Physics lesson for grade 11 on the topic “Harmonic oscillations. Amplitude, period, frequency. Oscillation phase"
The purpose of the lesson: to introduce students to the concept of harmonic oscillations, to the conditions under which oscillations are considered harmonic, their characteristics, to prove that the oscillations of mathematical and spring pendulums are harmonic, to derive the formula for the periods of these pendulums, to show the impossibility of studying physics without knowledge of mathematics, to show that differential calculus and the concept of derivative - are the most powerful tools for studying and researching physical processes and phenomena.
Lesson type: a lesson in learning new knowledge.
Lesson duration: one academic hour.
Equipment: mathematical pendulum and spring pendulum, long paper tape 25 cm wide, color ink dropper, multimedia projector with whiteboard and PC with installed packageMicrosoft officeAndUE GRAN1.
Lesson structure and estimated time
indicativetime expenditure
I. Organizing time
1 minute
ІІ.
7 min
3.1 Motivation of educational activity of students (messages of the topic, purpose, tasks of the lesson and motivation of educational activity of schoolchildren)
3.2 Perception and primary awareness of new material, understanding of connections and relationships in the objects of study
3.4 Problem solving
30 minutes
(5 min +
15 minutes
2 minutes
8 min)
IV.Summing up the lesson
( homework report and reflection)
7 min
Epigraph for the lesson
:
"Science is one and indivisible"
Vladimir Ivanovich Vernadsky (1863-1945), academicianRussian AcademySciences ,
, co-founder and first president .
During the classes
I. Organizing time
ІІ. Checking homework, reproduction and correction of students' basic knowledge ( frontal ODA os ).
1. In what units are the values of angles measured in SI? (SI
2. What is called 1 radian? (φ== = rad=360 0 ⇒ 1 rad = ≈
≈57,3 0)
3. What is called angular velocity and what are the units of its measurement in SI?
ω===2πυ ; (SI)
4. How do the coordinates of a point change as it moves along a circle? (x=R=x max = x max ; y=R=y max y max )
5. What is called the derivative of a functionf(x)? What is the formula for the derivative?
( x )=
6. What is the derivative ((=)
((=)
X n (() ׳ = n )
nx ( ( nx ) ׳ = n )
7. What is the physical (mechanical) meaning of the derivative?
a) uniform movement:x=x ) + vt ( x ׳ ( t )=( X 0 + vt ) ׳ = v .
b) uniformly accelerated movement:x =x 0 + v 0 t + ( x ׳ ( t )= (X 0 + v 0 t +) ׳ = v 0 + at = v .
Conclusion No. 1 : The І-th derivative of the body coordinate with respect to time is equal to the speed of the body.
in)(X ׳׳ ( t )= (X 0 + v 0 t +) ׳׳ =( v 0 + at ) ׳ =a
Conclusion No. 2 : І І The th derivative of the coordinate of the body with respect to time is equal to the acceleration of the body. With uniform motionX ׳׳ ( t )= (X 0 + v 0 t ) ׳ =a=0 no acceleration.
III. Learning new material
3.1 Motivation of educational activity of students (messages of the topic, goals, objectives of the lesson and the motivation of the educational activities of schoolchildren -determine together with students, pay attention to the meaning of the epigraph, to the fact that the material of the lesson as an object of study will be considered not only from a physical, but also from a mathematical (algebraic) point of view, where mathematics acts as a tool).
3.2. Perception and primary awareness of new material, understanding of connections and relationships in the objects of study .
3.2.1. What is called oscillation? (periodically repetitive motion)
3.2.2. What are the characteristics of oscillations (what are the characteristics of oscillations)? (coordinate, amplitude, speed, period, frequency)
3.2.3 Therefore, from the point of view of mathematics, what functions should describe oscillations - linear, non-linear (power, logarithmic, trigonometric (periodic))? - logically, since hesitation is whatperiodically repeats, therefore, periodically.
3.2.4. Of the above functions, which ones are periodic? (trigonometric )
3.2.5. What do you know about periodic trigonometric functions? ()
3.2.6. What do you think, during the oscillations of the pendulum, how does its coordinate, speed and acceleration change - continuously or abruptly (discretely)? (Position, velocity and acceleration changecontinuously )
3.2.7. And since it is continuous, then which of the 4 trigonometric functions () should the quantities characterizing any oscillatory process be described? (Onlybecausethey are continuous andhave a gapshow charts ).
3.2.8. Definition of harmonic vibrations.
The quantity X (physical quantity) is considered to be harmonically oscillating (changing) if the 2nd derivative of this quantity is proportional to this quantity x itself, taken with the opposite sign:
(*) X - diff. eq. 2nd order (harmony conditionX )
3.2.9. Let us prove that only equations of the type:x=x max sin ω t and x=x max cos ω t
satisfy equation (*): =(sin ω t ) ’ = ω x max cos ω t .
=( ω x max cos ω t ) ’ = - ω 2 x max sin ω t = - ω 2 x .
=( cos ω t) ’ =- ω x max sins ω t.
=(- ω x max sin ω t) ’ = - ω 2 x max code ω t=- ω 2 x. FROM consequently :
Output: type equationsx= x=x max sin ω t sin ω t And x=x max cos ω t areharmonic.
3.2.10. Characteristics of harmonic equations
x=x max sin ω t
x=x max cos ω t , X max – oscillation amplitude,ω t - phase of oscillations,
ω is the cyclic oscillation frequency.
SI -rad, SI -rad / s, SI - m (if we are talking about mechanical vibrations)
Definition 1 : Amplitude harmonic vibrationsX max called the largest value of the fluctuating quantity, which is in front of the signsin orcos in the equation of harmonic equations.
Definition 2 : The period of harmonic oscillations T is the time of one oscillation
T = ; SI - from
Definition 3 : Harmonic frequencyυ called the number of oscillations per unit time.
υ = ; SI - from -1 ; Hz.
Definition 4 : Harmonic phaseφ called the physical quantity under the signsin orcos in the equation of harmonic equations and which, for a given amplitude, uniquely determines the value of the oscillating quantity.
φ = ω t ; SI - glad.
3.2.11. Let us prove that the oscillations of the pendulums are harmonic:
a) spring: F ex = -kx = ma; ⇒ a = - x ; Because a = x ” , then we have:
x ” = - x ⇒ spring ω 2 = ⇒ ω = = ; whereT = 2 π - formula for the period of oscillation of a spring pendulum.
b) mathematical (a load suspended on a weightless and inextensible thread, the dimensions of which, compared with its length, can be neglected)
F equinodes =-mgsin φ = ma ; ⇒ - gsin φ = a = x ” ; Because sin φ = ⇒ - g = “ x = - ω 2 x ; ⇒ mathematical the pendulum swings harmoniously. Becauseω 2 = ⇒ ω = = ; whereT = 2 π - formula for the period of oscillation of a mathematical pendulum.
3.2.12. Experience with a pendulum-inkwell (sandbox).
Output: Experience confirms that the pendulum oscillates harmonically (because the trace has the shape of a sinusoid).
3.3 Summing up a brief summary of the study of theoretical material.
3.4 Problem solving
3.4.1 Experimental task: experimentally find the period of oscillation of a spring pendulum, itsX max , write down the equation of its oscillations and findv max Anda max .(spring with stiffness 40 N/m, weight 400g)
T ≈ 0.67 s ⇒ υ == ≈ 1.5 Hz ⇒ x \u003d 0.05 cos2 π 1,5 t = 0,05 cos 3 π t .
V= (t)= - 0.15 π sin3 π t a=(t)=-0.45 π 2 cos3 π t
3.4.2 Tasks No. 4.1.5 and 4.1.6 (Collection of problems in physics, O.I. Gromtseva,
Exam, Moscow, 2015), p.67
3.4.3 Tasks No. 4.2.1 and 4.3.1. - for weak students;
№ 4.3.12 and No. 12.3.2 - for average and strong students.
IV .Summing up the lesson (homework report and reflection).
4.1 D.z.§ 13,14,15, p. 65 (tasks of the USE No. A1, A3), p. 68 (tasks for independent solution - two tasks for the student to choose from).
4.2 Reflection
.
DEPARTMENT OF EDUCATION AND SCIENCE OF THE KEMEROVO REGION state budgetary educational institution of secondary vocational education "BELOVSKY TECHNICAL CUM OF RAILWAY TRANSPORT" Reshetnyak Natalya Alexandrovna, teacher groups of students of OU SPO for professions 150709.02 Welder (electric welding and gas welding), 230103.02 Master in digital information processing, 140446.03 Electrician for the repair and maintenance of electrical equipment (by industry). Lesson plan Topic: Mechanical vibrations Lesson topic: Harmonic vibrations Lesson type: learning new material Lesson objectives: * Mastering the necessary knowledge on the topic of the lesson * Forming practical experience for students to apply the theoretical knowledge gained in practice * Forming students' ability to plan their activities * Formation for students of practical experience to put a physical experiment * Formation of students to independently draw conclusions based on the experiments performed * Formation of the ability of students to defend their point of view * Formation of the ability to organize work in a group, distribute roles in a team * Formation of students' ability to evaluate their own work and the work of others students of the CMO lesson: lesson plan, list of students, blackboard, chalk, questions for frontal survey, cards with tasks on the topic "Free and forced vibrations", cards with tasks for experimental tasks, leaflets, tripods with couplings, weight on spring, a metal ball on a suspension, a tape measure, a container of water, threads, adhesive tape, scissors, magnets, workbooks, textbooks (Myakishev, G.Ya., Physics. Grade 11 [Text]: textbook. for general education institutions: basic and profile. Levels / G.Ya.Myakishev, B.B.Bukhovtsev, V.M. Charugin; ed. N.A. Parfenteva. - 21st ed. - M.: Education, 2012. - 399 p., ill.) stationery (pens, pencils, rulers), calculators, stopwatches (in cell phones). Duration of the lesson: 45 minutes Venue: Room No. 13 Level of students: 2nd year. Lecturer: Reshetnyak N.A. Technological map of the lesson TimeContent of the lessonTeacher's activityStudents' activityDidactic support3 minOrganizational part 1. Greeting 2. Roll call 3. Goal setting Greeting Roll call Greeting Roll call List of students 37 min Main part 8 min Actualization of basic knowledge 1. Frontal survey 2. Work on cards Poll Answers from the spot Work in a notebook Appendix A Appendix B8 min Learning new material 1. Free vibrations are made according to the law of sine or cosine 2. Determination of harmonic vibrations 3. Amplitude of harmonic vibrations 4. Frequency of harmonic vibrations 5. Small historical digression Story, dialogue, demonstration Listening, participation in dialogue, writing in a notebook of basic definitions and formulas Appendix B21 min, including: 4 min 5 min 4 min 8 min Consolidation of the studied material Solving experimental problems 1. Briefing, distribution of cards with tasks 2. Conducting experiments 3. Drawing up results in a notebook 4. Defense of works Briefing Consultation if necessary Listening, evaluation Work in microgroups Defense of works, mutual evaluation Appendix G5 min Final part Reflection. Homework The final form of courtesy Evaluation of the lesson Evaluation of the lesson Questions for reflection - Appendix E List of references and sources 1. Myakishev, G.Ya., Physics. Grade 11 [Text]: textbook. for general education institutions with adj. to an electron. media: base and profile. levels / G.Ya. Myakishev, B.B. Bukhovtsev, V.M. Charugin; ed. N.A. Parfenteva. - 21st ed. - M.: Education, 2012. - 399 p., L. ill. - (Classic course). 2. Volkov, V.A. Universal lesson developments in physics [Text]: Grade 11. / V.A. Volkov. - M. : VAKO, 2011. - 464 p. - (To help the school teacher). 3. Kabardin, O.F. Physics [Text]: Ref. materials. Proc. allowance for students. / O.F. Kabardin. - M.: Enlightenment, 1985. - 359 p., ill. 4. Landau, L.D. Physics for all [Text]: / L.D. Landau, A.I. Kitaygorodsky. - 3rd ed., erased. - M.: Nauka, 1974. - 392 p., ill. 5. Physics. 11 cells 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 high school [Text]: / V.N. Moshchansky, E.V. Savelov. - M.: Enlightenment, 1981. - 205 p., ill. 8. Enohovich, A.S. Handbook of Physics [Text]: / A.S. Enochovich. - 2nd ed., revised. and additional - M.: Enlightenment, 1990. - 384 p., ill. Appendix A Questions for a 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 the 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 vibrations" Which of the listed vibrations are free and which are forced? Option 1 a) Vibrations of leaves on trees during the wind. b) heartbeat. c) Fluctuations of the load on the spring. d) Vibrations of the string of a musical instrument after it is taken out of equilibrium and left to itself. 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) Vibrations of ears in the field in the wind. e) Swing oscillations. Appendix B The text of the historical digression Galileo established the independence of the period of oscillation of the pendulum from the amplitude and mass, observing during the divine service in the Pisa Cathedral how the lamps sway on a long suspension, and he measured the time by the beating of his own pulse. Appendix D Solution of experimental problems on the topic "Mechanical vibrations" Option 1 Make two pendulums with weights of the same size and with suspensions of the same length, but one with a greater mass than the other. Deviate them by the same angle from the equilibrium position. Calculate the periods of their oscillations. Compare the received values. Make a conclusion. Will the vibrations stop at the same time? Explain why. Option 2 Make an iron pendulum from improvised means. 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 improvised means. Calculate the period of its oscillations. How long does it take for oscillations to decay? Lower the pendulum into the water and again measure its oscillation period and decay time. Compare the received values. Explain the results of the experiment. Option 4 Make a pendulum from improvised means. Calculate the period of its oscillations. How should the length of the pendulum be changed so that the period doubles? Test your guess experimentally. Draw a conclusion about how the period of oscillation of the pendulum depends on its length. Option 5 Make a pendulum from improvised means. Calculate the frequency of its oscillations. How should the length of the pendulum be changed to double the frequency? Test your guess experimentally. Draw a conclusion about how the period of oscillation of the pendulum depends on its length. Appendix D Questions for reflection - What interested you most in the lesson today? - How did you learn the material you studied? - What were the difficulties? Have you managed to overcome them? - Did today's lesson help you better understand the issues of the topic? - Will the knowledge gained in the lesson today be useful to you? 2
LESSON 2/24
Topic. Harmonic vibrations
The purpose of the lesson: to acquaint students with the concept of harmonic oscillations.
Type of lesson: lesson learning new material.
LESSON PLAN
Knowledge control |
1. Mechanical vibrations. 2. Main characteristics of vibrations. 3. Free vibrations. Conditions for the occurrence of free oscillations |
|
Demonstrations |
1. Free vibrations of a load on a spring. 2. Recording of oscillatory motion |
|
Learning new material |
1. The equation of the oscillatory motion of a load on a spring. 2. Harmonic vibrations |
|
Consolidation of the studied material |
1. Qualitative questions. 2. Learn to solve problems |
STUDY NEW MATERIAL
In many oscillatory systems, with small deviations from the equilibrium position, the modulus of rotational force, and hence the modulus of acceleration, is directly proportional to the modulus of displacement relative to the equilibrium position.
Let us show that in this case the displacement depends on time according to the cosine (or sine) law. To this end, we analyze the oscillations of the load on the spring. Let us choose as the origin the point where the center of mass of the load on the spring is in the equilibrium position (see figure).
If a load of mass m is displaced from the equilibrium position by x (for the equilibrium position x = 0), then the elastic force Fx = - kx acts on it, where k is the spring stiffness (the “-” sign means that the force is directed at any time in the direction opposite to the offset).
According to Newton's second law Fx = m ah. Thus, the equation describing the movement of the load has the form:
Denote ω2 = k / m . Then the equation of the movement of the load will look like:
An equation of this kind is called a differential equation. The solution to this equation is the function:
Thus, for the vertical displacement of the load on the spring from the equilibrium position, it will oscillate freely. The coordinate of the center of mass in this case changes according to the cosine law.
It is possible to verify that oscillations occur according to the law of cosine (or sine) by experiment. It is advisable for students to show a record of the oscillatory movement (see figure).
Ø Oscillations in which the displacement depends on time according to the cosine (or sine) law are called harmonic.
Free vibrations of a load on a spring are an example of mechanical harmonic vibrations.
Let at some point in time t 1 the coordinate of the oscillating load be x 1 = xmax cosωt 1 . According to the definition of the oscillation period, at time t 2 \u003d t 1 + T, the coordinate of the body must be the same as at time t 1, that is, x2 \u003d x1:
The period of the function cosωt is equal to 2, therefore, ωТ = 2, or
But since T \u003d 1 / v, then ω \u003d 2 v, that is, the cyclic oscillation frequency ω is the number of complete oscillations made in 2 seconds.
QUESTION TO STUDENTS DURING THE PRESENTATION OF NEW MATERIAL
First level
1. Give examples of harmonic oscillations.
2. The body performs undamped oscillations. Which of the quantities characterizing this movement are constant, and which ones change?
Second level
How do the force acting on the body, its acceleration and speed change during the implementation of harmonic oscillations?
CONFIGURATION OF THE STUDYED MATERIAL
1. Write the equation of a harmonic oscillation if its amplitude is 0.5 m and the frequency is 25 Hz.
2. Fluctuations of the load on the spring are described by the equation x \u003d 0.1 sin 0.5. Determine the amplitude, circular frequency and oscillation frequency.
Private educational institution "Crimean Republican
gymnasium-school-garden Console»
Simferopol
Republic of Crimea
Synopsis of an open lesson built in block-modular technology in physics in grade 11
Theme of the lesson "Harmonic vibrations"
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 oscillation, characteristics of the oscillatory process.
Lesson objectives:
Educational:
repeat
types of fluctuations;
the simplest systems of mechanical oscillations;
sine and cosine graphs;
enter
the concept of harmonic oscillations;
equation of motion of harmonic oscillations;
oscillation characteristics
learn
solve problems on the topic "Harmonic oscillations";
give real life examples.
Developing: development of independent thinking.
Educational: the formation of a sense of mutual assistance, the ability to work in groups, pairs.
Work form: group.
Resources (equipment): textbook 11 cells. 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 actions | Student action |
| Organizing time (5 minutes) | greeting students; mark missing in the log the teacher talks about the form of work in the lesson, introduces the route sheets and the rules for working with them (but don't distribute them to groups!!!), establishes a grading system. | teacher greeting; the attendant informs about the absent; 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. | Orally answer the teacher's questions on the topic of the previous lesson. |
|
| Goal setting (10 min) | demonstrates experience: 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 graph does the trajectory “drawn” by the cone look like? How will we call the oscillations, the movement of which is described by a harmonic function?) With leading questions, the teacher helps students to formulate the goal of the lesson, fixes it on the board. | observe a physical phenomenon; answer the teacher's questions; harmonic; harmonic; students write down the date and topic of the lesson in a notebook; state the purpose of the lesson. |
|
| Discovery of new knowledge (15 minutes) | distributes route sheets and recalls the rules for working with them; controls the performance of each group of students tasks in the route sheet; after each module produces the correct result. | study route sheets; perform tasks in the route sheet; the groups exchange route lists, check the correctness of the module execution and give points to the team. |
|
| Anchoring (8 min) |
|||
| Reflection (3 min) | sums up the work of students; asks students to orally answer the questions of the route sheet. | count the number of points; answer the questions in the route sheet, while noting the most difficult stages of the lesson, |
|
| Homework (2 minutes) | writes the task on the board, comments on its implementation (draw up a summary in a notebook, learn formulas and definitions; complete the task). | write down DZ in a diary, ask questions. |
Appendix
Route sheet No. 1
| Module and its task | Student action | Time to perform an action | ||
| Repetition A task: | ||||
| Discovery of new knowledge A task: | Write out the definition page 59 in the textbook | |||
| Discovery of new knowledge A task: | Write out the equation with page 59 in the textbook | |||
| Discovery of new knowledge A task: | Write out definitions and formulas from pages 109 - 115 of the reference book | |||
| Discovery of new knowledge A task: | ||||
| Anchoring A task: consolidate the acquired knowledge | ||||
| Reflection A task: summarize | Total: |
Route sheet No. 2
| Module and its task | Student action | Time to perform an action | Maximum points per task |
|
| Repetition A task: repeat the graph of the sine and cosine function. | Draw a graph of the cosine and sine functions, determine their period. | |||
| Discovery of new knowledge A task: introduce the concept of harmonic oscillations | Find a definition in the reference book | |||
| Discovery of new knowledge A task: introduce the equation of motion of harmonic oscillations | Page 59 in the textbook | |||
| Discovery of new knowledge A task: enter the characteristics of harmonic oscillations | Page 60 - 61 in the textbook | |||
| Discovery of new knowledge A task: introduce the concept of oscillation phase | Study pages 62-64 in the textbook, write down the definition and formula | |||
| Anchoring A task: consolidate the acquired knowledge | Solve the problem from the collection number 945 | |||
| Reflection A task: summarize | Have you achieved your goal? What was the most difficult thing for you to understand or do? | Total: |
Group summary
| The result of working on the module | ||
Reference for verification 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. The period of oscillation of a mathematical pendulum Oscillation period of a spring pendulum Frequency is the number of complete oscillations per unit of time. |
Lesson type: a lesson in the formation of new knowledge.
Lesson Objectives:
Equipment: spring and mathematical pendulums, a projector, a computer, a teacher's presentation, a disk "Library of visual aids", a sheet of knowledge assimilation by students, cards with symbols of physical quantities, the text "Resonance Phenomenon".
On each table is a sheet of learning for each student, a text about the phenomenon of resonance.
Teacher: To understand what the lesson will be about today, read an excerpt from the poem “Morning” by N.A. Zabolotsky
Born of the desert
The sound oscillates
fluctuates blue
Spider on a thread.
The air oscillates
Transparent and pure
In shining stars
The leaf is shaking.
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 vibrations(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).
Teacher: We should:
Teacher: Look at the oscillations of the mathematical and spring pendulums (oscillations are demonstrated). Are the vibrations exactly repeated?
Students: No.
Teacher: Why? It turns out that the friction force interferes. So what is hesitation? (slide 6)
Students: Oscillations are movements that repeat exactly or approximately over time.(slide 6, click). The definition is written in a notebook.
Teacher: Why do the fluctuations continue for so long? (slide 7) On a spring and mathematical pendulum, 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 to start fluctuations?
Students: You need to push the body, apply force to it. In order for the oscillations to last for a long time, it is necessary to reduce the friction force (slide 8), the conditions are written in a notebook.
Teacher: There are a lot of fluctuations. Let's try to classify them. Forced oscillations are demonstrated, on spring and mathematical pendulums - free oscillations (slide 9). Students write down the types of vibrations in a notebook.
Teacher: If the external force is constant, then the oscillations are called automatic (mouse click). Students in a notebook write down the definitions of free (slide 10), forced (slide 10, mouse click), automatic oscillations (slide 10 with a mouse click).
Teacher: There are also damped and undamped oscillations (slide 11 with a mouse click). Damped oscillations are oscillations that, under the action 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 with time; friction forces, no resistance. To maintain undamped oscillations, an energy source is needed (slide 13), these oscillations are shown on the graph on the slide.
Examples of fluctuations are given (slide 14).
1 option writes out examples damped vibrations.
Option 2 writes out examples undamped oscillations.
students among the given oscillations, examples of free and forced oscillations are written out according to the options, then they exchange information, 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 vibrations are damped, and forced vibrations are undamped. Find automatic oscillations among the given examples. Students rate themselves on the learning sheet in paragraph 1 of the learning sheet ( Attachment 1)
Teacher: Among all types of oscillations, a special type of oscillations 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 plotted on the model?
Students: This is a graph of the sine and cosine function (slide 16 with a mouse click).
students write down the equations of harmonic oscillations in a notebook.
Teacher: Now we need to consider each quantity in the harmonic equation. (Displacement X is shown on the mathematical and spring pendulums) (slide 17). X-displacement - deviation of the body from the equilibrium position. What is the unit of displacement?
Students: Meter (slide 17, mouse click).
Teacher: On the oscillation graph, determine the offset at times 1 s, 2 s, 3 s, 4 s, 5 s, 6 s, and so on. (slide 17, click). The next value is X max. What's this?
Students: Maximum offset.
Teacher: The maximum offset is called the amplitude (slide 18, mouse click).
students on the graphs, the amplitude of damped and undamped oscillations is determined (slide 18, mouse click).
Teacher: Before considering the next value, let us recall the concepts of quantities studied in the 1st course. 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 the 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 with different colors on the graph.
students on the chart, the period is determined by finding it between points of different colors.
Teacher on a mathematical pendulum demonstrates different frequencies for different lengths of the pendulum. Frequency v- 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/T T=1/ν (slide 20 mouse click).
Teacher: The sine and cosine function repeats 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, click).
Teacher: Oscillation phase- (ωt + φ 0) is the value under the sine or cosine sign. Measured in radians (rad) (slide 22).
The oscillation phase at the initial time (t=0) is called initial phase - φ 0 . Measured in radians (rad) (slide 21, mouse click).
Teacher: And now we repeat the material.
a) Students are shown cards with values, they name these values. ( Annex 2)
b) Students are shown cards with units of measurement of physical quantities. You need to name these values.
c) Each four students are given a card with some value, you need to tell everything about it according to the plan on slide 23. Then the groups change cards with values and perform the same task.
students give themselves grades on the progress sheet (paragraph 2 of 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, it 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 inversely proportional (slide 25)
Teacher: How do you push a car out if it's stuck?
Students: It is necessary 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 Visual Aids Library demonstrates a resonance model (Mechanics, Model 27 "Swinging a Spring Pendulum" at >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 Flower Waltz ( Appendix 4). The text is marked with the following signs (they are on the stand in the office): V - interested; + knew; - did not know; ? - I would like to know more. The text remains with each student in a notebook. In the next lesson, you need to return to it and answer students' questions if they do not find answers at home.
takes place in the form of tasks (slide 27). The problem is discussed at the blackboard.
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.
Teacher: What new did you learn at the lesson today?
Everyone learn the lesson summary. Solve the problem: according to the equation of harmonic oscillation, find everything that is possible (slide 29). Find answers to questions while marking text. Those who wish can find material about the benefits of resonance and the dangers of resonance (you can make a message, an abstract, prepare a presentation).
