Physics Laboratory with Introduction to Statistics
A.Y. 2024/2025
Learning objectives
The course of Physics Laboratory with Introduction to Statistic has two main learning objectives: a) to provide the student the necessary mathematical competences for the statistical treatement of data from observations and experiments; b) to approach the physics of mechanical oscillating systems by a series of laboratory experiments. The latter allows the student to acquire skills in the planning of an experiment, in the collection of experimental data and in their statistical analysis, in the understanding of the issues met in the passing from an ideal theoretical model to a real-world experiment.
Expected learning outcomes
At the end of the course, the student:
1) will understand the concepts of statistical and systematic errors
2) will know the fundamentals of the theory of probability and the concepts of distributions, both discrete and continuous
3) will know some important distributions (binomial, Poisson, Gauss, chi-square, Student's t) and will be able to apply them in real-world applications.
4) will be able to perform the basic data analyses (computation of mean, standard deviation, correlation)
5) will be able to quantitatively check the observed data against models (probability distributions, linear functions, power functions, exponential functions) using linear regression and the chi-squared test.
6) will have a practical knowledge of the physics of mechanical oscillating systems (pendulum, spring and mass systems, strings, sound waves)
7) will be able to plan an experiment to study such phenomena
8) will be able to collect and analyse experimental data using the learned statistical methods
9) will acquire group working skills finalized to the realization of the experiments
10) will learn how to effectively present experimental results
The skills from 3) to 5) will be achieved by practical exercises
The skills from 6) a 10) will be achieved by the realization of laboratory experiments in small groups of students, followed by the preparation of written reports
1) will understand the concepts of statistical and systematic errors
2) will know the fundamentals of the theory of probability and the concepts of distributions, both discrete and continuous
3) will know some important distributions (binomial, Poisson, Gauss, chi-square, Student's t) and will be able to apply them in real-world applications.
4) will be able to perform the basic data analyses (computation of mean, standard deviation, correlation)
5) will be able to quantitatively check the observed data against models (probability distributions, linear functions, power functions, exponential functions) using linear regression and the chi-squared test.
6) will have a practical knowledge of the physics of mechanical oscillating systems (pendulum, spring and mass systems, strings, sound waves)
7) will be able to plan an experiment to study such phenomena
8) will be able to collect and analyse experimental data using the learned statistical methods
9) will acquire group working skills finalized to the realization of the experiments
10) will learn how to effectively present experimental results
The skills from 3) to 5) will be achieved by practical exercises
The skills from 6) a 10) will be achieved by the realization of laboratory experiments in small groups of students, followed by the preparation of written reports
Lesson period: Activity scheduled over several sessions (see Course syllabus and organization section for more detailed information).
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course can be attended as a single course.
Course syllabus and organization
CORSO A
Responsible
Lesson period
year
Course syllabus
The course consists of: an introduction to the treatment of measurement uncertainties and fundamentals of statistics for data analysis and of a series of experiments concerning oscillations and material waves, with an introduction to the laboratory instrumentation. The detailed topics are listed below:
Measurement uncertainties and statistics
- Sensitivity of measurement devices.
- Significant digits and measurement errors.
- Data organization and display in tables and graphs.
- Probability Distributions (Binomial, Poisson, Gaussian, ChiSquare, Student)
- Random errors and the Gaussian distribution.
- Mean and weighed mean.
- Error of derived quantities: error propagation.
- Curve fitting and statistical verification of functional dependencies
- Fit quality and chi-square as a confidence level test.
- Covariance for multiple dependent variables.
Carried out in the laboratory:
- Basic training experience on the collection, processing and communication of experimental data
- Basic introductory experiences on the measurement of physical quantities
- Experimental activity aimed at measuring physical quantities, for example:
- - the acceleration of gravity by means of a simple pendulum
- - the speed of sound through the Kundt tube
- - the elastic constants of springs and the response parameters of mechanical oscillators
Measurement uncertainties and statistics
- Sensitivity of measurement devices.
- Significant digits and measurement errors.
- Data organization and display in tables and graphs.
- Probability Distributions (Binomial, Poisson, Gaussian, ChiSquare, Student)
- Random errors and the Gaussian distribution.
- Mean and weighed mean.
- Error of derived quantities: error propagation.
- Curve fitting and statistical verification of functional dependencies
- Fit quality and chi-square as a confidence level test.
- Covariance for multiple dependent variables.
Carried out in the laboratory:
- Basic training experience on the collection, processing and communication of experimental data
- Basic introductory experiences on the measurement of physical quantities
- Experimental activity aimed at measuring physical quantities, for example:
- - the acceleration of gravity by means of a simple pendulum
- - the speed of sound through the Kundt tube
- - the elastic constants of springs and the response parameters of mechanical oscillators
Prerequisites for admission
Being a first year exam, there are no specific requirements in addition to what is requested to access the degree course.
Teaching methods
The section on to the analysis of uncertainties with elements of Statistics is mainly entrusted to lectures (given by Prof. Camera) which integrate exercises and examples of problem solving, as well as simple statistical experiments carried out in the classroom.
The practical activity (Profs. Arosio, Crespi, D'Angelo, Giugni, Piseri) is introduced by a dialectical experience carried out in a group, aimed at training basic skills (regarding the collection, processing and communication of the products of an experimental work) and at setting correct attitudes and behavioral practices. Among these, an experience with role-playing elements is offered, which involves reaching an internal consensus within the group before the answer to a series of questions is collectively provided. The questions are preceded by elementary measurement operations that are carried out without the support of conventional instrumentation.
The main practical activity takes place in the laboratory with mandatory participation: it is done in small groups, with the aid of instruments suitable for carrying out different experiments that are chosen according to their usefulness in providing an occasion to use the concepts and methods introduced in the classroom.
The practical activity (Profs. Arosio, Crespi, D'Angelo, Giugni, Piseri) is introduced by a dialectical experience carried out in a group, aimed at training basic skills (regarding the collection, processing and communication of the products of an experimental work) and at setting correct attitudes and behavioral practices. Among these, an experience with role-playing elements is offered, which involves reaching an internal consensus within the group before the answer to a series of questions is collectively provided. The questions are preceded by elementary measurement operations that are carried out without the support of conventional instrumentation.
The main practical activity takes place in the laboratory with mandatory participation: it is done in small groups, with the aid of instruments suitable for carrying out different experiments that are chosen according to their usefulness in providing an occasion to use the concepts and methods introduced in the classroom.
Teaching Resources
G. Cannelli "Metodologie Sperimentali in Fisica" Edises
Also recommended:
J.R. Taylor "Introduzione all'analisi degli errori. Lo studio delle incertezze nelle misure fisiche" Zanichelli
R. Piazza "I Capricci del Caso" Springer
P.R. Bevington, D.K. Robinson "Data Reduction and Error Analysis for the Physical Sciences" McGraw Hill
For the practical activity in the lab: Introduction and guide to individual experiences is provided through ad-hoc material made available on the Ariel platform and through web-interface questionnaires (access via https://fcamerafesa.ariel.ctu.unimi.it/v5/Home/)
Also recommended:
J.R. Taylor "Introduzione all'analisi degli errori. Lo studio delle incertezze nelle misure fisiche" Zanichelli
R. Piazza "I Capricci del Caso" Springer
P.R. Bevington, D.K. Robinson "Data Reduction and Error Analysis for the Physical Sciences" McGraw Hill
For the practical activity in the lab: Introduction and guide to individual experiences is provided through ad-hoc material made available on the Ariel platform and through web-interface questionnaires (access via https://fcamerafesa.ariel.ctu.unimi.it/v5/Home/)
Assessment methods and Criteria
Learning assessment is achieved through the combination of different methods:
1) a written test aimed at verifying the knowledge of the statistics topics covered in the part of the course held in the classroom: the test is performed in-itinere before the start of laboratory activity. Participation in the written test with a result at least close to a sufficiency threshold is identified as a prerequisite for a fruitful use of the practical activity. A written test is also done at the end of the course, before the final interview. This test is optional for those who have already passed the test.
2) evaluation of the behaviors and operations carried out during laboratory activity: with particular regard to attention and critical attitude in the preparation of the experimental apparatus, in the correct use of the instrumentation and of the methods for preliminary analysis of the results during the activity, to their individual participation in group activities and in the editing of laboratory notes.
3) production of a report paper (individual): for one of the activities carried out in the laboratory, the production of a detailed report is required that discusses the objectives, methods, implementation and results of the experience. The report is delivered at the end of the practical activity and can be updated, if deemed necessary, before the final interview.
4) final interview (face to face): taking a cue from the report prepared individually, the knowledge and skills acquired are assessed through the interview, with particular reference to the understanding of basic concepts, to methodological rigor, to the individual ability to re-elaborate and produce a synthesis of results.
The final evaluation, expressed through a mark out of thirty, is formulated by taking into consideration the outcome of each of the indicated learning assessment elements, with attention to the final result achieved by each learner in the context of an individual development path.
1) a written test aimed at verifying the knowledge of the statistics topics covered in the part of the course held in the classroom: the test is performed in-itinere before the start of laboratory activity. Participation in the written test with a result at least close to a sufficiency threshold is identified as a prerequisite for a fruitful use of the practical activity. A written test is also done at the end of the course, before the final interview. This test is optional for those who have already passed the test.
2) evaluation of the behaviors and operations carried out during laboratory activity: with particular regard to attention and critical attitude in the preparation of the experimental apparatus, in the correct use of the instrumentation and of the methods for preliminary analysis of the results during the activity, to their individual participation in group activities and in the editing of laboratory notes.
3) production of a report paper (individual): for one of the activities carried out in the laboratory, the production of a detailed report is required that discusses the objectives, methods, implementation and results of the experience. The report is delivered at the end of the practical activity and can be updated, if deemed necessary, before the final interview.
4) final interview (face to face): taking a cue from the report prepared individually, the knowledge and skills acquired are assessed through the interview, with particular reference to the understanding of basic concepts, to methodological rigor, to the individual ability to re-elaborate and produce a synthesis of results.
The final evaluation, expressed through a mark out of thirty, is formulated by taking into consideration the outcome of each of the indicated learning assessment elements, with attention to the final result achieved by each learner in the context of an individual development path.
FIS/01 - EXPERIMENTAL PHYSICS - University credits: 10
Laboratories: 48 hours
Lessons: 48 hours
Lessons: 48 hours
Professors:
Carpineti Marina, D'Angelo Davide, Gargano Marco, Giugni Andrea, Piseri Paolo Giuseppe Carlo
Shifts:
Professor:
Carpineti Marina
Lezioni in comune con studenti Turno 1-Turno 2-Turno 3-Turno 4-Turno 5-Turno 6
Professor:
Piseri Paolo Giuseppe CarloTurno 1
Professor:
D'Angelo DavideTurno 2
Professor:
Piseri Paolo Giuseppe CarloTurno 3
Professor:
Gargano MarcoTurno 4
Professor:
Giugni AndreaTurno 6
Professor:
Giugni AndreaCORSO B
Responsible
Lesson period
year
Course syllabus
The course consists of: an introduction to the treatment of measurement uncertainties and fundamentals of statistics for data analysis and of a series of experiments concerning oscillations and material waves, with an introduction to the laboratory instrumentation. The detailed topics are listed below:
Measurement uncertainties and statistics
- Sensitivity of measurement devices.
- Significant digits and measurement errors.
- Data organization and display in tables and graphs.
- Probability Distributions (Binomial, Poisson, Gaussian, ChiSquare, Student)
- Random errors and the Gaussian distribution.
- Mean and weighed mean.
- Error of derived quantities: error propagation.
- Curve fitting and statistical verification of functional dependencies
- Fit quality and chi-square as a confidence level test.
- Covariance for multiple dependent variables.
Oscillations and material waves, and connected experiments.
- Simple pendulum motion. Measurement of the gravity constant with the simple pendulum: best configuration, importance of the approximations, and data distribution curve.
- The elastic constant;
- Mass-spring simple oscillator. Measurement of frequency, static and dynamic elastic constant, damping, resonance and phase; elastic constant curve fitting.
- The oscilloscope: physics and characteristics.
- Speed. Speed measurement of a spring-hung mass as incremental ratio with a sonar, verification of the limit quality by fixing the sonar time interval and varying the mass speed (by changing the mass itself).
- Verification of harmonicity and anharmonicity in oscillatory motions by verifying the presence of spectral components.
- Two masses-three springs system (two degrees-freedom system) with longitudinal oscillations; measurements of modal frequencies, beat frequencies, damping constants, resonance curve, and the frequency of a generic oscillation.
- Spring modes (transversal stationary waves). Measurement of frequencies, damping constant and propagation speed of an impulse.
- Acoustical waves in an open and close tube (Kundt's tube), and measurement of the normal modes and the wave propagation speed.
- Automatic data acquisition (sensors, graphs, interpolations, extrapolations).
- Surface waves in water and stationary waves (optional part, not always performed)
Measurement uncertainties and statistics
- Sensitivity of measurement devices.
- Significant digits and measurement errors.
- Data organization and display in tables and graphs.
- Probability Distributions (Binomial, Poisson, Gaussian, ChiSquare, Student)
- Random errors and the Gaussian distribution.
- Mean and weighed mean.
- Error of derived quantities: error propagation.
- Curve fitting and statistical verification of functional dependencies
- Fit quality and chi-square as a confidence level test.
- Covariance for multiple dependent variables.
Oscillations and material waves, and connected experiments.
- Simple pendulum motion. Measurement of the gravity constant with the simple pendulum: best configuration, importance of the approximations, and data distribution curve.
- The elastic constant;
- Mass-spring simple oscillator. Measurement of frequency, static and dynamic elastic constant, damping, resonance and phase; elastic constant curve fitting.
- The oscilloscope: physics and characteristics.
- Speed. Speed measurement of a spring-hung mass as incremental ratio with a sonar, verification of the limit quality by fixing the sonar time interval and varying the mass speed (by changing the mass itself).
- Verification of harmonicity and anharmonicity in oscillatory motions by verifying the presence of spectral components.
- Two masses-three springs system (two degrees-freedom system) with longitudinal oscillations; measurements of modal frequencies, beat frequencies, damping constants, resonance curve, and the frequency of a generic oscillation.
- Spring modes (transversal stationary waves). Measurement of frequencies, damping constant and propagation speed of an impulse.
- Acoustical waves in an open and close tube (Kundt's tube), and measurement of the normal modes and the wave propagation speed.
- Automatic data acquisition (sensors, graphs, interpolations, extrapolations).
- Surface waves in water and stationary waves (optional part, not always performed)
Prerequisites for admission
Being a first year exam, there are no specific requirements in addition to what is requested to access the degree course.
Teaching methods
In the first semester, measurement uncertainties and statistics are covered by lectures with exercises. The acquired skills are applied in classroom experiments, involving the students.
In the second semester, students are divided in small groups and perform experiments on oscillations and material waves in laboratory sessions.
Attendance is compulsory for the experiments and it is strongly recommended for the rest of the course.
In the second semester, students are divided in small groups and perform experiments on oscillations and material waves in laboratory sessions.
Attendance is compulsory for the experiments and it is strongly recommended for the rest of the course.
Teaching Resources
Textbooks:
G. Cannelli, Metodologie sperimentali in Fisica, Edises
J.R.Taylor, Teoria degli errori di misura, Zanichelli.
Documentation of each laboratory experiment are available on the course's ARIEL web site: https://mmaugerilfes.ariel.ctu.unimi.it/v5/Home/
G. Cannelli, Metodologie sperimentali in Fisica, Edises
J.R.Taylor, Teoria degli errori di misura, Zanichelli.
Documentation of each laboratory experiment are available on the course's ARIEL web site: https://mmaugerilfes.ariel.ctu.unimi.it/v5/Home/
Assessment methods and Criteria
The assessment is a mark given by a synthesis of four components: a written exam of statistics; written laboratory reports on experiments performed during the course; evaluation of the student's laboratory activity; a practical test followed by an interview on all the experiments, which is held immediately after the end of the course.
The statistics exam assesses the student's knowledge of the fundamentals of probability and statistics, and his/her ability to critically apply them to practical cases. The examination is held at the end of the first semester, in order to verify the acquisition of the minimal skills required for the laboratory session, and it is required to pass this exam to access the laboratory. It can be repeated after the end of the course. It lasts 2 hours. Students are allowed to use a pocket calculator and numerical tables are provided. Access to past exercises and communication of the evaluations if provided through the ARIEL portal.
The practical test with interview aims to verify that the skills shown by the laboratory groups have been actually acquired by each group member, while the interview aims to verify that the student, in addition to practical experimental abilities, also has a clear overview of their theoretical aspects and is able to critically discuss the performed experiments.
The statistics exam assesses the student's knowledge of the fundamentals of probability and statistics, and his/her ability to critically apply them to practical cases. The examination is held at the end of the first semester, in order to verify the acquisition of the minimal skills required for the laboratory session, and it is required to pass this exam to access the laboratory. It can be repeated after the end of the course. It lasts 2 hours. Students are allowed to use a pocket calculator and numerical tables are provided. Access to past exercises and communication of the evaluations if provided through the ARIEL portal.
The practical test with interview aims to verify that the skills shown by the laboratory groups have been actually acquired by each group member, while the interview aims to verify that the student, in addition to practical experimental abilities, also has a clear overview of their theoretical aspects and is able to critically discuss the performed experiments.
FIS/01 - EXPERIMENTAL PHYSICS - University credits: 10
Laboratories: 48 hours
Lessons: 48 hours
Lessons: 48 hours
Professors:
Andreazza Attilio, D'Auria Saverio, Dell'Asta Lidia, Gariboldi Leonardo, Meroni Chiara, Rossi Lucio
Shifts:
Lezioni in comune con studenti Turno 1-Turno 2-Turno 3-Turno 4-Turno 5
Professor:
Rossi LucioTurno 1
Professor:
Meroni ChiaraTurno 2
Professor:
Gariboldi LeonardoTurno 3
Professor:
D'Auria SaverioTurno 4
Professor:
Andreazza AttilioTurno 5
Professor:
Dell'Asta LidiaEducational website(s)
Professor(s)
Reception:
by appointment
Office: Phys. Dep. - v. Celoria, 16 - Lita building, 3rd floor.
Reception:
after appointment
Office Room, LITA building, floor 0
Reception:
Monday 2-4 pm
LASA Laboratory or Physics Department (please send an e-mail)