Physics Laboratory with Introduction to Statistics
A.Y. 2021/2022
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 cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
CORSO A
Lesson period
year
More information will be provided in the next months, based on the evolution of the public health situation
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, with an introduction to the laboratory instrumentation. The detailed topics are listed below:
Measurement uncertainties and statistics, lessons and demonstrations
- 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.
Laboratory experiments
- The physical measurements: with simple experiments using common materials clarify the basic concepts underlying the physical measurements
- Simple pendulum motion. Measurement of the gravity constant with the simple pendulum: best configuration, effects of the oscillation angle and relevance of the approximations
- 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.
- Verification of harmonicity and anharmonicity in oscillatory motions by verifying the presence of spectral components.
- 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).
Measurement uncertainties and statistics, lessons and demonstrations
- 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.
Laboratory experiments
- The physical measurements: with simple experiments using common materials clarify the basic concepts underlying the physical measurements
- Simple pendulum motion. Measurement of the gravity constant with the simple pendulum: best configuration, effects of the oscillation angle and relevance of the approximations
- 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.
- Verification of harmonicity and anharmonicity in oscillatory motions by verifying the presence of spectral components.
- 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).
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.
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.
Teaching Resources
G. Cannelli, Metodologie sperimentali in Fisica, Edises
Documentation of each laboratory experiment are available on the course's ARIEL web site.
Documentation of each laboratory experiment are available on the course's ARIEL web site.
Assessment methods and Criteria
The evaluation of the student performance in the course is given by a synthesis of four components: a written exam of statistics; written laboratory reports on 1 of the experiments carried on in the laboratory, and on the throwing dice experiment performed during the first semester ; evaluation of the student's laboratory activity; an interview on all the experiments, with specific attention for the presented report and the related experiment.
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. 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 interview aims at verifying that the student, in addition to the ability of performing the experiments and reporting clearly and concisely their main features, also has a clear overview of their theoretical aspects and is able to critically discuss them.
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. 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 interview aims at verifying that the student, in addition to the ability of performing the experiments and reporting clearly and concisely their main features, also has a clear overview of their theoretical aspects and is able to critically discuss them.
FIS/01 - EXPERIMENTAL PHYSICS - University credits: 10
Laboratories: 48 hours
Lessons: 48 hours
Lessons: 48 hours
Professors:
Arosio Paolo, Camera Franco Ersilio, Crespi Fabio Celso Luigi, D'Angelo Davide, Giugni Andrea, Perini Laura, Piseri Paolo Giuseppe Carlo, Vecchi Roberta
Shifts:
Professor:
Camera Franco Ersilio
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 4
Professor:
Crespi Fabio Celso LuigiTurno 6
Professor:
Giugni AndreaCORSO B
Responsible
Lesson period
year
The course will be delivered entirely remotely in case of travel
restrictions due to Covid-19. In this case, the lectures will be offered
in virtual classrooms (zoom platform) in synchronous connection, with the
possibility of real-time interaction between the students and the teacher.
In case of partial restrictions, the practical sessions in the second semester may be performed by a different member of the laboratory group for each experiment.
The practical test may be replaced by an interview and the exam of Statistics will be held using the exam.net platform.
restrictions due to Covid-19. In this case, the lectures will be offered
in virtual classrooms (zoom platform) in synchronous connection, with the
possibility of real-time interaction between the students and the teacher.
In case of partial restrictions, the practical sessions in the second semester may be performed by a different member of the laboratory group for each experiment.
The practical test may be replaced by an interview and the exam of Statistics will be held using the exam.net platform.
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.
- Conic pendulum motion.
- 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.
- Conic pendulum motion.
- 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
Textbook: G. Cannelli, Metodologie sperimentali in Fisica, Edises
Alternative textbook: 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/
Alternative textbook: 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 course assessment is a mark given by a synthesis of four components: a written exam of statistics; written laboratory reports on two of the 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 3 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 3 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, Perini Laura, Rossi Lucio
Shifts:
Professors:
D'Auria Saverio, Perini Laura, Rossi Lucio
Lezioni in comune con studenti Turno 1-Turno 2-Turno 3-Turno 4-Turno 5
Professor:
Rossi LucioTurno 1
Professor:
Rossi LucioTurno 2
Professor:
Gariboldi LeonardoTurno 3
Professor:
D'Auria SaverioTurno 4
Professor:
Andreazza AttilioTurno 5
Professor:
Dell'Asta LidiaProfessor(s)
Reception:
Friday afternoon (15:00-17:00) - We strongly suggest to contact prof. Franco Camera via e-mail
Office
Reception:
write to [email protected]
LITA building, office a/1/C13, Physics Department via celoria 16
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)
Reception:
by appointment
office at the Physics Dept. (via Celoria 16), building E, room n.R007