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Lecturer(s)
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Opatrný Tomáš, prof. RNDr. Dr.
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Course content
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Free undamped harmonic oscillations: oscillators in nature and industry, equations of a harmonic oscillator, energy of the oscillations, phase space, superposition of oscillations. Free oscillations with damping: examples of damped oscillations, underdamped, critically damped and overdamped motion. Forced oscillations: examples of forced oscillators, equation of forced oscillations and its solution, resonance, Q-factor of a resonator, impedance. Coupled oscillators: examples of coupled oscillators, normal modes and methods of finding their frequencies. Coupled oscillators in nature and industry, mechanical and electrical oscillators. Waves in 1D: transversal wave equation of a string and its solution, normal modes of a finite string, Fourier metod. Propagation of a disturbance on an infinite string, reflection and transmission of a wave on a boundary, wave polarization. Longitudinal waves, sound propagation in air. Interference of waves: Mach-Zehnder interferometer, Michelson interferometer. Resonators, Fabry-Perot interferometer. Superposition of waves, modulation, wave packets, pulses. Waves in 2D and 3D: wave equation, estimation of the number of modes. Solution of the wave equation af a membrane and of a 3D body. Electromagnetic waves in vacuum and in dielectric. Dispersion: nonideal string with stiffness, phase and group velocity, propagation and dispersion of wave packets. Pulses in optical fibres, chirp, slow light in media with Electromagnetically Induced Transparency. Waves in nonlinear media: higher harmonic generation, downconversion. Solitons.
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Learning activities and teaching methods
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Lecture, Dialogic Lecture (Discussion, Dialog, Brainstorming), Work with Text (with Book, Textbook), Methods of Written Work
- Attendace
- 39 hours per semester
- Homework for Teaching
- 26 hours per semester
- Preparation for the Course Credit
- 10 hours per semester
- Preparation for the Exam
- 8 hours per semester
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Learning outcomes
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Understand basic principles of virational motion and apply them to solving problems of various physical systems. Understand principles of wave propagation in different media or fields and learn to solve corresponding model problems.
Ability to identify suitable models of vibrations and waves and apply them to solve typical problems in natural phenomena and in technical practice.
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Prerequisites
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Mathematics: derivatives, basics of integrals. Basics of differential equations (ordinary and partial) would be advantageous. Physics: Newton laws of motion, basics of electricity, magnetism and electromagnetic field.
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Assessment methods and criteria
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Mark, Written exam, Analysis of linguistic
Grading is based on the score of tests written during the semester, final test, and evaluation of a presentation given during the exercises. The full score is 100 points, out of which 40 is for the final test, 14 is for each of two intermediate tests, and 30 is for the work during exercises. Evaluation of the work during exercises is mostly based on 10-minute tests written at each exercise. Each of these tests will contain a modified version of one of the homework problems assigned during the preceding exercise. A part of the exercise work is a short (approx. 5 minutes) presentation referring about a scientific article from some international physical journal (e.g., Nature, Physics Today, American Journal of Physics, etc.). The topics of the article should be connected to vibrations and waves. The material will then be discussed with the class. Up to 5 points can be gained for this presentation. The presentation and getting at least 18 points during semester (score composed of the intermediate test plus 10-minute tests plus presentation) are a necessary condition for the course credit prior to examination. Grading: A 91 - 100 points B 82 - 90 points C 73 - 81 points D 64 - 72 points E 55 - 63 points
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Recommended literature
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Bajer, J. (2006). Mechanika 3. UP Olomouc.
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Feynman, R. P., Leighton, R. B., Sands, M. (2002). Feynmanovy přednášky z fyziky. Fragment, Havlíčkův Brod.
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Main, I.G. (1990). Kmity a vlny ve fyzice. Academia Praha.
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Pain, H. J. (2005). The Physics of Vibrations and Waves. J. Wiley and Sons LTD London, 6th ed.
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