## Toegangseisen

Optica, Klassieke Mechanica a, Analyse 2 (na), Experimentele Natuurkunde

## Beschrijving

The most interesting thing about this course is that it teaches you a relatively simple method to describe, solve, and predict physical phenomena.

These physical phenomena have to have the property that the output of the system changes linearly in response to a small change in the input of the system (linear systems). In the time domain such phenomena are describe by coupled linear differential equations. When, after a Fourier transform, we look at these phenomena in the frequency domain the differential equations become ordinary algebraic equations which are easily solvable.

To show the importance of this theory in doing research this course will contain practical work besides lectures and exercise classes. The practical work will connect theory and practice and will show how the theory applies to various problems. Python is used in both the exercise classes and the practical work.

During the exercise classes you will learn how to implement the Discrete Fourier transform in Python and how to use that to model various physical phenomena also in Python.

During the practical work your knowledge of Python will be deepened in the areas of designing a graphical user interface (GUI) and object oriented programming (OOP). Furthermore you will learn how to control experiments and measure data using the MyDAQ and Python and thereby be able to measure transfer functions experimentally.

Because of this structure of the course you will not only get to know a powerful theory that is applicable to many physical phenomena, but also be able to use that theory in practice.

This course treats the following subjects in a physically relevant context:

Fourier series & Fourier transform

Discrete Fourier transform

Converting time domain signals to frequency domain signals and vice versa

Signal analysis of time-dependent signals in the frequency domain

Drafting and solving linear differential equations for physical phenomena

Complex impedance of electronic and mechanical components (resistance, coil, capacitor, damping of a spring, mass, spring constant)

Transfer functions & Bodeplots for mechanical systems (filters & harmonic oscillators)

Transfer functions & Bodeplots for electronic systems (filters & harmonic oscillators)

Transfer functions for optical systems (single slit, double slit & gratings)

Fourier relations

## Leerdoelen

At the end of this course you will be able to:

To describe periodic phenomena by means of a Fourier series

Calculate and apply the coefficients of a Fourier series in a physically relevant context

Draft simple differential equations for electronic, mechanical and optical physical phenomena

Implement the Fourier transformations of a number of physically relevant functions independently

Analyze time-dependent signals in the frequency domain by applying a Fourier transformation

Model simple physical systems in the time domain by determining the transfer function in the frequency domain

To name and explain the analogy and differences in the description of electronic, mechanical and optical systems

Perform numerical Fourier transformations using Python and interpret these calculate and describe the transfer functions of simple electronic filters by using complex impedance and Bodeplots

Describe and calculate the transfer function of a driven damped harmonic oscillator

Model and predict the behavior of linear systems numerically using Fourier transforms and transfer functions

Create a simple graphical user interface (GUI) in Python

Perform simple data acquisition by controlling hardware using Python

Independently set up experiments to determine the transfer function of a system

Identify and name different sources of noise by using the frequency domain

Explain diffraction of single slit, double slit and gratings using Fourier transforms

Name Fourier relations between k and x, and ω and t

## Generic skills (soft skills)

The following skills will be trained during this course:

Thinking in a different domain from the time domain.

Attaining new Python skills that you can use again in all other courses.

## Rooster

## Onderwijsvorm

Practicum, lectures, exercise classes

## Toetsing

Practicum, exam

## Blackboard

Op Blackboard vindt men de handleidingen voor de proeven, de namen, tel nummer en emails van alle deelnemende studenten en assistenten en de meest recente versies van het rooster. Voor toegang tot Blackboard is een ULCN-account nodig).Blackboard UL

## Literatuur

Handleidingen

## Contact

Contact data lecturers: Dr. Jelmer Wagenaar) Dr.ir. Paul Logman)