Modern structural forms computer modeling. Computer modeling of physical processes. according to the type of mathematical scheme

Computer modeling is one of the effective methods studying physical systems. Computer models are often simpler and more convenient to study; they make it possible to carry out computational experiments, the real implementation of which is difficult or may give an unpredictable result. Logicality and formality computer models allows you to identify the main factors that determine the properties of the objects under study, to study the response physical system to changes in its parameters and initial conditions.

Computer modeling requires abstracting from the specific nature of phenomena, building first a qualitative and then a quantitative model. This is followed by a series of computational experiments on a computer, interpretation of the results, comparison of modeling results with the behavior of the object under study, subsequent refinement of the model, etc.

To the main stages computer modeling include: statement of the problem, definition of the modeling object; development conceptual model, identification of the main elements of the system and elementary acts of interaction; formalization, that is, the transition to a mathematical model; creating an algorithm and writing a program; planning and conducting computer experiments; analysis and interpretation of results.

There are analytical and simulation modeling. Analytical models are called models of a real object that use algebraic, differential and other equations, and also provide for the implementation of an unambiguous computational procedure leading to their exact solution. Simulation models are mathematical models that reproduce the algorithm of functioning of the system under study by sequentially executing large quantity elementary operations.

The modeling principles are as follows:

1. The principle of information sufficiency. At complete absence It is impossible to build a model using information about the object. In the presence of complete information modeling makes no sense. There is a level of information sufficiency, upon reaching which a model of the system can be built.
2. The principle of feasibility. The created model must ensure the achievement of the stated research goal in a finite time.
3. The principle of multiple models. Any specific model reflects only some aspects real system. For a complete study, it is necessary to build a number of models of the process under study, and each subsequent model must clarify the previous one.
4. Systematic principle. The system under study can be represented as a set of subsystems interacting with each other, which are modeled by standard mathematical methods. Moreover, the properties of the system are not the sum of the properties of its elements.
5. Principle of parameterization. Some subsystems of the simulated system can be characterized by a single parameter: vector, matrix, graph, formula.

Computer modeling of systems often requires solutions differential equations. An important method is the grid method, which includes Euler's finite difference method. It consists in replacing the area of continuous change of one or more arguments with a finite set of nodes forming a one-dimensional or multidimensional grid, and working with the function of a discrete argument, which makes it possible to approximately calculate derivatives and integrals. In this case, infinitesimal increments of the function f = f(x, y, z, t) and increments of its arguments are replaced by small but finite differences.

In the last decade, computer experiment has taken a prominent place in physical research. Computer modeling of physical systems allows one to obtain numerical information about them, as well as based on graphic images makes it possible to get an idea of the object, with the help of which optimal ways to study the object can be developed. Among the mathematical methods for describing physical systems and phenomena and their numerical analysis, one of the main ones is modeling these objects and processes based on the Monte Carlo method. This method is especially useful for complex physical systems with cumbersome mathematical descriptions. Serious progress in the use of the Monte Carlo method is associated to a large extent with the new capabilities of modern computer technology. If twenty years ago, at the initial stage of modeling, the object under study could be divided in one dimension into about a hundred Monte Carlo steps, now in simple models the scale of one dimension is millions of Monte Carlo steps. The speed of obtaining information has also increased significantly. As a result, it is possible to study the properties of physical systems using realistic models. Currently, the capabilities of computer modeling in solving a number of problems significantly exceed the capabilities of experiment, both in terms of the speed of obtaining information and its cost. This increases the role of computer experiment in modern physics, and in a number of areas of physics our modern ideas are based mainly on information obtained from computer modeling.

It is clear that for progress in the area under consideration, along with perfect computer technology It is necessary to have algorithms and approaches that allow you to effectively manage it. These problems, together with the analysis of the corresponding physical systems, constitute the modern content of computer simulation using the Monte Carlo method.

Let's start with the definition of the word modeling.

Modeling is the process of constructing and using a model. A model is understood as a material or abstract object that, in the process of study, replaces the original object, preserving its properties that are important for this study.

Computer modeling as a method of cognition is based on mathematical modeling. A mathematical model is a system of mathematical relationships (formulas, equations, inequalities and sign logical expressions) reflecting the essential properties of the object or phenomenon being studied.

It is very rarely possible to use a mathematical model for specific calculations without the use of computer technology, which inevitably requires the creation of some kind of computer model.

Let's look at the computer modeling process in more detail.

2.2. Introduction to Computer Modeling

Computer modeling is one of the effective methods of studying complex systems. Computer models are easier and more convenient to study due to their ability to conduct computational experiments in cases where real experiments are difficult due to financial or physical obstacles or may give unpredictable results. The logic of computer models makes it possible to identify the main factors that determine the properties of the original object under study (or an entire class of objects), in particular, to study the response of the simulated physical system to changes in its parameters and initial conditions.

Computer modeling how new method scientific research is based on:

1. Construction of mathematical models to describe the processes being studied;

2. Using the latest computers, with high performance (millions of operations per second) and capable of conducting a dialogue with a person.

Distinguish analytical And imitation modeling. In analytical modeling, mathematical (abstract) models of a real object are studied in the form of algebraic, differential and other equations, as well as those involving the implementation of an unambiguous computational procedure leading to their exact solution. In simulation modeling, mathematical models are studied in the form of an algorithm that reproduces the functioning of the system under study by sequentially performing a large number of elementary operations.

2.3. Building a computer model

The construction of a computer model is based on abstraction from the specific nature of phenomena or the original object being studied and consists of two stages - first creating a qualitative and then a quantitative model. Computer modeling consists of conducting a series of computational experiments on a computer, the purpose of which is to analyze, interpret and compare the modeling results with the real behavior of the object under study and, if necessary, subsequent refinement of the model, etc.

So, The main stages of computer modeling include:

1. Statement of the problem, definition of the modeling object:

on at this stage information is collected, a question is formulated, goals are defined, forms for presenting results, and data is described.

2. System analysis and research:

system analysis, meaningful description of the object, development information model, analysis of technical and software, development of data structures, development of a mathematical model.

3. Formalization, that is, the transition to a mathematical model, the creation of an algorithm:

choosing a method for designing an algorithm, choosing a form for writing an algorithm, choosing a testing method, designing an algorithm.

4. Programming:

choosing a programming language or application environment for modeling, clarifying ways to organize data, writing an algorithm in the selected programming language (or in an application environment).

5. Conducting a series of computational experiments:

debugging syntax, semantics and logical structure, test calculations and analysis of test results, finalization of the program.

6. Analysis and interpretation of results:

modification of the program or model if necessary.

There are many software systems and environments that allow the construction and study of models:

Graphics environments

Text editors

Programming environments

Spreadsheets

Math packages

HTML editors

2.4. Computational experiment

An experiment is an experience that is performed with an object or model. It consists of performing certain actions to determine how the experimental sample reacts to these actions. A computational experiment involves carrying out calculations using a formalized model.

Using a computer model that implements a mathematical one is similar to conducting experiments with a real object, only instead of a real experiment with an object, a computational experiment is carried out with its model. By specifying a specific set of values of the initial parameters of the model, as a result of a computational experiment, a specific set of values of the required parameters is obtained, the properties of objects or processes are studied, and they are found optimal parameters and operating modes, specify the model. For example, having an equation that describes the course of a particular process, you can, by changing its coefficients, initial and boundary conditions, study how the object will behave. Moreover, it is possible to predict the behavior of an object in different conditions. To study the behavior of an object with a new set of initial data, it is necessary to conduct a new computational experiment.

To check the adequacy of the mathematical model and the real object, process or system, the results of computer research are compared with the results of an experiment on a prototype full-scale model. The test results are used to adjust the mathematical model or the question of the applicability of the constructed mathematical model to design or research is resolved given objects, processes or systems.

A computational experiment allows you to replace an expensive full-scale experiment with computer calculations. It allows you to carry out research in a short time and without significant material costs. large number options for the designed object or process for different modes its operation, which significantly reduces the development time of complex systems and their implementation in production.

2.5. Simulation in various environments

2.5.1. Simulation in a programming environment

Modeling in a programming environment includes the main stages of computer modeling. At the stage of building an information model and algorithm, it is necessary to determine which quantities are input parameters and which are results, and also determine the type of these quantities. If necessary, an algorithm is drawn up in the form of a block diagram, which is written in the selected programming language. After this, a computational experiment is carried out. To do this, you need to download the program to RAM computer and run it. A computer experiment necessarily includes an analysis of the results obtained, on the basis of which all stages of solving the problem (mathematical model, algorithm, program) can be adjusted. One of the most important stages is testing the algorithm and program.

Debugging a program (the English term debugging means “catching bugs” appeared in 1945, when electrical circuits one of the first Mark-1 computers was hit by a moth and blocked one of the thousands of relays) - this is the process of finding and eliminating errors in the program, carried out based on the results of a computational experiment. During debugging, localization and elimination occurs syntax errors and obvious coding errors.

In modern software systems, debugging is carried out using special software tools called debuggers.

Testing is checking the correct operation of the program as a whole or its components. The testing process checks the functionality of the program and does not contain obvious errors.

No matter how carefully the program is debugged, the decisive stage that establishes its suitability for work is monitoring the program based on the results of its execution on the test system. A program can be considered correct if, for the selected system of test input data, correct results are obtained in all cases.

2.5.2. Modeling in Spreadsheets

Modeling in spreadsheets covers a very wide class of problems in different subject areas. Spreadsheets are a universal tool that allows you to quickly perform labor-intensive work on calculating and recalculating the quantitative characteristics of an object. When modeling using spreadsheets, the algorithm for solving the problem is somewhat transformed, hiding behind the need to develop a computing interface. The debugging stage is retained, including the elimination of data errors in connections between cells and in computational formulas. Additional tasks also arise: work on the convenience of presentation on the screen and, if it is necessary to output the received data on paper, on their placement on sheets.

The spreadsheet modeling process is performed using general scheme: goals are defined, characteristics and relationships are identified, and a mathematical model is compiled. The characteristics of the model are necessarily determined by purpose: initial (affecting the behavior of the model), intermediate, and what is required to be obtained as a result. Sometimes the representation of an object is supplemented with diagrams and drawings.

To visually display the dependence of calculation results on the initial data, charts and graphs are used.

Testing uses a certain set of data for which the exact or approximate result is known. The experiment consists of introducing input data that satisfies the modeling goals. Analysis of the model will make it possible to find out how well the calculations meet the modeling goals.

2.5.3. Modeling in a DBMS environment

Modeling in a DBMS environment usually pursues the following goals:

Storing information and editing it in a timely manner;

Organizing data according to certain criteria;

Creation of various data selection criteria;

Convenient presentation of selected information.

In the process of developing the model, the structure of the future database is formed based on the initial data. The described characteristics and their types are summarized in a table. The number of table columns is determined by the number of object parameters (table fields). The number of rows (table records) corresponds to the number of rows of described objects of the same type. A real database may have not one, but several tables interconnected. These tables describe the objects included in a certain system. After defining and specifying the structure of the database in the computer environment, they proceed to filling it.

During the experiment, data is sorted, searched and filtered, and calculation fields are created.

The computer dashboard provides the ability to create various screen forms and forms for displaying information in printed form– reports. Each report contains information relevant to the purpose of the particular experiment. It allows you to group information according to specified characteristics, in any order, with the introduction of final calculation fields.

If the results obtained do not correspond to the planned ones, you can conduct additional experiments by changing the conditions for sorting and searching for data. If there is a need to change the database, you can adjust its structure: change, add and delete fields. The result is a new model.

2.6. Using a computer model

Computer modeling and computational experiment as a new method of scientific research makes it possible to improve the mathematical apparatus used in constructing mathematical models, allowing, using mathematical methods, clarify, complicate mathematical models. The most promising for conducting a computational experiment is its use for solving major scientific, technical and socio-economic problems of our time, such as the design of reactors for nuclear power plants, the design of dams and hydroelectric power plants, magnetohydrodynamic energy converters, and in the field of economics - drawing up a balanced plan for the industry, region, country, etc.

In some processes where a natural experiment is dangerous to human life and health, a computational experiment is the only possible one (thermonuclear fusion, space exploration, design and research of chemical and other industries).

2.7. Conclusion

In conclusion, it can be emphasized that computer modeling and computational experiment make it possible to reduce the study of a “non-mathematical” object to a solution mathematical problem. This opens up the possibility of using a well-developed mathematical apparatus in combination with powerful computing technology to study it. This is the basis for the use of mathematics and computers to understand laws. real world and their use in practice.

3. List of references used

1. S. N. Kolupaeva. Mathematical and computer modeling. Tutorial. – Tomsk, School University, 2008. – 208 p.

2. A. V. Mogilev, N. I. Pak, E. K. Henner. Computer science. Tutorial. – M.: Center “Academy”, 2000. – 816 p.

3. D. A. Poselov. Computer science. Encyclopedic Dictionary. – M.: Pedagogika-Press, 1994. 648 p.

4. Official website of the publishing house "Open Systems". Internet University of Information Technologies. - Access mode: http://www.intuit.ru/. Date of access: October 5, 2010

Kobelnitsky Vladislav

Computer modelling. Simulation of physical and mathematical processes on a computer.

Download:

Preview:

Research

"COMPUTER MODELLING"

COMPLETED:

KOBELNITSKY VLADISLAV

9TH CLASS STUDENT

MKOU secondary school No. 17

Supervisor:

mathematics and computer science teacher

Tvorozova E.S.

KANSK, 2013

INTRODUCTION………………………………………………………………………………3
COMPUTER SIMULATION…………………………………...5
PRACTICAL PART……………………………………………………………..10
CONCLUSION……………………………………………………………...18
REFERENCES……………………………………………………………...20

INTRODUCTION

In most areas of human activity it is currently used computer technology. For example, in a hairdresser you can use a computer to select in advance the hairstyle that the client will like. For this client, a photograph is taken, a photograph in in electronic format are entered into a program containing a wide variety of hairstyles, a photo of the client is displayed on the screen, to whom you can “try on” any hairstyle. You can also easily choose hair color and makeup. Using a computer model, you can see in advance whether a particular hairstyle will suit the client. Of course, this option is better than conducting the experiment in reality, in real life It is much more difficult to correct an undesirable situation.

While studying a topic in computer science, “Computer Modeling,” I became interested in the question: “Can any process or phenomenon be simulated using a PC?” This was the choice for my research.

Topic of my research:"Computer modelling".

Hypothesis: any process or phenomenon can be simulated using a PC.

Goal of the work - study the possibilities of computer modeling and its use in various subject areas.

To achieve this goal, the work solves the following: tasks:

- give theoretical information about modeling;

– describe the stages of modeling;

– give examples of models of processes or phenomena from various subject areas;

Draw a general conclusion about computer modeling in subject areas.

I decided to take a closer look at computer modeling in MS Excel and Living Mathematics. The paper discusses the advantages of MS Excel. Using these programs, I built computer models from various subject areas, such as mathematics, physics, and biology.

Building and studying models is one of the most important methods of cognition; the ability to use a computer to build models is one of the requirements today, hence I think this work relevant. It is important for me, since I want to continue my further studies in this direction, as well as consider other programs when developing computer models, this is the goal for further continuation of this work.

COMPUTER MODELLING

Analyzing the literature on the topic of research, I found out that in almost all natural and social sciences, the construction and use of models is powerful tool research. Real objects and processes are so multifaceted and complex that the best way their study turns out to be the construction of a model that reflects only some part of reality and is therefore many times simpler than this reality.

Model (Latin modulus - measure) is a substitute object for the original object, providing the study of some properties of the original.

Model - a specific object created for the purpose of receiving and (or) storing information (in the form of a mental image, description by means of signs, or material system), reflecting the properties, characteristics and connections of an object - an original of arbitrary nature, essential for the problem solved by the subject.

Modeling – the process of creating and using a model.

Modeling Goals

Knowledge of reality
Conducting experiments
Design and management
Predicting the behavior of objects
Training and education of specialists
Data processing

Classification by presentation form

Material - reproduce the geometric and physical properties of the original and always have a real embodiment (children's toys, visual teaching aids, layouts, models of cars and airplanes, etc.).

a) geometrically similar scale, reproducing the spatial and geometric characteristics of the original regardless of its substrate (models of buildings and structures, educational models, etc.);
b) based on the theory of similarity, substrate-like, reproducing with scaling in space and time the properties and characteristics of the original of the same nature as the model (hydrodynamic models of ships, purging models of aircraft);
c) analog instruments that reproduce the studied properties and characteristics of the original object in a modeling object of a different nature based on some system of direct analogies (a type of electronic analog modeling).

Information - a set of information characterizing the properties and states of an object, process, phenomenon, as well as their relationship with the outside world).

2.1. Verbal - verbal description in natural language).
2.2. Iconic - information model expressed special signs(by means of any formal language).

2.2.1. Mathematical - mathematical description of the relationships between the quantitative characteristics of the modeling object.
2.2.2. Graphic - maps, drawings, diagrams, graphs, diagrams, system graphs.
2.2.3. Tabular - tables: object-property, object-object, binary matrices and so on.

Ideal – a material point, an absolutely rigid body, a mathematical pendulum, an ideal gas, infinity, a geometric point, etc....

3.1. Unformalizedmodels are systems of ideas about the original object that have developed in the human brain.
3.2. Partially formalized.

3.2.1. Verbal - a description of the properties and characteristics of the original in some natural language (text materials of project documentation, verbal description of the results of a technical experiment).
3.2.2. Graphic iconic - features, properties and characteristics of the original that are actually or at least theoretically accessible directly to visual perception (art graphics, technological maps).
3.2.3. Graphical symbols - observational data and experimental research in the form of graphs, diagrams, diagrams.

3.3. Quite formalized(mathematical) models.

Model properties

Limb : the model reflects the original only in a finite number of its relations and, in addition, modeling resources are finite;
Simplification : the model displays only the essential aspects of the object;
Approximation: reality is represented roughly or approximately by the model;
Adequacy : how successfully the model describes the system being modeled;
Information content: the model must contain sufficient information about the system - within the framework of the hypotheses adopted when constructing the model;
Potentiality: predictability of the model and its properties;
Complexity : ease of use;
Completeness : all necessary properties are taken into account;
Adaptability.

It should also be noted:

The model is a “quadruple construct”, the components of which are the subject; problem solved by the subject; the original object and description language or method of reproducing the model. The problem solved by the subject plays a special role in the structure of the generalized model. Outside the context of a problem or class of problems, the concept of a model has no meaning.
Each material object, generally speaking, corresponds to an infinite number of equally adequate, but essentially different models associated with different tasks.
The task-object pair also corresponds to many models that contain, in principle, the same information, but differ in the forms of its presentation or reproduction.
A model, by definition, is always only a relative, approximate similarity to the original object and in informationally fundamentally poorer than the latter. This is its fundamental property.
The arbitrary nature of the original object, which appears in the accepted definition, means that this object can be material, can be of a purely informational nature, and, finally, can be a complex of heterogeneous material and information components. However, regardless of the nature of the object, the nature of the problem being solved and the method of implementation, the model is an information formation.
A particular, but very important for theoretically developed scientific and technical disciplines is the case when the role of a modeling object in research or applied problem What plays is not a fragment of the real world, considered directly, but some ideal construct, i.e. in fact, another model, created earlier and practically reliable. Such is secondary, and in general case n-fold simulation can be carried out theoretical methods with subsequent verification of the results obtained using experimental data, which is typical for fundamental natural sciences. In less theoretically developed areas of knowledge (biology, some technical disciplines), the secondary model usually includes empirical information that is not covered by existing theories.

The process of building a model is called modeling.

Due to the polysemy of the concept of “model”, there is no such thing as science and technology. unified classification types of modeling: classification can be carried out by the nature of the models, by the nature of the objects being modeled, by the areas of application of modeling (in engineering, physical sciences, cybernetics, etc.). For example, you can highlight the following types modeling:

Information Modeling
Computer modelling
Math modeling
Mathematical cartographic modeling
Molecular modeling
Digital modeling
Logic modeling
Pedagogical modeling
Psychological modeling
Statistical Modeling
Structural Modeling
Physical modeling
Economic and mathematical modeling
Simulation modeling
Evolutionary modeling
Graphic and geometric modeling
Full-scale modeling

Computer modellingincludes the process of implementing an information model on a computer and researching a modeling object using this model - conducting a computational experiment. With the help of computer modeling, many scientific and industrial issues are solved.

Isolating the essential aspects of a real object and abstracting from its secondary properties from the point of view of the task at hand allows one to develop analytical skills. Implementing an object model on a computer requires knowledge application programs, as well as programming languages.

In the practical part, I built models according to the following scheme:

Statement of the problem (description of the problem, modeling goals, formalization of the problem);
Model development;
Computer experiment;
Analysis of simulation results.

PRACTICAL PART

Modeling of various processes and phenomena

Work 1 “Determination of the specific heat capacity of a substance.”

Purpose of the work: to experimentally determine the specific heat capacity of a given substance.

First stage

Second phase

Entering the values of the measured quantities.
Introduction of formulas for calculating the specific heat capacity of a substance.
Calculation of specific heat capacity.

Third stage . Compare the tabulated and experimental values of heat capacity.

Determination of the specific heat capacity of a substance

Exchange of internal energy between bodies and environment without committing mechanical work called heat transfer.

During heat exchange, the interaction of molecules of bodies having different temperatures leads to the transfer of energy from the body with higher temperature to a body with a lower temperature.

If heat exchange occurs between bodies, then the internal energy of all heating bodies increases by as much as the internal energy of cooling bodies decreases.

Work order:

Weigh the inner aluminum vessel of the calorimeter. Pour water into it, up to about half of the vessel and weigh it again to determine the mass of water in the vessel. Measure the initial temperature of the water in the vessel.

From a vessel with boiling water common to the whole class, carefully, so as not to burn your hand, remove a metal cylinder with a wire hook and lower it into the calorimeter.

Monitor the increase in water temperature in the calorimeter. When the temperature reaches its maximum value and stops increasing, record its value in the table.

Remove the cylinder from the vessel, dry it with filter paper, weigh it and record the mass of the cylinder in the table.

From the heat balance equation

c 1 m 1 (T-t 1 )+c 2 m 2 (T-t 1 )=cm(t 2 -T)

Calculate the specific heat capacity of the substance from which the cylinder is made.

m 1 – mass of the aluminum vessel;

c 1 – specific heat capacity of aluminum;

m 2 - mass of water;

from 2 - specific heat capacity of water;

t 1 - initial water temperature

m - cylinder mass;

t 2 - initial temperature of the cylinder;

T - general temperature

Work 2 “Study of oscillations of a spring pendulum”

Purpose of the work: to determine experimentally the stiffness of the spring and determine the frequency of oscillation of the spring pendulum. Find out the dependence of the oscillation frequency on the mass of the suspended load.

First stage . A mathematical model is compiled.

Second phase . Working with the compiled model.

Enter formulas to calculate the spring constant value.
Introduction to the cells of formulas for calculating the theoretical and experimental values of the oscillation frequency of a spring pendulum.
Conducting experiments by suspending loads of various masses from a spring. Enter the results in the table.

Third stage . Draw a conclusion about the dependence of the oscillation frequency on the mass of the suspended load. Compare the theoretical and experimental frequency values.

Description of work in the laboratory workshop:

A load suspended on a steel spring and brought out of equilibrium moves under the influence of gravity and the elasticity of the spring harmonic vibrations. The natural frequency of oscillation of such a spring pendulum is determined by the expression

where k – spring stiffness; m – body weight.

Task laboratory work is to experimentally verify the theoretically obtained pattern. To solve this problem, you first need to determine the stiffness k springs used in a laboratory installation, mass m load and calculate the natural frequency 0 pendulum oscillations. Then, hanging a load of mass m on the spring, experimentally verify the theoretical result obtained.

Completing of the work.

1. Fasten the spring in the tripod leg and hang a load weighing 100 g from it. Next to the load, attach a measuring ruler vertically and mark starting position cargo

2. Hang two more weights of 100 g each to the spring and measure its elongation caused by the action of force F2Н. Enter the force value F and extension x into the table and you will get the hardness value k springs, calculated by the formula

3. Knowing the spring stiffness, calculate the natural frequency 0 oscillations of a spring pendulum weighing 100, 200, 300 and 400 g.

4. For each case, experimentally determine the oscillation frequency pendulum. To do this, measure the time intervalt, during which the pendulum will make 10-20 complete oscillations, and you will receive the frequency value calculated by the formula

where n – number of oscillations.

5. Compare calculated values natural frequency 0 oscillations of a spring pendulum with a frequency , obtained experimentally.

Work 3 “Law of conservation of mechanical energy”

Purpose of the work: to experimentally test the law of conservation of mechanical energy.

First stage . Drawing up a mathematical model.

Second phase . Working with the compiled model.

Entering data into a spreadsheet.
Enter formulas to calculate the value of potential and kinetic energy.
Conducting experiments. Enter the results in the table.

Third stage . Compare the kinetic energy of the ball and the change in its potential energy and draw a conclusion.

Description of work in laboratory workshop

CHECKING THE LAW OF CONSERVATION OF MECHANICAL ENERGY.

In the work, it is necessary to experimentally establish that the total mechanical energy of a closed system remains unchanged if only gravitational and elastic forces act between the bodies.

The setup for the experiment is shown in Figure 1. When rod A deviates from a vertical position, the ball at its end rises to a certain height h relative to entry level. In this case, the Earth-ball system of interacting bodies acquires an additional reserve of potential energyΔEp=mgh.

If the rod is released, it will return to vertical position to a special stop. Considering the friction forces and changes in the potential energy of elastic deformation of the rod to be very small, we can assume that during the movement of the rod only gravitational forces and elastic forces act on the ball. Based on the law of conservation of mechanical energy, we can expect that the kinetic energy of the ball at the moment of passing starting position will be equal to the change in its potential energy:

To determine the kinetic energy of the ball, it is necessary to measure its speed. To do this, fix the device in the tripod leg at a height H above the table surface, move the rod with the ball to the side and then release it. When the rod hits the stop, the ball jumps off the rod and, due to inertia, continues to move at speed v in the horizontal direction. Measuring the range of the ball l when it moves along a parabola, you can determine the horizontal speed v:

where t - time of free fall of a ball from a height H.

Having determined the mass of the ball m using scales, you can find its kinetic energy and compare it with the change in potential energyΔEp.

In the practical part of this work, I built models physical processes, as well as mathematical models, a description of laboratory work is given.

As a result of the work, I built the following models:

Physical models of body motion (Ms Excel, physics subject)

Uniform rectilinear motion, uniformly accelerated motion (Ms Excel, physics subject);

Movements of a body thrown at an angle to the horizon (Ms Excel, physics subject);

Movements of bodies taking into account the force of friction (Ms Excel, physics subject);

Movements of bodies taking into account many forces acting on the body (Ms Excel, physics subject);

Determination of the specific heat capacity of a substance (Ms Excel, physics subject);

Oscillations of a spring pendulum (Ms Excel, physics subject);

Mathematical model for calculating arithmetic and algebraic progression; (Ms Excel, subject algebra);

Computer model of modification variability (Ms Excel, biology subject);

Construction and study of function graphs in the “Living Mathematics” program.

After building the models, we can conclude: in order to correctly build a model, it is necessary to set a goal, I adhered to the scheme presented in the theoretical part.

Conclusion

I have discovered the benefits of using Excel programs:

A) functionality Excel programs obviously cover all the needs for automation of experimental data processing, construction and research of models; b) has understandable interface; V) learning Excel is provided for by general education programs in computer science, therefore, it is possible efficient use Excel; G) this program it is accessible to study and easy to manage, which is fundamentally important for me as a student; e) results of activities at work Excel sheet(texts, tables, graphs, formulas) are “open” to the user.

Among all known software Excel tools has perhaps the richest tools for working with charts. The program allows you to use auto-completion techniques to present data in tabular form, quickly convert them using a huge library of functions, build graphs, edit them for almost all elements, enlarge the image of any fragment of the graph, select functional scales along the axes, extrapolate graphs, etc.

To summarize the work, I would like to conclude: the goal set at the beginning of this study was achieved. My research has shown that it is indeed possible to simulate any process or phenomenon. The hypothesis I posed is correct. I was convinced of this when I built a sufficient number of such models. To build any model, you need to adhere to certain rules, which I described in the practical part of this work.

This research will be continued, other programs that allow modeling processes will be studied.

BIBLIOGRAPHY

Degtyarev B.I., Degtyareva I.B., Pozhidaev S.V. , Solving problems in physics on programmable calculators, M., Prosveshchenie, 1991.
Demonstration experiment in physics in high school. Ed. Pokrovsky A.A., M. Education, 1972
Dolgolaptev V. Working in Excel 7.0. for Windows 95.M., Binom, 1995
Efimenko G.E. Solving environmental problems using spreadsheets. Informatics, No. 5 – 2000.
Zlatopolsky D.M., Solving equations using spreadsheets. Informatics, No. 41 – 2000
Ivanov V. Microsoft Office System 2003. Russian version. Publishing house "Peter", 2005
Izvozchikov V.A., Slutsky A.M., Solving problems in physics on a computer, M., Prosveshchenie, 1999.
Nechaev V.M. Spreadsheets and databases. Informatics, No. 36-1999
Programs for general education institutions. Physics grades 7-11, M., Bustard, 2004
Saikov B.P. Excel: charting. Computer Science and Education No. 9 – 2001
Collection of problems in physics. Ed. S.M. Kozela, M., Science, 1983
Semakin I.G. , Sheina T.Yu, Teaching basic course computer science in high school., M., publishing house Binom, 2004.
Physics lesson in modern school. Ed. V.G.Razumovsky, M.Prosveshchenie, 1993

Modeling is one of the ways to understand the world.

The concept of modeling is quite complex; it includes a huge variety of modeling methods: from creating natural models (reduced and or enlarged copies of real objects) to deriving mathematical formulas.

For various phenomena and processes are appropriate different ways modeling for the purpose of research and knowledge.

The object that is obtained as a result of modeling is called model. It should be clear that this is not necessarily a real object. It could be mathematical formula, graphical representation and so on. However, it may well replace the original when studying it and describing behavior.

Although a model can be an exact copy of the original, most often the models recreate some elements that are important for a given study, and neglect the rest. This simplifies the model. But on the other hand, to create a model - exact copy original - can be an absolutely unrealistic task. For example, if the behavior of an object in space conditions is simulated. We can say that a model is a certain way of describing the real world.

Modeling goes through three stages:

Creating a model.
Studying the model.
Application of research results in practice and/or formulation of theoretical conclusions.

Types of modeling great amount. Here are some examples of model types:

Mathematical models. These are iconic models that describe certain numerical relationships.

Graphic models. Visual representation objects that are so complex that describing them in other ways does not give a person a clear understanding. Here the clarity of the model comes to the fore.

Simulation models. They allow you to observe changes in the behavior of elements of the model system and conduct experiments by changing some parameters of the model.

Specialists from different areas, because In modeling, the role of interdisciplinary connections is quite large.

Features of computer modeling

Improved computing technology and widespread distribution personal computers modeling has opened up enormous prospects for studying the processes and phenomena of the surrounding world, including human society.

Computer modeling is to a certain extent, the same modeling described above, but implemented using computer technology.

For computer modeling, it is important to have certain software.

Wherein software, by means of which computer modeling can be carried out, can be quite universal (for example, ordinary text and GPUs), and very specialized, intended only for certain type modeling.

Very often computers are used for mathematical modeling. Here their role is invaluable in performing numerical operations, while the analysis of the problem usually falls on the shoulders of a person.

Typically in computer simulation different kinds simulations complement each other. So, if the mathematical formula is very complex, which does not give a clear idea of the processes it describes, then graphical and simulation models. Computer imaging can be much cheaper real creation natural models.

With the advent of powerful computers, graphic modeling based on engineering systems to create drawings, diagrams, graphs.