Physics teacher :
When solving any problem, we can follow two paths: inductive and deductive. The inductive path presupposes the possibility of generalization when analyzing the solution of particular problems; by the deductive method we can go from general principles to specific ones.
Which method is preferable in our case?
Discuss the question in pairs and express your opinion.
So, based on the results of the discussion, we can conclude that in this case we need to use the inductive method; we must obtain techniques common to any oscillation that allow us to describe the stateoscillatory system at an arbitrary point in time.
Therefore, we will begin the discussion with a particular problem.
Task 1.
The charge on the capacitor plates changes according to the law:
πt+
At what points in time during the period is the current in the circuit at its maximum value? What is the voltage at these moments in time? What fraction of the maximum is it at these moments of time? The capacitance of the capacitor in the circuit is 2 μF.
Offer a scheme for solving the problem, try to find different approaches to the solution. (Work in pairs)
So let's put the results of your discussion together. (Ideas proposed by various pairs are collected on the board, discussed, and as a result, two approaches to solving the problem are formed: analytical and graphic).
What actions are required to implement the analytical solution?
Mathematic teacher:
By studying the physical laws connecting changes in charge and current in a circuit, you came to the conclusion that
(
t)=
i(
t) , therefore, it is necessary to remember how to find the derivative of a trigonometric function.
-Let's remember the formulas for the derivatives of trigonometric functions and the derivatives of complex functions.
-Find derivatives of the following functions (Slide No. 6)
Physics teacher:
So, the mathematical principles of finding the derivative of a complex trigonometric function are applicable to solving our problem.
Write down the equation for changing the current strength yourself.
Present your results for general discussion.
So, the equation for changing the current strength is as follows:
i(t)= - 0.03πsin(πt+3π).
Using the fact that the current strength at the desired time is from the maximum value equal to 0.03π, we create the equation
0.03πsin(πt+3π).
Mathematic teacher:
This type of equation is trigonometric.
What types of trigonometric equations do you know and what are the methods for solving them?
-Solve the proposed equations yourself
(Slide No. 8)
Is it possible to solve the equation from the problem in a similar way?
Physics teacher:
- Let's solve our trigonometric equation and find the required moments of time. (A student is called to the board).
To find the voltage on the capacitor at a given time, it is necessary to obtain the equation of dependenceu( t). Knowing the relationship between capacitor charge and voltage, obtain an equation and find the desired voltage value. (Tasks are completed independently on the Appendix sheet).
Let's create a solution algorithm based on the capabilities of mathematical analysis.
1.Let's write down the equations
changes in current strength over time, using the mathematical relationship between changes in charge and current strength.
2. Knowing that the current strength at the desired moment of time is 1/6 of the maximum value, we will compose and solve a trigonometric equation and find the corresponding moments of time.
3. Let's write down the equation for the change in voltage and calculate it at the previously found times.
A similar solution scheme can be used to analyze any oscillatory process.
As homework you are given task 2:
The point performs harmonic oscillations with a period of 2 seconds, an amplitude of 50 mm, and the initial phase is zero. Find the speed and acceleration of the point at the moment of time when the displacement of the point from the equilibrium position is 25 mm.
Let's move on to the second method of solving the original problem - graphically.
Mathematic teacher:
What do you need to know to graph this function?
Which function is the original graph??
What graph transformations need to be made to graph a function?
I (t)= - 0.03πsin(πt+3π)?
How to construct the function graphs shown on slide number 10?
Physics teacher:
Let's use a graph of the function that reflects changes in charge and current over time (Slide No. 12. What information about the conditions of the problem will the graphs tell you? Answer the question of the problem yourself, using the Appendix sheet.
Are the answers given the same?
Which method is preferable and why?
Is there another solution? Think about this question at home.
The inductive method is often used when it is necessary to analyze and compare data from an experiment or observation. In one of the previous lessons, we conducted laboratory work to study the dependence of the period of oscillation of a mathematical pendulum on its length. As an additional task, you plotted the dependence of the coordinates of an oscillating pendulum on timex( t)=0,1 cost. Let's use this graph to answer the following questions:
During what part of the period will a body performing harmonic oscillations travel the following path:
from middle position to extreme
the first half of the journey
the second half of the journey
Is it possible to estimate these time intervals experimentally?
In what period of time is the body's speed less than 2 times its maximum speed?
What mathematical methods should be used to answer the questions posed?
1. Harmonic oscillation
Oscillatory motion- this is a movement that is repeated over time, in which a point, having left the equilibrium position, moves in space in a certain limited interval.
Oscillations are called free , if they occur due to the initially imparted energy in the subsequent absence of external influences on the oscillating point.
If during an oscillatory motion there is some time after which the location of the point in space is repeated, then such an oscillation is called periodic.
Periodic processes are widespread in nature and technology. The rotation of the Earth around its axis and around the Sun, the work of the heart, the swing of a pendulum, waves on water, alternating electric current, light, sound, etc. are examples of periodic processes.
Of the periodic movements, the simplest are harmonic vibrations – oscillations in which the oscillating quantity changes over time according to the law of sine or cosine. Any complex vibration can be decomposed into a series of harmonic vibrations.
Harmonic oscillations are periodic oscillations with a period.
X - the displacement of a point from the equilibrium position is determined by sine or cosine.
A is the amplitude of oscillations, the maximum deviation from the equilibrium position that is achieved during oscillatory motion.
– oscillation phase. The phase characterizes the fraction of the amplitude that the displacement will have at a given time.
– the initial phase characterizes the fraction of the amplitude that the displacement will have at the initial moment of time.
Let us consider under the influence of what forces the oscillations occur. To do this you need to know m And X. Analyzing the oscillations of the weight, we see that the weight stops in extreme positions and then moves in the opposite direction, i.e. the weight has variable speed and acceleration.
Speed
Acceleration
From Newton's second law:
Under force
the load undergoes harmonic vibrations.
m and ω are constants,
Harmonic vibrations occur under the action of elastic or quasi-elastic forces.
The role of a quasi-elastic force can be played by the resultant force:
or 
Equation (7) is called the differential equation of harmonic vibration.
2. Physical and mathematical pendulum.
Let us consider a physical pendulum with a deflection angle φ. A physical pendulum is a body that has an axis of rotation.
For a physical pendulum it is necessary to use the basic equation of dynamics
If we designate the distance from the center of rotation to the point of application of force - A, shoulder – p, then the moment of force can be represented:
The minus sign shows that the moment of force leads to a decrease in the angle of rotation φ.
Since the angular velocity
If the angle φ is small, then 
(**)
Let's compare (*) and (**)
Period of oscillation of a physical pendulum
The period of oscillation of a physical pendulum depends on the distribution of mass relative to the axis of rotation for small angles of deviation.
There is a mathematical pendulum - a pendulum whose suspension length is many times greater than the size of the pendulum itself. Let A is the length of the mathematical pendulum, then the moment of inertia of the mathematical pendulum:
Period of a mathematical pendulum:
The movement of a mathematical pendulum at large angles of deflection will be periodic, but not harmonic (the period of oscillation will depend on the swing). Oscillations will be harmonic at small angles of deflection.
Given length apr of a physical pendulum is the length of a mathematical pendulum such that the period of the physical pendulum is equal to the period of the mathematical pendulum. T physical = T mat
A point removed from the center of rotation by an amount is called rolling center. The rolling axis and the rolling center are mutually reversible.
3. Free electromagnetic oscillations in an oscillatory circuit
In a circuit containing inductance and capacitance, electrical oscillations may occur, in which electrical quantities (charges, currents, voltages) periodically change and are accompanied by mutual transformations of the energy of the electric and magnetic fields. Let's consider a circuit consisting of a coil with inductance L, a capacitor with capacitance C, and a resistor with resistance R connected in series (Fig. 1). Such a circuit is called an oscillatory circuit. Oscillations in the circuit can be caused by imparting a certain initial charge ±q to the capacitor plates. Then, at the initial moment of time at t = 0, an electric field arises between the plates of the capacitor, the energy of which is . Since the capacitor is closed to the inductance coil, it will begin to discharge, and electric current I will flow in the circuit. As a result of this, the charge on the capacitor plates (and therefore the electric field energy) will decrease, and the energy of the magnetic field of the coil, which is equal to, will be increase.
Lesson type: lesson in the formation of new knowledge.
Lesson objectives:
- formation of ideas about vibrations as physical processes;
- clarification of the conditions for the occurrence of oscillations;
- formation of the concept of harmonic vibration, characteristics of the oscillatory process;
- formation of the concept of resonance, its application and methods of dealing with it;
- developing a sense of mutual assistance, the ability to work in groups and pairs;
- development of independent thinking
Equipment: spring and mathematical pendulums, projector, computer, teacher’s presentation, CD “Library of Visual Aids”, student learning sheet, cards with symbols of physical quantities, text “Resonance Phenomenon”.
On each table there is a sheet of knowledge acquisition for each student, a text about the phenomenon of resonance.
During the classes
I. Motivation.
Teacher: So that you understand what will be discussed in the lesson today, read an excerpt from the poem “Morning” by N.A. Zabolotsky
Born of the desert
The sound fluctuates
Blue wavers
There's a spider on a thread.
The air vibrates
Transparent and clean
In the shining stars
The leaf sways.
So today we're going to talk about fluctuations. Think and name where fluctuations occur in nature, in life, in technology.
Students name different examples of oscillations(slide 2).
Teacher: What do all these movements have in common?
Students: These movements are repeated (slide 3).
Teacher: Such movements are called oscillations. Today we will talk about them. Write down the topic of the lesson (slide 4).
II. Updating knowledge and learning new material.
Teacher: We have to:
- Find out what oscillation is?
- Conditions for the occurrence of oscillations.
- Types of vibrations.
- Harmonic vibrations.
- Characteristics of harmonic vibration.
- Resonance.
- Problem solving (slide 5).
Teacher: Look at the oscillations of the mathematical and spring pendulums (oscillations are demonstrated). Are the oscillations absolutely repeatable?
Students: No.
Teacher: Why? It turns out that the force of friction is interfering. So what is hesitation? (slide 6)
Students: Oscillations are movements that repeat themselves exactly or approximately over time.(slide 6, mouse click). The definition is written down in a notebook.
Teacher: Why does the oscillation continue for so long? (slide 7) Using spring and mathematical pendulums, the transformation of energy during oscillations is explained with the help of students.
Teacher: Let us find out the conditions for the occurrence of oscillations. What does it take for oscillations to begin?
Students: You need to push the body, apply force to it. To make the oscillations last a long time, you need to reduce the friction force (slide 8), the conditions are written down in a notebook.
Teacher: There are a lot of fluctuations. Let's try to classify them. Forced oscillations are demonstrated, and free oscillations are demonstrated on spring and mathematical pendulums (slide 9). Students write down the types of vibrations in their notebooks.
Teacher: If the external force is constant, then the oscillations are called automatic (mouse click). Students write down in their notebooks the definitions of free (slide 10), forced (slide 10, mouse click), automatic vibrations (slide 10, mouse click).
Teacher: Oscillations can also be damped or undamped (slide 11 with a mouse click). Damped oscillations are oscillations that, under the influence of friction or resistance forces, decrease over time (slide 12); these oscillations are shown on the graph on the slide.
Continuous oscillations are oscillations that do not change over time; There are no frictional forces or resistance. To maintain undamped oscillations, an energy source is required (slide 13); these oscillations are shown on the graph on the slide.
Examples of oscillations are given (slide 14).
1 option writes out examples damped oscillations.
Option 2 writes out examples undamped oscillations.
- vibrations of leaves on trees during the wind;
- heartbeat;
- swing vibrations;
- oscillation of the load on the spring;
- rearrangement of legs when walking;
- vibration of the string after it is removed from its equilibrium position;
- vibrations of the piston in the cylinder;
- vibration of a ball on a thread;
- the swaying of grass in a field in the wind;
- vibration of the vocal cords;
- vibrations of windshield wiper blades (windshield wipers in a car);
- vibrations of the janitor's broom;
- vibrations of the sewing machine needle;
- vibrations of the ship on the waves;
- swinging arms while walking;
- vibrations of the phone membrane.
Students Among the given oscillations, they write down examples of free and forced oscillations according to the options, then exchange information and work in pairs (slide 15). They also perform tasks on dividing into damped and undamped oscillations in the same examples, then exchange information, work in pairs.
Teacher: You see that all free oscillations are damped, and forced oscillations are undamped. Find automatic oscillations among the examples given. Students give themselves a grade on the knowledge mastery sheet in point 1 of the knowledge mastery sheet ( Annex 1)
Teacher: Among all types of oscillations, a special type of oscillation is distinguished - harmonic.
The manual “Library of Visual Aids” demonstrates a model of harmonic oscillations (mechanics, model 4 harmonic oscillations) (slide 16).
What mathematical function is graphed by the model?
Students: This is a graph of the sine and cosine function (click slide 16).
Students write down the equations of harmonic vibrations in a notebook.
Teacher: Now we need to look at each quantity in the harmonic vibration equation. (Displacement X is shown on the mathematical and spring pendulums) (slide 17). X-displacement is the deviation of a body from its equilibrium position. What is the unit of displacement?
Students: Meter (slide 17, mouse click).
Teacher: On the oscillation graph, determine the displacement at times 1 s, 2 s, 3 s, 4 s, 5 s, 6 s, etc. (slide 17, mouse click). The next value is X max. What is this?
Students: Maximum displacement.
Teacher: The maximum displacement is called amplitude (slide 18, mouse click).
Students The amplitude of damped and undamped oscillations is determined on the graphs (slide 18, mouse click).
Teacher: Before considering the next quantity, let us recall the concepts of quantities studied in 1st year. Let's count the number of oscillations on a mathematical pendulum. Is it possible to determine the time of one oscillation?
Students: Yes.
Teacher: The time of one complete oscillation is called a period - T (slide 19, mouse click). Measured in seconds (slide 19, mouse click). You can calculate the period using the formula if it is very small (slide 19, mouse click). Points are marked in different colors on the graph.
Students The period is determined on the graph by finding it between points of different colors.
Teacher on a mathematical pendulum shows different frequencies for different lengths of the pendulum. Frequency ν– the number of complete oscillations per unit of time (slide 20).
The unit of measurement is Hz (slide 20 mouse click). There are relationship formulas between period and frequency. ν=1/Т Т=1/ν (slide 20 mouse click).
Teacher: The sine and cosine function is repeated through 2π. Cyclic (circular) frequency ω(omega) oscillations is the number of complete oscillations that occur in 2π units of time (slide 21). Measured in rad/s (slide 21, mouse click) ω=2 πν (slide 21, mouse click).
Teacher: Oscillation phase– (ωt+ φ 0) is a quantity under the sine or cosine sign. It is measured in radians (rad) (slide 22).
The oscillation phase at the initial time (t=0) is called initial phase – φ 0. It is measured in radians (rad) (slide 21, click).
Teacher: Now let's repeat the material.
a) Students are shown cards with quantities, they name these quantities. ( Appendix 2)
b) Students are shown cards with units of measurement of physical quantities. We need to name these quantities.
c) Each four students are given a card with a value; they need to tell everything about it according to the plan on slide 23. Then the groups exchange cards with values and complete the same task.
Students give themselves grades on their report card (clause 2, Appendix 1)
Teacher: Today we worked with spring and mathematical pendulums; the formulas for the periods of these pendulums are calculated using formulas. On a mathematical pendulum, he demonstrates periods of oscillation at different lengths of the pendulum.
Students find out that the period of oscillation depends on the length of the pendulum (slide 24)
Teacher on a spring pendulum demonstrates the dependence of the period of oscillation on the mass of the load and the stiffness of the spring.
Students find out that the period of oscillation depends on the mass in direct proportion and on the stiffness of the spring in inverse proportion (slide 25)
Teacher: How do you push a car out if it's stuck?
Students: You need to rock the car together on command.
Teacher: Right. In doing so, we use a physical phenomenon called resonance. Resonance occurs only when the frequency of natural oscillations coincides with the frequency of the driving force. Resonance is a sharp increase in the amplitude of forced oscillations (slide 26). The manual “Library of Visual Aids” demonstrates a resonance model (mechanics, model 27 “Swinging of a spring pendulum” at a frequency of >2Hz).
For students It is proposed to mark the text about the influence of resonance. While the work is being done, Beethoven's Moonlight Sonata and Tchaikovsky's Waltz of the Flowers are playing ( Appendix 4). The text is marked with the following signs (they are located on the stand in the office): V – interested; + knew; - did not know; ? – I would like to know more. The text remains in each student's notebook. Next lesson, you should come back to it and answer students' questions if they don't find the answers at home.
III. Fixing the material.
takes place in the form of tasks (slide 27). The problem is discussed at the board.
For students It is proposed to independently solve problems according to the options on the progress sheets (slide 28). As a result of work in the lesson, the teacher gives an overall grade.
IV. Lesson summary.
Teacher: What new did you learn in class today?
V. Homework.
Everyone learn the lesson notes. Solve the problem: using the equation of harmonic vibration, find everything you can (slide 29). Find answers to questions when marking the text. Those who wish can find material about the benefits of resonance and the dangers of resonance (you can make a message, an abstract, or prepare a presentation).
Private educational institution "Crimean Republican
gymnasium-school-garden Console"
Simferopol
Republic of Crimea
Summary of an open lesson, built in block-modular technology, in physics in grade 11
Lesson topic: “Harmonic oscillations”
Compiled by a physics teacher
Radish E.S.
October, 2016
Lesson type: lesson in the formation of new knowledge
The purpose of the lesson: formation of the concept of harmonic vibration, characteristics of the oscillatory process.
Lesson objectives:
Educational:
repeat
types of vibrations;
the simplest systems of mechanical vibrations;
sine and cosine graphs;
enter
concept of harmonic vibrations;
equation of motion of harmonic oscillations;
vibration characteristics
learn
solve problems on the topic “Harmonic oscillations”;
give examples from life.
Developmental: development of independent thinking.
Educational: developing a sense of mutual assistance, the ability to work in groups and pairs.
Form of work: group.
Resources (equipment): textbook 11th grade in physics G.Ya. Myakishev, reference book on physics B.M. Yavorsky, encyclopedia of elementary physics S.V. Gromov, collection of problems by A.P. Rymkevich, paper cone on a thread with a hole, dry sand, paper tape.
During the classes:
| № p/p | Lesson module, time | Teacher's actions | Student action |
| Organizing time (5 minutes) | greeting students; marking those missing in the journal the teacher talks about the form of work in the lesson, introduces route sheets and the rules for working with them (but does not distribute them to groups!!!), establishes an evaluation system. | teacher's greeting; the duty officer reports absences; Students, listening carefully to the teacher, learn about the organization of work in the lesson. |
|
| Update (2 minutes) | Oral survey on the topic of the previous lesson. | Answer orally the teacher’s questions on the topic of the previous lesson. |
|
| Goal setting (10 min) | demonstrates the experiment: a cone with sand, swinging, draws the trajectory of its movement - a harmonic function (cosine or sine); The teacher asks leading questions to formulate the topic and purpose of the lesson. (What function does the trajectory “drawn” by the cone resemble? What do we call oscillations whose motion is described by a harmonic function?) With guiding questions, the teacher helps students formulate the purpose of the lesson and records it on the board. | observe a physical phenomenon; answer teacher questions; harmonic; harmonic; students write down the date and topic of the lesson in their notebooks; formulate the purpose of the lesson. |
|
| Discovery of new knowledge (15 minutes) | distributes route sheets and reminds the rules for working with them; monitors the completion of each group of students with tasks on the route sheet; after each module produces the correct result. | study route sheets; complete tasks on the route sheet; groups exchange route sheets, check the correct completion of the module and assign points to the team. |
|
| Consolidation (8 min) |
|||
| Reflection (3 min) | summarizes the students' work; asks students to orally answer the questions on the route sheet. | count the number of points; answer questions on the route sheet, noting the most difficult stages of the lesson, |
|
| Homework (2 minutes) | writes the task on the board, comments on its completion (write out notes in a notebook, learn formulas and definitions; complete the problem). | write down the data in a diary, ask questions. |
Application
Route sheet No. 1
| Module and its task | Student action | Time to perform an action | ||
| Repetition Task: | ||||
| Discovery of new knowledge Task: | Write down the definition with page 59 in the textbook | |||
| Discovery of new knowledge Task: | Write down the equation with page 59 in the textbook | |||
| Discovery of new knowledge Task: | Write down definitions and formulas from pages 109 – 115 of the reference book | |||
| Discovery of new knowledge Task: | ||||
| Consolidation Task: consolidate acquired knowledge | ||||
| Reflection Task: summarize | Total: |
Route sheet No. 2
| Module and its task | Student action | Time to perform an action | Maximum number of points for a task |
|
| Repetition Task: repeat the graph of the sine and cosine function. | Draw a graph of the cosine and sine functions and determine their period. | |||
| Discovery of new knowledge Task: introduce the concept of harmonic oscillations | Find the definition in the reference book | |||
| Discovery of new knowledge Task: introduce the equation of motion of harmonic oscillations | Page 59 in the textbook | |||
| Discovery of new knowledge Task: introduce the characteristics of harmonic oscillations | Page 60 – 61 in the textbook | |||
| Discovery of new knowledge Task: introduce the concept of oscillation phase | Study pp. 62-64 in the textbook, write down the definition and formula | |||
| Consolidation Task: consolidate acquired knowledge | Solve the problem from collection No. 945 | |||
| Reflection Task: summarize | Have you achieved your goal? What was the hardest thing for you to understand or do? | Total: |
Group summary
| The result of working on the module | ||
Test Standard No. 1
| The result of working on the module | ||
| T= | ||
| Harmonic oscillations are periodic changes in a physical quantity depending on time, occurring according to the sine or cosine formula. | ||
| Period is the time of one complete oscillation. Period of oscillation of a mathematical pendulum Oscillation period of a spring pendulum Frequency is the number of complete oscillations per unit of time. |
DEPARTMENT OF EDUCATION AND SCIENCE OF KEMEROVSK REGION State budgetary educational institution of secondary vocational education "BELOVSKY TECHNIQUE OF RAILWAY TRANSPORT" Reshetnyak Natalya Aleksandrovna, teacher HARMONIC VIBRATIONS METHODOLOGICAL DEVELOPMENT OF AN OPEN PHYSICS LESSON Belovo 2013 Belt A comprehensive note. The methodological development is intended for conducting a physics lesson on the topic “Harmonic oscillations” in groups of students studying at the educational institution of secondary vocational education in professions 150709.02 Welder (electric welding and gas welding work), 230103.02 Digital information processing master, 140446.03 Electrician for repair and maintenance of electrical equipment (by industry). Lesson plan Topic: Mechanical oscillations Lesson topic: Harmonic oscillations Lesson type: learning new material Lesson objectives: * Students mastering the necessary knowledge on the lesson topic * Forming practical experience for students to apply acquired theoretical knowledge in practice * Forming students’ ability to plan their activities * Formation students have practical experience in performing a physical experiment * Formation in students to independently draw conclusions based on the experiments * Formation in students the ability to defend their point of view * Formation of the ability to organize work in a group, distribute roles in a team * Formation in students the ability to evaluate their own work and the work of others students of the KMO lesson: lesson plan, list of students, blackboard, chalk, questions for frontal survey, cards with tasks on the topic “Free and forced oscillations”, cards with tasks for experimental tasks, leaves, tripods with couplings, a load on a spring, a metal ball hanging, tape measure, container with water, threads, tape, scissors, magnets, workbooks, textbooks (Myakishev, G.Ya., Physics. 11th grade [Text]: textbook. for general education institutions: basic and profile. Levels / G.Ya.Myakishev, B.B. Bukhovtsev, V.M. Charugin; edited by N.A.Parfentieva. - 21st ed. - M.: Education, 2012. - 399 p., ill.) stationery (pens, pencils, rulers), calculators, stopwatches (in cell phones). Lesson duration: 45 minutes Venue: office No. 13 Level of students: 2nd year. Teacher: Reshetnyak N.A. Technological map of the lesson Time Content part of the lesson Teacher's activities Students' activities Didactic support 3 min Organizational part 1. Greeting 2. Roll call 3. Goal setting Greeting Roll call Greeting Roll call List of students 37 min Main part 8 min Updating basic knowledge 1. Frontal survey 2. Work on cards Survey Answers from the place Work in a notebook Appendix A Appendix B8 min Study of new material 1. Free vibrations occur according to the law of sine or cosine 2. Definition of harmonic vibrations 3. Amplitude of harmonic vibrations 4. Frequency of harmonic vibrations 5. A small historical digression Story, dialogue, demonstration Listening, participation in dialogue, writing down basic definitions and formulas in a notebook Appendix B21 min, including: 4 min 5 min 4 min 8 min Consolidating the learned material Solving experimental problems 1. Instruction, distribution of task cards 2. Conducting experiments 3. Recording the results in a notebook 4. Defense of work Briefing Consultation if necessary Listening, evaluation Work in small groups Defense of work, mutual evaluation Appendix D5 minFinal part Reflection. Homework Final form of politeness Lesson assessment Lesson assessmentQuestions for reflection - Appendix E List of references and sources 1. Myakishev, G.Ya., Physics. 11th grade [Text]: textbook. for general education institutions with adj. per electron media: basic and profile. levels / G.Ya.Myakishev, B.B.Bukhovtsev, V.M. Charugin; edited by N.A.Parfentieva. - 21st ed. - M.: Education, 2012. - 399 p., l. ill. - (Classical course). 2. Volkov, V.A. Universal lesson developments in physics [Text]: 11th grade. / V.A. Volkov. - M. : VAKO, 2011. - 464 p. - (To help the school teacher). 3. Kabardin, O.F. Physics [Text]: Reference. materials. Textbook manual for students. / O.F. Kabardin. - M.: Education, 1985. - 359 p., ill. 4. Landau, L.D. Physics for everyone [Text]: / L.D. Landau, A.I. Kitaygorodsky. - 3rd ed., erased. - M.: Nauka, 1974. - 392 p., ill. 5. Physics. 11th grade Basic level [Text]: / workbook for the textbook. - M.: VAP, 1994. - 286 p., ill. 6. Grigoriev, V.I. Forces in nature [Text]: / V.I. Grigoriev, G.Ya. Myakishev. - 5th ed., revised. - M.: Nauka, 1977. - 416 p., ill. 7. Moshchansky, V.N. History of physics in secondary school [Text]: / V.N Moshchansky, E.V. Savelova. - M.: Education, 1981. - 205 p., ill. 8. Enochovich, A.S. Handbook of Physics [Text]: / A.S. Enochovich. - 2nd ed., revised. and additional - M.: Education, 1990. - 384 p., ill. Appendix A Questions for frontal survey 1. What mechanical vibrations are called free, forced, damped? Give examples. 2. What is a mathematical pendulum? List the characteristics of a mathematical pendulum. 3. How do the speed and acceleration of a pendulum change during one period? What happens to the energy of the pendulum at this time? Appendix B Cards with tasks on the topic “Free and forced oscillations” Which of the listed oscillations are free and which are forced? Option 1 a) Fluctuations of leaves on trees during the wind. b) Heartbeat. c) Oscillations of a load on a spring. d) Vibrations of the string of a musical instrument after it is taken out of its equilibrium position and left to its own devices. e) Vibrations of the needle in the sewing machine. Option 2 a) Vibrations of the piston in the cylinder. b) Vibrations of a ball suspended on a thread. c) Vibrations of the vocal cords during singing. d) Oscillations of ears of corn in a field in the wind. e) Oscillations of the swing. Appendix B Text of a historical digression Galileo established the independence of the period of oscillation of a pendulum from amplitude and mass, observing during a service in the Pisa Cathedral how lamps swayed on a long suspension, and he measured the time by the beat of his own pulse. Appendix D Solution of experimental problems on the topic “Mechanical vibrations” Option 1 Make two pendulums from available means with weights of the same size and with suspensions of the same length, but one with a greater mass than the other. Deflect them at the same angle from the equilibrium position. Calculate the periods of their oscillations. Compare the obtained values. Draw a conclusion. Will the oscillations stop at the same time? Explain why. Option 2 Make an iron pendulum from available materials. Calculate the period of its oscillations. Will the period change if a magnet is placed under the pendulum? Check your assumption experimentally (place the magnet at a distance of 5-10 mm from the pendulum). Explain the results of the experiment. Option 3 Make a pendulum from available materials. Calculate the period of its oscillations. How long will it take for the vibrations to die out? Lower the pendulum into the water and again measure its period of oscillation and decay time. Compare the obtained values. Explain the results of the experiment. Option 4 Make a pendulum from available materials. Calculate the period of its oscillations. How should the length of the pendulum be changed so that the period doubles? Test your assumption experimentally. Draw a conclusion about how the period of oscillation of a pendulum depends on its length. Option 5 Make a pendulum from available materials. Calculate the frequency of its oscillations. How should the length of the pendulum be changed so that the frequency doubles? Test your assumption experimentally. Draw a conclusion about how the period of oscillation of a pendulum depends on its length. Appendix E Questions for reflection - What interested you most in class today? - How did you learn the material you covered? - What were the difficulties? Did you manage to overcome them? - Did today's lesson help you better understand the issues of the topic? - Will the knowledge you gained in today’s lesson be useful to you? 2