The physical quantity characterizing the stage of the oscillatory process is called. What characterizes oscillatory motion

oscillatory movement. The main quantities characterizing the oscillatory motion. Solving graphic problems.

If you look at the history of physics, you can see that the main discoveries were essentially related to oscillations

L. I. Mandelstam

Objectives: to form the concept of oscillatory motion, understanding the conditions for the occurrence of oscillatory motion. To form knowledge of the basic quantities characterizing the oscillatory motion.

To have: the concept of oscillatory motion, to know the difference between oscillatory motion and other types of oscillatory motion. Know the quantities characterizing the oscillatory motion. Know the concept of free vibrations, harmonic vibrations

Be able to: solve problems using theoretical material

Develop attention, logic of thinking, memory

Cultivate interest in the subject

Type: learning new material

Equipment: textbook, workbook, flipchart, testers, GLX Explorer, force sensor, spring, 500g weight

During the classes

Organizing time (1 min) Preparation for learning new material (2-3 min)

Flashanimation: areas of the heart and lungs periodically move, tree branches oscillate in a gust of wind, legs and arms oscillate when walking, guitar strings oscillate, an athlete on a trampoline oscillates and a schoolboy trying to pull himself up on a crossbar, stars pulsate (as if breathing), atoms oscillate in the nodes of a crystalline grids...

Let's stop! What is the commonality of these movements? (these movements are repeated) What is the difference between this movement and other types of movement?

3. Explaining new material (20 min)

The scientist L. I. Mandelstam said that if you look at the history of physics, you can see that the main discoveries were essentially connected with oscillations. And we also have openings today.

The purpose of our lesson –

An oscillation is a movement of a body that is exactly or approximately exactly repeated at regular intervals. Movements near the position of stable equilibrium always have an oscillatory character.

Consider what conditions the forces acting on the body must satisfy in order for it to perform an oscillatory motion

Demonstration: the load is suspended by a spring.

On the board is a diagram of a load suspended on a spring
Flipchart p3 Problem? What forces act on the load. Why is the load at rest?

The load on the tripod is at rest, provided that the modulus of the oppositely directed gravity forces Fstrand and Fcontrol acting on it are equal

F= Fstrand + Fcontrol=0

Flipchart page 4 Moving the load down

Diagram on the board

Problem: How do the forces acting on a load shifted down change?

Fcontrol increases, Fstrength remains unchanged. The resultant force acting on the load is directed upwards.

Problem: How do the forces acting on a load shifted upwards change?

Fcontrol decreases, Fstrength remains unchanged. The resultant force acting on the load is directed downward.

Hence the resultant of all forces acting on a load suspended on a spring at any point in the trajectory directs the load to the equilibrium position

CONCLUSION The force that returns the load to the equilibrium position is the elastic force, which depends on the deflection and on the equilibrium position.

Problem: What law obeys the force of elasticity.

Hooke's law: Fcontrol = -kx.

how the elastic force and displacement depend (they are directly proportional)

Mechanical vibrations that occur under the action of a force proportional to the displacement and directed opposite to it are harmonic vibrations

Conclusion: For an oscillatory movement to occur, it is necessary:

1. The force that returns to its original position

2. Friction should be as small as possible, as this leads to damping of the oscillations

https://pandia.ru/text/80/288/images/image004_9.gif" width="42" height="42"> The main quantities characterizing the fluctuations - amplitude, period and frequency.
We have already met with periodic movement. Let us recall what values this type of movement was characterized by?

The oscillatory motion is also characterized

Problem: define these quantities, units of measurement, formulas

The oscillation period is the minimum period of time after which the movement of the body is repeated.

T-period (s)

One revolution of the body around the circumference is called a cycle
Oscillation frequency - the number of oscillations that the body makes in 1 second.

Frequency (Hz=s-1)

Another quantity that characterizes the oscillatory motion

Oscillation amplitude - the maximum deviation of the body from the average position (equilibrium position)..gif" width="26" height="14 src=">= - A and point DIV_ADBLOCK205">

Acceleration, on the contrary, at the point x \u003d 0 is a-maximum, at \u003d - A and at the point \u003d A, the acceleration is zero
The vibrations that a system makes after it is taken out of equilibrium and then left to itself are called free vibrations.

For a visual representation of the motion of a body during mechanical vibrations, the following experiment can be carried out

On the tables at the guys installation:

2. force sensor

3. spring

4. weight of 500 grams

We bring the load out of equilibrium on the screen, we get a graph of oscillatory motion.

A harmonic oscillation is an oscillation in which the displacement of the body from the equilibrium position varies from time to time according to the law of sine or cosine. For example,

The value is called the phase, - the initial phase..jpg" align="left" width="360" height="149 src=">the figure shows the oscillation graph

using which we can determine the period, frequency, amplitude of oscillations

1) oscillatory movement

2) Conditions necessary for oscillatory motion

3) quantities characterizing the oscillatory motion

4) At what points of the trajectory of an oscillating body is the speed equal to: zero, maximum? At what points of the trajectory of an oscillating body is the acceleration equal to: zero, maximum?

5. Fixing.

Work with the schedule Fig. 80 exercise 21 (1-3)

Qualitative task: Will the ball, fixed on the spring, be able to oscillate if the whole system comes to a state of weightlessness

· The frequency of voltage fluctuations in the electrical network is 50 Hz. Determine the period of oscillation

· When a person's pulse changed, 75 blood pulsations were recorded in 1 min. Determine the period of contraction of the heart muscle

What is the frequency of vibrations of the piston of a car engine if the piston makes 600 vibrations in 0.5 minutes

How to write the equation of harmonic oscillatory motion, if the initial phase is zero, the period is 4s, the amplitude is 0.1m

6. Homework § 24-25 answer questions for self-control, learn definitions. exercise 21 (4)

7. checking understanding

1. A characteristic feature of oscillatory motion

A) progress

B) straightness

C) periodicity

D) uniformity

E) there is no correct answer

2. The maximum displacement of the body from the equilibrium position is ...

A) amplitude

During the period

C) frequency

D) hardness

3. What does the oscillation frequency indicate?

C) maximum displacement

D) there is no correct answer

E) number of cycles

4. What does the oscillation period show?

A) the time of one complete oscillation

C) the number of oscillations per unit time

C) maximum displacement

D) there is no correct answer

E) number of cycles

5. What is the frequency of oscillation of the load, if its period of oscillation is 0.5 sec

6. The oscillation frequency of the sparrow's wings is approximately 10 Hz. What is the period of these oscillations?

With the help of this video tutorial, you can independently study the topic "Quantities characterizing the oscillatory motion." In this lesson, you will learn how and by what quantities oscillatory movements are characterized. The definition of such quantities as amplitude and displacement, period and frequency of oscillation will be given.

Topic: Mechanical oscillations and waves. Sound

Lesson 29

Yeryutkin Evgeny Sergeevich

Let's discuss the quantitative characteristics of oscillations. Let's start with the most obvious characteristic, amplitude. Amplitude denoted by a capital letter A and measured in meters.

Definition: amplitude called the maximum displacement from the equilibrium position.

Often the amplitude is confused with the range of oscillations. A swing is when a body swings from one extreme point to another. And the amplitude is the displacement, i.e. distance from the point of balance, from the line of balance to the extreme point at which it hit. In addition to amplitude, there is another characteristic - displacement. This is the current deviation from the equilibrium position.

A - amplitude - [m]

x - displacement - [m]

Rice. 1. Difference of amplitude from displacement

The next feature we move on to is called .

Definition: period of oscillation is the time interval during which one complete oscillation takes place.

Please note that the value of "period" is denoted by a capital letter T, it is defined as follows: . The period is measured in seconds. Here I would like to add one more interesting thing. It consists in the fact that the more we take oscillations, the number of oscillations over a longer time, the more accurately we will determine the period of oscillations.

The next value is . Definition: The number of oscillations per unit of time is called the oscillation frequency.

Frequency - Þ [Hz]

The frequency is indicated by the Greek letter, which is read as "nu". We define the frequency, how many oscillations occurred per unit of time. The frequency is measured by the value , or . This unit is called hertz in honor of the German physicist Heinrich Hertz. Look, it is no accident that we placed two quantities - period and frequency - side by side. If you look at these quantities, you will see how they are related to each other: - period [c]. - frequency - Þ [Hz]

The period and frequency are related through the number of oscillations and the time during which this oscillation takes place. For each oscillatory system, the frequency and period are constant values. The relationship between these quantities is quite simple: .

In conclusion, consider another characteristic of oscillations - phase. We will talk about what a phase is in more detail in the senior classes. Today we must consider what this characteristic can be compared with, compared and how to determine it for ourselves. It is most convenient to compare the phase of oscillations with the speed of the pendulum.

(with identical phases)

out of phase

Our example shows two different pendulums. The first pendulum was deflected to the left by a certain angle, the second was also deflected to the left by a certain angle, the same as the first one. Both pendulums will make exactly the same oscillations. In this case, we can say the following, that the pendulums oscillate with the same phase, since the speeds of the pendulum are the same.

Two similar pendulums, but one is deflected to the left and the other to the right. They also have the same modulus of speed, but the direction is opposite. In this case, the pendulums are said to oscillate in antiphase.

Of course, in addition to oscillations and those characteristics that we talked about, there are other equally important characteristics of oscillatory motion. But we'll talk about them in high school.

List of additional literature:

Kikoin A.K. On the law of oscillatory motion // Kvant. - 1983. - No. 9. - S. 30-31.
Kikoin I.K., Kikoin A.K. Physics: Proc. for 9 cells. avg. school - M.: Enlightenment, 1992. - 191 p.
Chernoutsan A.I. Harmonic oscillations - ordinary and amazing // Kvant. - 1991. - No. 9. - S. 36-38.

KSU "Suvorov secondary school"

(grade 9)

Prepared by: Kochutova G.A.

Lesson topic: Oscillatory motion. Basic quantities,

characterizing the oscillatory motion.

Lesson Objectives :

Formed students' ideas about oscillatory motion; to study the properties and main characteristics of periodic (oscillatory) movements. Introduce the main characteristics of the oscillatory motion.

Find out what determines the period of oscillation of a mathematical pendulum.
To develop logical thinking, speech of students, independence in conducting the experiment.

Cultivate interest in the subject.

Lesson type: Learning new material

Teaching method: practical

Equipment: presentation, flipchat, video material

During the classes.

Organizing time.

Learning new material.

1) We divide the class into two groups (colored stickers). I remind you of the rule of working in a group.

Crossword. Make a question according to the given words.

1. The value that characterizes the speed of movement (speed);

2.Speed of change of speed (acceleration);

3.Measure of interaction of bodies (force);

4. A segment connecting the initial position with its subsequent position (moving);

5. Fall in the absence of medium resistance (free);

6. Price division of the thermometer (degree);

7. Changing the position of the body in space (movement);

8. Force directed against the movement (friction);

9. What the clock shows (time).

2) Each group gives examples of "Oscillations of bodies".

1. The conclusion must be made by the guys: the movements are repeated or the oscillatory movement is characterized by periodicity.

Demonstration of bodies that oscillate: a mathematical pendulum and a spring pendulum.

Vibrations are a very common type of movement. This is the swaying of tree branches in the wind, the vibration of the strings of musical instruments, the movement of a piston in a car engine cylinder, the swinging of a pendulum in a wall clock, and even the beating of our heart.
Consider the oscillatory movement on the example of two pendulums - mathematical and spring.
a mathematical pendulum is a ball attached to a thin, light thread. If this ball is shifted away from the equilibrium position and released, then it will begin to oscillate, i.e., make repeated movements, periodically passing through the equilibrium position.
A spring pendulum is a weight that can oscillate under the action of the elastic force of a spring.

2. conclusion: What conditions are necessary for the occurrence of oscillatory motion? First, there must be a force returning the body to its original position and the absence of friction, which is directed against the movement.

A - amplitude; T - period; v - frequency.

Oscillation amplitude is the maximum distance that an oscillating body moves away from its equilibrium position. The oscillation amplitude is measured in units of length - meters, centimeters, etc.
Oscillation period is the time it takes to complete one oscillation. The oscillation period is measured in units of time - seconds, minutes, etc.
Oscillation frequency is the number of oscillations in 1 second. The SI unit of frequency is named hertz (Hz) in honor of the German physicist G. Hertz (1857-1894). If the oscillation frequency is equal to! 1 Hz, this means that one oscillation is made for every second. If, for example, the frequency v \u003d 50 Hz, then this means that 50 oscillations are made in every second.
For the period T and frequency ν of oscillations, the same formulas are valid as for the period and frequency of revolution, which were considered in the study of uniform motion along a circle.
1. To find the period of oscillations, it is necessary to divide the time t, during which several oscillations are made, by the number n of these oscillations:

2. To find the frequency of oscillations, it is necessary to divide the number of oscillations by the time during which they occurred:

When counting the number of oscillations in practice, it should be clearly understood what constitutes one (full) oscillation. If, for example, the pendulum starts moving from position 1, then one oscillation is such a movement when it, having passed the equilibrium position 0, and then the extreme position 2, returns through the equilibrium position 0 again to position 1.
The period and frequency of oscillations are mutually inverse quantities, i.e.

T = 1/v
In the process of oscillations, the position of the body is constantly changing. A graph of the dependence of the coordinate of an oscillating body on time is called an oscillation graph. The time t is plotted along the horizontal axis on this graph, and the x coordinate is plotted along the vertical axis. The module of this coordinate shows at what distance from the equilibrium position is the oscillating body (material point) at a given time. When the body passes through the equilibrium position, the sign of the coordinate changes to the opposite, thereby indicating that the body is on the other side of the average position.
With sufficiently small friction and over short time intervals, the oscillation graph of each of the pendulums is a sinusoidal curve, or briefly a sinusoid.
According to the schedule of oscillations, you can determine all the characteristics of the oscillatory movement. So, for example, the graph describes oscillations with amplitude A = 5 cm, period T = 4 s and frequency ν = 1 / T = 0.25 Hz.

Fizminutka page 91.

Consolidation.

Answer the questions with average motivation (Aizhan, Zhenya, Masha):

What movement is called oscillatory?

What is body vibration?

What is the oscillation frequency? What is the unit of intent?

What is called the amplitude of oscillations?

What is called the period of oscillation?

What is the unit of measure for the period of oscillation?

What is a pendulum? What kind of pendulum is called mathematical?

Which pendulum is called a spring pendulum?

Which of the movements listed below are rolled by mechanical vibrations a) swing movement; b) the movement of the ball falling to the ground; c) the movement of a sounding guitar string?

With low motivation (Vagin A., Matyash A.): conduct a practical task:The shape of the oscillation graph can be judged on the basis of the following experiments.

Let's connect a spring pendulum to a writing device (for example, a brush) and start moving the paper tape evenly in front of the oscillating body. The brush will draw a line on the tape, which will coincide in shape with the oscillation graph.
Solve problems with high motivation (Yanna, Nurzhan, Asker): exercise 21 p. 91

Summarizing. Grading. Homework §24,25

Learning new material

Anchoring

Answered all questions 2 points

Experience 1 point

Problem solved 3 points

Total:

10-12 points score "5"

7-9 points score "4"

4-6 points score "3"

1-3 points score "2"

Group assessment sheet.

Learning new material

1. Concluded what an oscillatory movement is - 1 point

2. Made a conclusion about the condition for the occurrence of oscillatory movements - 2 points

3. They gave a definition, designation and units of measurement of the values of oscillatory motion -3 points

Anchoring

Answered all questions - 2 points

Conducted experience -1 point

Solved problems -3 points

Total:

10-12 points score - "5"

7-9 points score - "4"

4-6 points score - "3"

1-3 points score - "2"

Let us discuss the quantitative characteristics of oscillations. Let's start with the most obvious characteristic - amplitude. Amplitude denoted by a capital letter A and measured in meters.

Definition

Amplitude called the maximum displacement from the equilibrium position.

Often the amplitude is confused with the range of oscillations. A swing is when a body oscillates from one extreme point to another. And the amplitude is the maximum displacement, that is, the distance from the equilibrium point, from the equilibrium line to the extreme point at which it hit. In addition to amplitude, there is another characteristic - displacement. This is the current deviation from the equilibrium position.

BUT – amplitude –

X – offset –

Rice. 1. Amplitude

Let's see how the amplitude and offset differ in an example. The mathematical pendulum is in a state of equilibrium. The line of location of the pendulum at the initial moment of time is the line of equilibrium. If you take the pendulum to the side, this will be its maximum displacement (amplitude). At any other time, the distance will not be an amplitude, but simply a displacement.

Rice. 2. Difference between amplitude and offset

The next feature we move on to is called oscillation period.

Definition

Oscillation period is the time interval during which one complete oscillation takes place.

Please note that the "period" value is denoted by a capital letter , it is defined as follows: , .

Rice. 3. Period

It is worth adding that the more we take the number of oscillations over a longer time, the more accurately we will determine the period of oscillations.

The next value is frequency.

Definition

The number of oscillations per unit time is called frequency fluctuations.

Rice. 4. Frequency

The frequency is indicated by the Greek letter, which is read as "nu". Frequency is the ratio of the number of oscillations to the time during which these oscillations occurred:.

Frequency units. This unit is called "hertz" in honor of the German physicist Heinrich Hertz. Note that period and frequency are related in terms of the number of oscillations and the time during which this oscillation takes place. For each oscillatory system, the frequency and period are constant values. The relationship between these quantities is quite simple: .

In addition to the concept of "oscillation frequency", the concept of "cyclic oscillation frequency" is often used, that is, the number of oscillations per second. It is denoted by a letter and is measured in radians per second.

Graphs of free undamped oscillations

We already know the solution to the main problem of mechanics for free oscillations - the law of sine or cosine. We also know that graphs are a powerful tool for studying physical processes. Let's talk about how the graphs of the sinusoid and cosine wave will look like when applied to harmonic oscillations.

To begin with, let's define the singular points during oscillations. This is necessary in order to correctly choose the scale of construction. Consider a mathematical pendulum. The first question that arises is: which function to use - sine or cosine? If the oscillation starts from the top point - the maximum deviation, the cosine law will be the law of motion. If you start moving from the point of equilibrium, the law of motion will be the law of sine.

If the law of motion is the law of cosine, then after a quarter of the period the pendulum will be in the equilibrium position, after another quarter - at the extreme point, after another quarter - again in the equilibrium position, and after another quarter it will return to its original position.

If the pendulum oscillates according to the sine law, then after a quarter of the period it will be at the extreme point, after another quarter - in the equilibrium position. Then again at the extreme point, but on the other side, and after another quarter of the period, it will return to the equilibrium position.

So, the time scale will not be an arbitrary value of 5 s, 10 s, etc., but a fraction of the period. We will build a chart in quarters of the period.

Let's move on to construction. varies either according to the law of sine or according to the law of cosine. The ordinate axis is , the abscissa axis is . The time scale is equal to quarters of the period: The chart will lie in the range from to .

Rice. 5. Dependency graphs

The graph for oscillation according to the sine law goes out of zero and is indicated in dark blue (Fig. 5). The graph for oscillation according to the cosine law leaves the position of maximum deviation and is indicated in blue in the figure. The graphs look absolutely identical, but are shifted in phase relative to each other by a quarter of a period or radians.

Dependence graphs and will have a similar look, because they also change according to the harmonic law.

Features of the oscillations of a mathematical pendulum

Mathematical pendulum is a material point of mass suspended on a long inextensible weightless thread of length .

Pay attention to the formula for the period of oscillation of a mathematical pendulum: , where is the length of the pendulum, is the acceleration of free fall.

The longer the pendulum, the longer the period of its oscillations (Fig. 6). The longer the thread, the longer the pendulum swings.

Rice. 6 Dependence of the period of oscillation on the length of the pendulum

The greater the free fall acceleration, the shorter the oscillation period (Fig. 7). The greater the acceleration of free fall, the stronger the celestial body attracts the weight and the faster it tends to return to the equilibrium position.

Rice. 7 Dependence of the oscillation period on the free fall acceleration

Please note that the oscillation period does not depend on the mass of the load and the oscillation amplitude (Fig. 8).

Rice. 8. The oscillation period does not depend on the oscillation amplitude

Galileo Galilei was the first to draw attention to this fact. Based on this fact, a pendulum clock mechanism is proposed.

It should be noted that the accuracy of the formula is maximum only for small, relatively small deviations. For example, for the deviation, the error of the formula is . For larger deviations, the accuracy of the formula is not so great.

Consider qualitative problems that describe a mathematical pendulum.

Task.How will the course of pendulum clocks change if they are: 1) transported from Moscow to the North Pole; 2) transport from Moscow to the equator; 3) lift high uphill; 4) take it out of the heated room into the cold.

In order to correctly answer the question of the problem, it is necessary to understand what is meant by the “running of a pendulum clock”. Pendulum clocks are based on a mathematical pendulum. If the oscillation period of the clock is less than we need, the clock will start to rush. If the oscillation period becomes longer than necessary, the clock will lag behind. The task is reduced to answering the question: what will happen to the period of oscillation of a mathematical pendulum as a result of all the actions listed in the task?

Let's consider the first situation. The mathematical pendulum is transferred from Moscow to the North Pole. We recall that the Earth has the shape of a geoid, that is, a ball flattened at the poles (Fig. 9). This means that at the Pole the magnitude of the free fall acceleration is somewhat greater than in Moscow. And since the acceleration of free fall is greater, then the period of oscillation will become somewhat shorter and the pendulum clock will start to rush. Here we neglect the fact that it is colder at the North Pole.

Rice. 9. Acceleration of free fall is greater at the poles of the Earth

Let's consider the second situation. We move the clock from Moscow to the equator, assuming that the temperature does not change. The free fall acceleration at the equator is slightly less than in Moscow. This means that the period of oscillation of the mathematical pendulum will increase and the clock starts to slow down.

In the third case, the clock is raised high uphill, thereby increasing the distance to the center of the Earth (Fig. 10). This means that the free fall acceleration at the top of the mountain is less. The period of oscillation increases the clock will be behind.

Rice. 10 Gravity is greater at the top of the mountain

Let's consider the last case. The clock is taken out of the warm room into the cold. As the temperature decreases, the linear dimensions of the bodies decrease. This means that the length of the pendulum will be slightly reduced. Since the length has become smaller, the period of oscillation has also decreased. The clock will rush.

We examined the most typical situations that allow us to understand how the formula for the oscillation period of a mathematical pendulum works.

Figure 11 shows two identical pendulums. The first pendulum was deflected to the left by a certain angle, the second was also deflected to the left by a certain angle, the same as the first one. Both pendulums will make exactly the same oscillations. In this case, we can say that the pendulums oscillate with the same phase, since the speeds of the pendulum have the same direction and equal modules.

Figure 12 shows two similar pendulums, but one is tilted to the left and the other to the right. They also have the same velocities modulo, but the direction is opposite. In this case, the pendulums are said to oscillate in antiphase.

In all other cases, as a rule, mention is made of the phase difference.

Rice. 13 Phase difference

The phase of oscillations at an arbitrary point in time can be calculated by the formula , that is, as the product of the cyclic frequency and the time that has elapsed since the beginning of the oscillations. The phase is measured in radians.

Features of oscillations of a spring pendulum

The formula for the oscillation of a spring pendulum: . Thus, the period of oscillation of a spring pendulum depends on the mass of the load and the stiffness of the spring.

The greater the mass of the load, the greater its inertia. That is, the pendulum will accelerate more slowly, the period of its oscillations will be longer (Fig. 14).

Rice. 14 Dependence of the oscillation period on the mass

The greater the stiffness of the spring, the faster it tends to return to its equilibrium position. The period of the spring pendulum will be less.

Rice. 15 Dependence of the period of oscillation on the stiffness of the spring

Consider the application of the formula on the example of the problem.

Rice. 17 Oscillation period

If we now substitute all the necessary values \u200b\u200bin the formula for calculating the mass, we get:

Answer: weight of the weight is approximately 10 g.

Just as in the case of a mathematical pendulum, for a spring pendulum the oscillation period does not depend on its amplitude. Naturally, this is true only for small deviations from the equilibrium position, when the deformation of the spring is elastic. This fact was the basis for the construction of spring clocks (Fig. 18).

Rice. 18 Spring watch

Conclusion

Bibliography

Kikoin A.K. On the law of oscillatory motion // Kvant. - 1983. - No. 9. - S. 30-31.
Kikoin I.K., Kikoin A.K. Physics: textbook. for 9 cells. avg. school - M.: Enlightenment, 1992. - 191 p.
Chernoutsan A.I. Harmonic vibrations - ordinary and amazing // Kvant. - 1991. - No. 9. - S. 36-38.
Peryshkin A.V., Gutnik E.M. Physics. Grade 9: textbook for general education. institutions / A.V. Peryshkin, E.M. Gutnik. - 14th ed., stereotype. - M.: Bustard, 2009. - 300 p.

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Homework

What are mathematical and spring pendulums? What's the difference between them?
What is harmonic oscillation, oscillation period?
A weight of 200 g oscillates on a spring with a stiffness of 200 N/m. Find the total mechanical energy of oscillations and the maximum speed of movement of the load if the amplitude of oscillations is 10 cm (neglect friction).