CONTENTS 



INTRODUCTION 



AKT. PAGE 



1. Simple Vibrations and Pure Tones 1 



2. Musical Notes 3 



3. Musical Intervals. Diatonic Scale . .5 



CHAPTER I 



THEORY OF VIBRATIONS 



4. The Pendulum 8 



5. Simple- Harmonic Motion 9 



6. Further Examples 11 



7. Dynamics of a System with One Degree of Freedom. Free 



Oscillations 12 



8. Forced Oscillations of a Pendulum 16 



9. Forced Oscillations in any System with One Degree of 



Freedom. Selective Resonance 20 



10. Superposition of Simple Vibrations 22 



11. Free Oscillations with Friction ...... 24 



12. General Dissipative System with One Degree of Freedom. 



Effect of Periodic Disturbing Forces .... 27 



13. Effect of Damping on Resonance 32 



14. Systems of Multiple Freedom. Examples. The Double 



Pendulum 34 



15. General Equations of a Multiple System . . . . 41 



16. Free Periods of a Multiple System. Stationary Property . 44 



17. Forced Oscillations of a Multiple System. Principle of 



Reciprocity 47 



18. Composition of Simple-Harmonic Vibrations in Different 



Directions 48 



19. Transition to Continuous Systems 52 



20. On the Use of Imaginary Quantities 53 



21. Historical Note 58 



