Collection of questions and problems in physics - Lukashik V.I. Industrial leasing - analysis, publications, manuals

When Masha was one year old, her height was 70 cm, when she was 3 years old - 100 cm, 5 years old - 120 cm and 7 years old - 130 cm. Using these data, you can construct a diagram (Fig. 123).

Rice. 123

This diagram does not fully show how Masha's height changed: she grew all the time, and the diagram shows her growth only when she was 1 year old, 3 years old, 5 years old and 7 years old. Let's connect the upper ends of the columns with segments. You will get a broken line, which more clearly shows how Masha’s growth has changed (Fig. 124). We see that at 4 years old her height was approximately 110 cm, and at 6 years old - 125 cm.

Rice. 124

If Masha’s height were measured all the time, the result would be not a broken line, but a smooth line, the same as in Figure 125. Using this line, you can find out Masha’s height at any age from 1 year to 7 years. So, for example, at 2 years old her height was 90 cm. This line is called Masha’s growth graph.

Rice. 125

For greater accuracy in constructing graphs, they are drawn on graph paper. For example, a graph of Masha’s growth on graph paper is shown in Figure 126. Graphs are also drawn using computers, which provide even greater accuracy.

Rice. 126

Graphs are used to depict movements.

Let a train traveling at a speed of 60 km/h leave the city of Romsk at 3 a.m. Then at 4 o’clock he will be at a distance of 60 km from Romsk, at 5 o’clock - at a distance of 120 km from it, etc. The following table shows the distance from Romsk to the train at different times:

Let us represent pairs of numbers (3; 0), (4; 60), (5; 120), etc. as points on coordinate plane. In this case, it is more convenient to select different scales on the coordinate axes. We will depict 1 hour on the abscissa axis as a segment of 1 cm, and on the ordinate axis - 60 km as a segment of 1 cm. We will obtain points A, B, C, D, E, F and H (Fig. 127).

Rice. 127

All these points lie on the same straight line.

If the train did not leave Romsk at 3 a.m., but passed by it at that time, then the table can be continued to the left:

The “-” sign here shows that the train has not yet reached the city of Romsk, but is heading towards it. Points with coordinates (0; -180), (1; -120); (2; -60) lie on the same straight line as those previously found. This straight line is called the train schedule (see Fig. 127). According to the schedule, you can find out where the train was at 6:30 a.m. (it departed 210 km from Romsk), where it was at 1:30 a.m. (it did not reach Romsk 90 km), when it departed from Romsk. . Romsk at 270 km (at 7 hours 30 minutes), etc.

1441. Figure 128 shows a graph of changes in Petit's mass depending on his age. What is Petit's mass at the age of 6 years; 8.5 years; 10 years?

Rice. 128

1442. Figure 129 shows a graph of air temperature changes during the day. Answer the following questions:

a) What was the air temperature at 3 o’clock; at 12 o'clock?
b) At what hours was the air temperature negative?
c) At what hours was the air temperature positive?
d) When the air temperature was zero; 2°C; -6° C?
e) By how many degrees did the temperature change from 2 a.m. to 1 p.m.; from 18:00 to 24:00?

Rice. 129

1443. The height of the pine tree varied depending on its age as follows:

Plot a graph of the height of a pine tree depending on its age. Using the graph, find:

a) the height of a pine tree at 15 years old; at 35 years old; at 75 years old;
b) the age of the pine when its height was 10 m; 16 m; 20 m;
c) how many meters the pine tree grew in the first 20 years; for the second 20 years; for the third 20 years;
d) how many meters the pine tree has grown over the period from 15 to 45 years.

1444. A glass containing 0.2 liters of water is poured into an empty decanter (Fig. 130), and the height of the water in the decanter is noted each time.

Rice. 130

Figure 131 shows the resulting graph. Using the graph, determine:

a) what will be the water level in the decanter if you pour 0.8 liters of water into it; 2 liters of water;
b) how much water should be poured into the carafe so that the water level is at a height of 7 cm; at a height of 13 cm;
c) why at first the water level in the decanter rises faster, then slower, and then faster again.

Rice. 131

1445. Figure 132 shows the movement graphs of two cars: a truck (graph AB) and a passenger car (graph CD). Determine using the graph:

Rice. 132

a) at what time the cars left the city;
b) at what distance from the city was the car at 4 hours 30 minutes; at 7 o'clock;
c) at what distance from the city was the truck at 4 hours; c b h 30 min;
d) at what time the truck was 135 km from the city; 210 km from the city;
e) at what time the car was 135 km from the city; 225 km from the city;
f) at what time and at what distance from the city the passenger car caught up with the truck;
g) which car was moving at a constant speed;
h) what was the speed of the truck between 5 o'clock and 6 o'clock; between 6 o'clock and 7 o'clock;
i) at what distance were the cars from each other at 5 hours; at 7 o'clock

1446. The fisherman said that, leaving the house, he walked for 2 hours along the bank of the river and reached the place where a tributary flows into it. There he fished for 1.5 hours, and then moved on. After 1 hour, he chose a new place, where for 2 hours he fished, cooked fish soup, and had lunch. After lunch he went home. He spent 9 hours on all this. The fisherman’s movement graph is shown in Figure 133. Answer the following questions.

Rice. 133

a) At what distance from the house was the fisherman after 30 minutes; after 4 hours 40 minutes; 5.5 hours after leaving home?
b) How many hours after leaving home was the fisherman 5 km from home?
c) When the distance from home increased; decreased; hasn't changed?
d) How many kilometers did the fisherman walk in the last 2 hours?
e) At what speed did the fisherman walk during the first hour and at what speed during the last hour? What is the angler's speed in the time interval between 4 and 4.5 hours after leaving home?

1447. Calculate orally:

1448. Find:

1449. Find the number if:

a) his are 35;
b) 0.12 are equal to 48;
c) 18% of it is equal to 24.

1450. Define:

a) what part of 12 is 18;
b) what part of 70 is from 100;
c) what percentage of 8 is 40.

1451. Calculate:

0,6-0,24; 0,6 0,24; 0,6:0,24.

1452. Where is the point M(x, y) located on the coordinate plane if:

a) x > 0, y > 0;
b) x< 0, у < 0;
c) x< 0, у > 0;
d) x = 0, y = 0;
e) x > 0, y< 0;
e) x = 0?

1453. Solve the equation:

1454. Solve the equation:

a) |x| + |-12| = |-22|;
b) |-7|-|x| = |-49|.

1455. Find entire solutions to the inequalities:

1456. Draw a segment on the coordinate plane such that the abscissas and ordinates of its points satisfy the conditions:

a) -2 ≤ x &≤ 5, -3 ≤ y ≤ 7;
b) |x| ≤ 6, |y| ≤ 4.

1457. The sum of two numbers is 75, and one number is equal to the other. Find these numbers.

1458. The mass of three carp is 10.8 kg. The mass of the third carp was 50% of the mass of the first, the mass of the second was 1.5 times greater than the mass of the first. Find the mass of each carp.

1459. The motor boat traveled 60 km up the river and 150 km down the river. Find average speed boat all the way if its own speed is 20 km/h and the speed of the current is 4 km/h.

1460. Solve the problem:

1461. Find the meaning of the expression:

1462. Figure 134 shows a graph of the water temperature in an electric samovar. On the x line we plotted the time in minutes after turning on the samovar, and on the y line we plotted the water temperature in degrees Celsius. Determine from the schedule:

a) water temperature 20 minutes after turning on the samovar;
b) the moment of boiling of water in the samovar;
c) how many minutes did the water boil in the samovar;
d) when the water temperature in the samovar was 88 °C.

Rice. 134

1463. There are 750 stamps in two albums, and in the first album the stamps available were foreign stamps. In the second album, foreign stamps accounted for 0.9 of the stamps available there. How many stamps were there in each album if the number of foreign stamps in them was the same?

1464. The boat traveled 240 km from one pier to another and returned back. Find the average speed of the boat along the entire journey if its own speed is 18 km/h and the speed of the current is 2 km/h.

1465. One day after school, all students went to the Math Olympiad, all students went to sports sections, and the remaining 142 students went home. How many students are there in school if there were no absentees that day?

1466. Figure 135 shows the train schedule. Determine from the schedule:

a) how far the train traveled in the first 2 hours;
b) how many minutes the train stood at each stop;
c) what is the distance between train stops;
d) average speed of movement for 3 hours.

Rice. 135

1467. Figure 136 shows a motion graph. Create a story for this graph.

Rice. 136

1468. Find the meaning of the expression:

Stories about the history of the emergence and development of mathematics

The idea of specifying the position of a point on a plane using numbers originated in ancient times - primarily among astronomers and geographers when compiling star charts and geographical maps, calendar. Already in the 2nd century. The ancient Greek astronomer Claudius P only used latitude and longitude as coordinates.

In the 17th century French mathematicians René Descartes and Pierre Fermat first discovered the importance of using coordinates in mathematics.

A description of the use of coordinates was given in the book “Geometry” in 1637 by R. Descartes, therefore the rectangular coordinate system is often called Cartesian. The words “abscissa”, “ordinate”, “coordinates” were first used at the end of the 17th century. Gottfried Wilhelm Leibniz.

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Rice. 124
Rice. 125
Bine Sea of Azov-14 m (take the density of water in it to be 1020 kg/m3).
429. Determine from the graph (Fig. 125) the depth of immersion of the body in the lake, corresponding to a pressure of 100; 300 and 500 kPa.
430. The aquarium is filled to the top with water. With what average force does water press on the wall of an aquarium 50 cm long and 30 cm high?
431. An aquarium 32 cm high, 50 cm long and 20 cm wide is filled with water, the level of which is 2 cm below the edge. Calculate: a) the pressure on the bottom; b) weight of water;
c) the force with which water acts on a wall 20 cm wide.
432. The width of the lock is 10 m. The lock is filled with water to a depth of 5 m. With what force does the water press on the gate of the lock?
433*. A crane with an area of 30 cm2 is installed in a tank filled with oil at a depth of 4 m. With what force does oil flow to the tap?
434. A rectangular vessel with a capacity of 2 liters is half filled with water and half with kerosene. a) What is the pressure of the liquids at the bottom of the vessel? b) What equal to weight liquids in a container? The bottom of the vessel has the shape of a square with a side of 10 cm.
435*. Determine the force with which kerosene acts on a square plug with a cross-sectional area of 16 cm2, if the distance from the plug to the kerosene level in the vessel is 400 mm (Fig. 126).
436. What power does everyone experience? square meter surface area of a diving suit when immersed in sea water to a depth of 10 m?
437. A flat-bottomed barge received a hole in the bottom with an area of 200 cm2. How much force must be applied to the plaster used to cover the hole to hold back the pressure of water at a depth of 1.8 m? (Do not take into account the weight of the patch.)
438. Determine the height of the water level in the water tower if the pressure gauge installed at its base shows a pressure of 220,000 Pa.
439. At what depth is the water pressure in the sea equal to 412 kPa?
440. The water pressure in the water pump is created by pumps. To what height does the water rise if the pressure created by the pump is 400 kPa?
441. A block measuring 0.5x0.4X0.1 m is located in a tank of water at a depth of 0.6 m (Fig. 127). Calculate: a) with what pH. 126
40
4 Order 6256
49
Rice. 127 Fig. 128 Fig. 129
water presses forcefully on the upper edge of the block; b) on the lower edge and c) how much the water displaced by the block weighs.
442. Make a calculation using the data from the previous problem, assuming that the water was replaced with kerosene.
443*. Using the results of the two previous problems, calculate how much greater the force acting on the body from below than from above: a) in water; b) in kerosene. Compare your answers with the weight of the displaced water and the weight of the displaced kerosene.
444. Why does one of the coffee pots shown in Figure 128 hold more liquid than the other?
445. Point A indicates the water level in the left elbow of the tube (Fig. 129). Make a drawing and mark the water level in the right elbow of the tube with a point B.
446°. Water is poured into communicating vessels. What will happen and why if you add a little water to the left vessel (Fig. 130)? if in the middle vessel (Fig. 131)?
447*. Is the law of communicating vessels valid under conditions of weightlessness?
ftalattamtik
I in
EL* ¦
Rice. 133
Rice. 134
Rice. 135
448. How can you use communicating vessels to check whether the panel is applied horizontally (the line separating the painted panel from the top of the wall)?
449. Explain the action of the fountain (Fig. 132).
450. Water is poured into the left elbow of the communicating vessels (Fig. 133), and kerosene is poured into the right. The height of the kerosene column is 20 cm. Calculate how much the water level in the left knee is below the top level of the kerosene.
451*. The communicating vessels contain mercury and water (Fig. 134). The height of the water column is 68 cm. How high should the kerosene column be poured into the left knee so that the mercury is established at the same level?
452*. The communicating vessels contained mercury. When a layer of kerosene 34 cm high was poured into the right tube, the level of mercury in the left tube rose by 2 cm. What height should a layer of water be poured into the left tube so that the mercury in the tubes is at the same level (Fig. 135)?
453. Mercury, water and kerosene are poured into communicating vessels (see Fig. 135). What is the height of the kerosene layer if the height of the water column is 20 cm and the level of mercury in the right knee is 0.5 cm lower than in the left?
454. One cylinder contains air with a volume of 1 m3, and another exactly the same 1 m3 of propane. Which cylinder should it be attached to? great strength to lift it?
455. The student calculated that over the past 24 hours the mass of air that passed through his lungs was 15 kg. What is the volume at normal pressure and the temperature occupied by the air passing through the student’s lungs? Compare
1 When calculating, take g=10 N/kg.
22. ATMOSPHERIC PRESSURE1
4*
51
G
drink this volume with the volume of air filling your room.
456. Why, when air is pumped out, does water rise in tube B, and not in tube A (Fig. 136)?
457°. Why doesn’t water pour out of a bottle turned upside down if its neck is immersed in water (Fig. 137)?
458°. The boy picked a leaf from a branch, put it to his mouth, and when he sucked in air, the leaf burst. Why did the leaf burst?
459°. While tap K is closed, water does not flow out of the tube (Fig. 138). When the tap is opened, the water level in the tube drops to the level of the water in the vessel. Why?

[ 58 ]

Calculation of the main jet. Theoretical fuel velocity when exiting the main jet

ot.r = Y2(Drd/r -gD) = Y 2(12 499/740 - 9.81 0.004) =

where Рт =740 is the density of gasoline, kg/m*; A/g = 4 mm =0.004 m.

Actual fuel velocity when exiting the main jet

a»„.g = Vm.rW.r = 0.798 5.8054 = 4.6327 « 4.6 m/s,

where Tzh.r = 0.798 - is determined from Fig. 130 when choosing a jet with Ijd = 2.

The actual fuel consumption of the engine at n = 5600 rpm according to the thermal calculation is 18.186 kg/h or 0.00505 kg/s. Since fuel is supplied through two jets - the main and compensation ones, it is necessary to select their sizes so that they ensure the dependence of a on the rotation speed selected in the thermal calculation. We preliminarily assume the fuel consumption through the main jet St.g = 0.00480 kg/s, and through the compensation jet - k = = St - St.g = 0.00505 - 0.00480 = 0.00025 kg/s.

Main jet diameter [see formula (450)]

V zh.gt.gR V 3.14 - 0.798 - 5,

0.0013355 m «1.33 MM.

Calculation of the compensation jet. Theoretical fuel velocity when flowing out of the compensation jet

Sh.k = V2gH = 1/2. 9.81 - 0.05 = 0.9905 m/s,

where H = 50 mm = 0.05 m is the fuel level in the float chamber above the compensation jet.

The outflow of fuel at a speed sh.k = 0.9905 m/s approximately corresponds to a vacuum.

Ar = yu1«p/2 = 0.9905* - 740/2 = 726 Pa « 0.7 kPa.

Therefore, the flow coefficient of the compensation jet can be determined from Fig. 130 at Ar 0.7 kPa. We choose a compensation jet with a ratio l/d l? 5, then Czh.k = 0.65 (Fig. 130).

Diameter of compensation jet

3,14 0,65 0,9905 740

0.0008175 mE!0.82 mm.

Calculation of carburetor characteristics. The characteristics of the carburetor are built in the range from Ar„ at “shsh = 1000/minDO Ar„ at “max =

6000 rpm (see § 20 and 21) according to the formula

The determination of Ap„ with the throttle valve fully open and a given value n is carried out by selecting the value of Cd corresponding to the resulting value of Ard. According to the graph in Fig. 127 is determined at Ard = 0.5 - 0.6 kPa [Хд = 0.70 and at Ard = 12-13 kPa Cd = 0.838. Then at “tsh = 1000 rpm

at Ptah = 6000 rpm

G0.8609 / 0.078 N2

0,838 \ 0,02527

where riv = 0.8744 and 7jv = 0.8609 are taken from the thermal calculation, and the accepted values \i„ = 0.70 and [Хд = 0.838 correspond to the obtained values Ard = 569 Pa and Ard = 13,860 Pa (see Fig. 127).

We accept nine design points of the characteristic ranging from Ard = 569 Pa to Ard = 13,860 Pa (Table 70).

The diffuser flow coefficient is determined from the graph in Fig. 127 for the accepted calculated values of Ard and are entered in the table. 70.

The second air flow through the diffuser depending on the vacuum is determined by the formula (438)

LAo-i- 3.14-0.025272 t/o i icqAo

U 2roArd = - 1Хд U 2 -1.189Ard =

0.000773(Ad 1/Arya kg/s.

The main jet flow coefficient is determined from the graph in Fig. 130 for accepted values Ard.

Theoretical fuel flow rate from the main jet

= -(Ard-A/gr,) = (Api-9.81 -0.004-740) =

0.05198U Ard-29.04 m/s.

Fuel consumption through the main jet

3.14-0.00133552 Gt.p = !*f.gIt.gRt =--1- 1*f.

0.001036r,zh.gSh)t.gKg/s.

Fuel consumption through the compensation jet does not depend on the vacuum and was previously assumed to be G.k = 0.00025 kg/s. Total fuel consumption

gt = c.r + g.k = g.r + 0.00025 kg/s. Excess air ratio

0.02527g(LdU 1.189Drd

14.957 M0004656(Ld/D

0.0000485a /Drd - 29.04 + 0.000225

QM 0.05 0.0 It 0.03 0.02

All calculated data are summarized in table. 70 and based on them the characteristic 1.00 of the carburetor is built (Fig. 131). 0.95

As can be seen from the figure, 0.90 the resulting curve of dependence of a on D/7d is very close to the values of a adopted in the thermal calculation (these values are marked in Fig. 131 by dots). Consequently, the calculated carburetor, to a close approximation, meets the requirements imposed on it when work engine based on r„s. 131. Calculated characteristics of carburetor operating modes. ratora

§ 75. CALCULATION OF DIESEL FUEL SYSTEM ELEMENTS

The diesel fuel system includes the following main elements: fuel tank, booster pump low pressure, filters, pump high pressure, nozzles and pipelines.

In modern automobile and tractor diesel engines greatest distribution received fuel systems, including a multi-section high-pressure pump and closed injectors connected by a discharge pipeline. Fuel equipment of the undivided type, in which the high-pressure pump and injector are combined into one unit: pump-injector, have limited use.

IN lately Fuel systems are also becoming widespread, in which they use a distribution-type pump with one or two plunger pairs, which dispenses fuel, pumps it and distributes it among the engine cylinders.

Calculation of a diesel fuel supply system usually comes down to determining the parameters of its main elements: the high-pressure fuel pump and injectors.

High pressure fuel pump

The high pressure fuel pump is the main structural element of the diesel power system. It is designed to measure the required amount of fuel and supply it under high pressure to the cylinders at a set moment in accordance with the operating order of the engine.

For automobile and tractor diesel engines, high-pressure spool-type fuel pumps with plungers loaded with springs and driven by cams of a rotating shaft are currently used.

Calculation of the fuel pump section involves determining the diameter and stroke of the plunger. These main design parameters of pump 1 depend on its cyclic supply at the rated diesel power mode.

Cyclic supply, i.e. fuel consumption per cycle:

in mass units (g/cycle)

ga=g“A?”V(120m-); in volumetric units (mm*/cycle)

Due to fuel compression and leaks through leaks, as well as due to deformation of high-pressure pipelines, the pump performance must be greater than the value Vc.

The influence of the above factors on the amount of cyclic feed is taken into account by the pump feed coefficient, which represents the ratio of the volume of cyclic feed to the volume described by the plunger during the geometric active stroke:

Г1„ = V/V, (457)

where Vr = /pact - theoretical cyclic flow of the pump, mm*/cycle (fn - cross-sectional area of the plunger, mm*; 5act - active stroke of the plunger, mm).

Therefore, the theoretical flow of the fuel pump section

The value ti„ for automobile and tractor diesel engines at rated load varies within the range of 0.70-0.90.

Full capacity of the fuel pump section (mm*/cycle), taking into account fuel bypass, diesel overload and ensuring reliable starting at low temperatures determined by the formula

Y„ = (2.5 + 3.2)U,.

This amount of fuel must be equal to the volume corresponding to the full stroke of the plunger.

The main dimensions of the pump are determined from the expression

where edpl and 5pl are diameter and full speed plunger, mm. Plunger diameter

The SJd ratio varies between 1.0-1.7. The diameter of the pump plunger must be at least 6 mm. With smaller diameters, processing and fitting of the plunger in the sleeve becomes more difficult.

According to statistical data for naturally aspirated diesel engines, the diameter of the plunger depends mainly on the diameter of the cylinder and does not depend on the method of mixture formation and the nominal speed limit engine. The ratio dn„/D = 0.065 - 0.08 is valid for naturally aspirated diesel engines with both divided and undivided chambers, with

(2) , where A=

In this dependence, and are values for the analogue river. The coefficient of variation can also be determined using a nomogram constructed by G.A. Alekseev according to formula (2) Fig. 155.

Fig. 127 . Average long-term layer of spring surface runoff in forest-steppe and steppe regions of the European territory of the USSR (in millimeters) The maximum average daily runoff intensity of a given supply is calculated by the formula:

, where hp is the layer of spring runoff of a given supply in mm; f l and f b – relative values of forest cover and swampiness (in fractions of the basin area); V – climatic coefficient equal to 0.003 for the territory of the USSR (with the dimension of maximum runoff modules in m 3 /sec per 1 km 2); A and are coefficients taken equal for coniferous forests and moss bogs 2.0, for mixed forests and transitional swamps 1.5, and for deciduous forest And lowland swamps 1.0. The regulation coefficient (reduction of maximum flow rates due to accumulation in ponds and lakes) is equal to , where is the surface area of ponds and lakes in fractions of the basin area. After transformations and substitution of all coefficients into formula (1), we finally obtain the expression:

,where is the coefficient that reduces Q max due to the accumulation of water in reservoirs, where

- consumption of ground nutrition; where is the time it takes for water to reach in days. Further calculations are carried out using the approximation method. Require special training and fundamental knowledge. 4.Formula for determining the maximum flow rates of mixed flow. Q = m 3 /sec; W=

thousand m 3; Where is the flow rate of snow runoff, is the flow rate of storm runoff in the spring in m 3 /sec, is the volume of snow runoff, is the volume of storm runoff in the spring. Further calculations are performed individually for each region, using maps, nomograms and tables of calculated coefficients. 1.4 Normalization of the calculated values of the highest water flows The degree of risk of destruction or disruption of the normal operation of structures depends on the value of the calculated probability of the highest water flow. To prevent disasters, a Guarantee Amendment to the Design Maximums is introduced. It is appointed in order to take into account the possibility of the coincidence of the period of observation of the maximum river flow with relatively low floods or relatively high floods and floods. The guarantee correction Q max .р = is calculated. Or = x 100%, where Q max. p – maximum flow rate of a given supply; - warranty amendment; E p – relative mean square error of flow rate Q max. p for n = 1, characterizing the degree of variability of the maxima and determined from the graph (Fig. 7.2) depending on the calculated supply P% and the coefficient of variation C v ; a – coefficient characterizing the hydrological knowledge of the river equal to 1.5 for areas that are poorly studied hydrologically. The guarantee amendment is accepted to be no more than 20% of the maximum water flow Q max. p. Then the corrected flow rate is determined by the formula

In the practice of design calculations, national economic objects are divided into classes of capital of structures (five classes) with the corresponding calculated security. In addition, there are State General Construction Standards GOST.

(lat. amplitude- magnitude) is the greatest deviation of the oscillating body from the equilibrium position.

For a pendulum, this is the maximum distance by which the ball moves away from its equilibrium position (figure below). For oscillations with small amplitudes, such a distance can be taken as the length of the arc 01 or 02, as well as the lengths of these segments.

The amplitude of oscillations is measured in units of length - meters, centimeters, etc. On the oscillation graph, the amplitude is defined as the maximum (modulo) ordinate of the sinusoidal curve (see figure below).

Oscillation period.

Oscillation period- this is the shortest period of time through which a system oscillating returns again to the same state in which it was at the initial moment of time, chosen arbitrarily.

In other words, the oscillation period ( T) is the time during which one complete oscillation occurs. For example, in the figure below, this is the time it takes for the pendulum bob to move from the extreme right point through the equilibrium point ABOUT to the far left point and back through the point ABOUT again to the far right.

Over a full period of oscillation, the body thus travels a path equal to four amplitudes. The period of oscillation is measured in units of time - seconds, minutes, etc. The period of oscillation can be determined from a well-known graph of oscillations (see figure below).

The concept of “oscillation period”, strictly speaking, is valid only when the values of the oscillating quantity are exactly repeated after a certain period of time, i.e. for harmonic oscillations. However, this concept also applies to cases of approximately repeating quantities, for example, for damped oscillations.

Oscillation frequency.

Oscillation frequency- this is the number of oscillations performed per unit of time, for example, in 1 s.

The SI unit of frequency is named hertz(Hz) in honor of the German physicist G. Hertz (1857-1894). If the oscillation frequency ( v) is equal to 1 Hz, this means that every second there is one oscillation. The frequency and period of oscillations are related by the relations:

In the theory of oscillations they also use the concept cyclical, or circular frequency ω . It is related to the normal frequency v and oscillation period T ratios: