MP205: Vibrations and Waves

Lecturer: Dr. Jiří Vala
Office: Room 1.9, Mathematical Physics, Science Building, North Campus
Phone: (1) 708 3553
E-Mail: jiri DOT vala AT nuim DOT ie

Course Syllabus

• Simple harmonic motion
• Superposition of periodic motions
• Forced and damped oscillators and resonance
• Coupled oscillators and normal modes
• Vibrations in continuous systems and Fourier analysis
• Traveling and standing waves
• Sound and light as transverse and longitudinal waves
• Dispersion and group velocity
• Boundary effects and interference

Primary text that the lectures are based on

A. P. French, Vibrations and Waves (The MIT Introductory Physics Series, Norton)

Supplementary text

I. G. Main, Vibrations and Waves in Physics (Cambridge University Press)

Lecture notes

This is the latest updated collection of the lecture notes. For animations please refer to the webpages below.

1. Periodic Motions
2. The Superposition of Periodic Motions
3. The Free Vibrations of Physical Systems
4. Forced Vibrations and Resonance
5. Coupled Oscillators and Normal Modes
6. Normal Modes of Continuous Systems and Fourier Analysis
7. Fourier Analysis. Progressive Waves
8. Wave pulses
9. Introduction to classical string theory (optional)
10. Boundary Effects and Interference I
11. Boundary Effects and Interference II
12. Introduction to Quantum Mechanics I
13. Introduction to Quantum Mechanics II

Chapter Webpages

Please refer to the webpages only for animations. For lecture notes, please use those in pdf format above; I will try to update the html files accordingly asap.

1. Periodic Motions
2. The Superposition of Periodic Motions
3. The Free Vibrations of Physical Systems
4. Forced Vibrations and Resonance
5. Coupled Oscillators and Normal Modes
6. Normal Modes of Continuous Systems and Fourier Analysis
7. Progressive Waves
8. Classical Nonrelativistic String Theory
9. Boundary Effects and Interference
10. Introduction to Quantum Mechanics

Assignments and Solutions

1. Assignment 1 and solutions
2. Assignment 2 and solutions
3. Assignment 3 and solutions
4. Assignment 4 and solutions
5. Assignment 5 and solutions
6. Assignment 6 and solutions
7. Assignment 7 and solutions
8. Assignment 8 and solutions
9. Assignment 9 and solutions
10. Assignment 10 and solutions