Oscillations and waves are the most fundamental motions in nature and are observed ubiquitously in the real world. In this course, we learn basic concepts and properties of oscillations in various oscillatory systems ranging from a single pendulum to continuous systems. We also consider oscillations and waves in actual physical systems such as elastic waves and electromagnetic waves. Learning the principles of oscillations will provide us with a general approach to oscillatory phenomena in various areas of science and technology and will also be useful in applying oscillatory phenomena for practical purposes.
By the end of this course, the students will be able to:
1) Understand the basic concepts of oscillations and waves.
2) Learn the systematic approach to oscillations and waves.
3) Explain the characteristics of various kinds of oscillatory phenomena.
Harmonic oscillations, damped oscillations, forced oscillations, transient responses, parametric oscillations, coupled oscillations, wave equation, elastic waves, waves in fluids, electromagnetic waves, matter waves, nonlinear oscillations / waves, random oscillations
|Intercultural skills||Communication skills||✔ Specialist skills||Critical thinking skills||Practical and/or problem-solving skills|
lectures, exercises, homework
|Course schedule||Required learning|
|Class 1||Harmonic oscillations||Properties of harmonic and damped oscillations|
|Class 2||Forced oscillations||Properties of forced oscillations, resonance|
|Class 3||Transient responses||Properties of transient responses, impulse/step response|
|Class 4||Parametric oscillations||Properties of parametric oscillations, resonance|
|Class 5||Coupled oscillations: two oscillators||Properties of coupled oscillators, normal modes|
|Class 6||Waves in continuous systems: wave equation||Properties of waves in continuous systems, wave equation|
|Class 7||Waves in continuous systems: superposition of waves||Properties of waves in continuous systems, superposition of waves, wave packets|
|Class 8||Waves in physical systems: elastic waves||Properties of elastic waves, transverse/longitudinal waves|
|Class 9||Waves in physical systems: waves in fluids||Properties of waves in fluids, sound waves|
|Class 10||Waves in physical systems: electromagnetic waves||Properties of electromagnetic waves, Maxwell's equations|
|Class 11||Waves in physical systems: matter waves||Properties of matter waves, Schrodinger's equation|
|Class 12||Waves in physical systems: matter waves||Properties of matter waves, Schrodinger's equation|
|Class 13||Nonlinear oscillations / waves||Examples of oscillations and waves in nonlinear systems|
|Class 14||Random oscillations||Properties of oscillations subjected to random excitation|
1) Students will be assessed on their understanding of the basic theory and its application associated with oscillations and waves.
2) Students’ course scores are based on final exam and exercise reports.
Lectures will be given in Japanese.