibration frequency. A body, an atom, a road bridge, a train, an airplane - they all make certain movements, which are called so. Even if these processes are not visible to the eye, they exist. The units of measurement in which oscillation frequency is calculated are hertz. They received their name in honor of the physicist of German origin Heinrich Hertz.

Instantaneous frequency

A periodic signal can be characterized by an instantaneous frequency, which, up to a coefficient, is the rate of phase change. It can be represented as a sum of harmonic spectral components that have their own constant oscillations.

Cyclic frequency

It is convenient to use in theoretical physics, especially in the section on electromagnetism. Cyclic frequency (also called radial, circular, angular) is a physical quantity that is used to indicate the intensity of the origin of oscillatory or rotational motion. The first is expressed in revolutions or oscillations per second. During rotational motion, the frequency is equal to the magnitude of the angular velocity vector.

This indicator is expressed in radians per second. The dimension of cyclic frequency is the reciprocal of time. In numerical terms, it is equal to the number of oscillations or revolutions that occurred in the number of seconds 2π. Its introduction for use makes it possible to significantly simplify the various range of formulas in electronics and theoretical physics. The most popular example of use is calculating the resonant cyclic frequency of an oscillatory LC circuit. Other formulas can become significantly more complex.

Discrete event rate

This value means a value that is equal to the number of discrete events that occur in one unit of time. In theory, the indicator usually used is the second minus the first power. In practice, Hertz is usually used to express the pulse frequency.

Rotation frequency

It is understood as a physical quantity that is equal to the number of full revolutions that occur in one unit of time. The indicator used here is also the second minus the first power. To indicate the work done, phrases such as revolutions per minute, hour, day, month, year and others can be used.

Units

How is oscillation frequency measured? If we take into account the SI system, then the unit of measurement here is hertz. It was originally introduced by the International Electrotechnical Commission back in 1930. And the 11th General Conference on Weights and Measures in 1960 consolidated the use of this indicator as an SI unit. What was put forward as the “ideal”? It was the frequency when one cycle is completed in one second.

But what about production? Arbitrary values ​​were assigned to them: kilocycle, megacycle per second, and so on. Therefore, when you pick up a device that operates at GHz (like a computer processor), you can roughly imagine how many actions it performs. It would seem how slowly time passes for a person. But the technology manages to perform millions and even billions of operations per second during the same period. In one hour, the computer already does so many actions that most people cannot even imagine them in numerical terms.

Metrological aspects

Oscillation frequency has found its application even in metrology. Different devices have many functions:

1. The pulse frequency is measured. They are represented by electronic counting and capacitor types.
2. The frequency of spectral components is determined. There are heterodyne and resonant types.
3. Spectrum analysis is carried out.
4. Reproduce the required frequency with a given accuracy. In this case, various measures can be used: standards, synthesizers, signal generators and other techniques in this direction.
5. The indicators of the obtained oscillations are compared; for this purpose, a comparator or oscilloscope is used.

Example of work: sound

Everything written above can be quite difficult to understand, since we used the dry language of physics. To understand the information provided, you can give an example. Everything will be described in detail, based on an analysis of cases from modern life. To do this, consider the most famous example of vibrations - sound. Its properties, as well as the features of the implementation of mechanical elastic vibrations in the medium, are directly dependent on the frequency.

The human hearing organs can detect vibrations that range from 20 Hz to 20 kHz. Moreover, with age, the upper limit will gradually decrease. If the frequency of sound vibrations drops below 20 Hz (which corresponds to the mi subcontractave), then infrasound will be created. This type, which in most cases is not audible to us, can still be felt tangibly by people. When the limit of 20 kilohertz is exceeded, oscillations are generated, which are called ultrasound. If the frequency exceeds 1 GHz, then in this case we will be dealing with hypersound. If we consider a musical instrument such as a piano, it can create vibrations in the range from 27.5 Hz to 4186 Hz. It should be taken into account that musical sound does not consist only of the fundamental frequency - overtones and harmonics are also mixed into it. All this together determines the timbre.

Conclusion

As you have had the opportunity to learn, vibrational frequency is an extremely important component that allows our world to function. Thanks to her, we can hear, with her assistance computers work and many other useful things are accomplished. But if the oscillation frequency exceeds the optimal limit, then certain destruction may begin. So, if you influence the processor so that its crystal operates at twice the performance, it will quickly fail.

A similar thing can be said with human life, when at high frequencies his eardrums burst. Other negative changes will also occur in the body, which will lead to certain problems, even death. Moreover, due to the peculiarities of the physical nature, this process will stretch over a fairly long period of time. By the way, taking this factor into account, the military is considering new opportunities for developing weapons of the future.

Harmonic oscillations are oscillations performed according to the laws of sine and cosine. The following figure shows a graph of changes in the coordinates of a point over time according to the cosine law.

picture

Oscillation amplitude

The amplitude of a harmonic vibration is the greatest value of the displacement of a body from its equilibrium position. The amplitude can take on different values. It will depend on how much we displace the body at the initial moment of time from the equilibrium position.

The amplitude is determined by the initial conditions, that is, the energy imparted to the body at the initial moment of time. Since sine and cosine can take values ​​in the range from -1 to 1, the equation must contain a factor Xm, expressing the amplitude of the oscillations. Equation of motion for harmonic vibrations:

x = Xm*cos(ω0*t).

Oscillation period

The period of oscillation is the time it takes to complete one complete oscillation. The period of oscillation is designated by the letter T. The units of measurement of the period correspond to the units of time. That is, in SI these are seconds.

Oscillation frequency is the number of oscillations performed per unit of time. The oscillation frequency is designated by the letter ν. The oscillation frequency can be expressed in terms of the oscillation period.

ν = 1/T.

Frequency units are in SI 1/sec. This unit of measurement is called Hertz. The number of oscillations in a time of 2*pi seconds will be equal to:

ω0 = 2*pi* ν = 2*pi/T.

Oscillation frequency

This quantity is called the cyclic frequency of oscillations. In some literature the name circular frequency appears. The natural frequency of an oscillatory system is the frequency of free oscillations.

The frequency of natural oscillations is calculated using the formula:

The frequency of natural vibrations depends on the properties of the material and the mass of the load. The greater the spring stiffness, the greater the frequency of its own vibrations. The greater the mass of the load, the lower the frequency of natural oscillations.

These two conclusions are obvious. The stiffer the spring, the greater the acceleration it will impart to the body when the system is thrown out of balance. The greater the mass of a body, the slower the speed of this body will change.

Free oscillation period:

T = 2*pi/ ω0 = 2*pi*√(m/k)

It is noteworthy that at small angles of deflection the period of oscillation of the body on the spring and the period of oscillation of the pendulum will not depend on the amplitude of the oscillations.

Let's write down the formulas for the period and frequency of free oscillations for a mathematical pendulum.

then the period will be equal

T = 2*pi*√(l/g).

This formula will be valid only for small deflection angles. From the formula we see that the period of oscillation increases with increasing length of the pendulum thread. The longer the length, the slower the body will vibrate.

The period of oscillation does not depend at all on the mass of the load. But it depends on the acceleration of free fall. As g decreases, the oscillation period will increase. This property is widely used in practice. For example, to measure the exact value of free acceleration.