2021 Theory of Oscillations

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Academic unit or major
Undergraduate major in Systems and Control Engineering
Nakao Hiroya 
Class Format
Media-enhanced courses
Day/Period(Room No.)
Tue3-4(S422)  Fri3-4(S422)  
Course number
Academic year
Offered quarter
Syllabus updated
Lecture notes updated
Language used
Access Index

Course description and aims

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.

Student learning outcomes

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

Competencies that will be developed

Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

Class flow

lectures, exercises, homework

Course schedule/Required learning

  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
Class 15 Examination Examination

Out-of-Class Study Time (Preparation and Review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.


None specified

Reference books, course materials, etc.

None specified

Assessment criteria and methods

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.

Related courses

  • SCE.M201 : Fundamental Kinematics and Kinetics for Mechanical Systems
  • SCE.M202 : Fundamentals of Analytical Dynamics (Systems and Control)

Prerequisites (i.e., required knowledge, skills, courses, etc.)

No prerequisites


Lectures will be given in Japanese.

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