Physics Laboratory with Introduction to Statistics

In the first part of the course the students will learn the basics of statistics and the different technique to analyze data, in particular:

1) Errors, Average, Standard Deviation
2) Representation by histograms and estimation of central and spread parameters
3) Theoretical distributions: Binomial and Poisson
4) The Gaussian function as probability distribution of repeated and independent measurements and errors
5) Confidence interval and level, discarding data , combination and propagation of errors
6) Covariance and correlation. Method of least squares.
7) Test for distributions, Chi-square test

In the second part of the course the students will use the statistics learned in the first part to measure important physical observables. The experimental activity

1) Measurement technique and Rolling Dice
2) Pendulum and the acceleration of gravity
3) The moment of inertia of different solids
4) The harmonic oscillator, the damped and force driven motion
5) The vibration of a strings
6) The acoustic waves and the Kundt tube
7) The Coulomb Force

Program
Measurement uncertainties and statistics
1) Sensitivity of measurement devices.
2) Significant digits and measurement errors.
3) Random errors and Gaussian distribution.
4) Mean and weighed mean.
5) Error of derived quantities: error propagation.
6) Covariance for multiple dependent variables.
7) Confidence level.
8) Data organization in table and graphs.
9) Curve fitting and law verification.
10) Fit quality and chi-square as a confidence level test.
Oscillations and material waves, and connected experiments.
1) Conic pendulum motion.
2) Simple pendulum motion. Measurement of the gravity constant with the simple pendulum: best configuration, importance of the approximations, and data distribution curve.
3) The elastic constant;
4) Mass-spring simple oscillator. Measurement of frequency, static and dynamic elastic constant, damping, resonance and phase; elastic constant curve fitting.
5) The oscilloscope: physics and characteristics.
6) 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).
7) Verification of harmonicity and inharmonicity in oscillatory motions by verifying the presence of spectral components.
8) Two masses-three springs system (two degrees-freedom system) with longitudinal and transversal oscillations; measurements of modal frequencies, beating frequencies, damping constants, resonance curve, and the frequency of a generic oscillation.
9) Spring modes (transversal stationary waves). Measurement of frequencies, damping constant and propagation speed of an impulse.
10) Acoustical waves in an open and close tube (Kundt's tube), and measurement on the normal modes and the wave propagation speed.
11) Automatic data acquisition (sensors, graphs, interpolations, extrapolations).
12) Surface waves in water and stationary waves.