CONTENTS 



CHAPTER II 



STKINGS 



ART. PAGE 



22. Equation of Motion. Energy ...... 59 



23. Waves on an Unlimited String 61 



24. Eeflection. Periodic Motion of a Finite String ... 64 



25. Normal Modes of Finite String. Harmonics ... 68 



26. String excited by Plucking, or by Impact .... 72 



27. Vibrations of a Violin String 75 



28. Forced Vibrations of a String 80 



29. Qualifications to the Theory of Strings .... 81 



30. Vibrations of a Loaded String ...... 82 



31. Hanging Chain . . . .... . . 84 



CHAPTER III 

 FOURIER'S THEOREM 



32. The Sine-Series . ... . . . . . 87 



33. The Cosine-Series 92 



34. Complete Form of Fourier's Theorem. Discontinuities . 92 



35. Law of Convergence of Coefficients ... . . . 94 



36. Physical Approximation. Case of Plucked String . 96 



37. Application to Violin String . . . . . . 98 



38. String Excited by Impact 99 



39. General Theory of Normal Functions. Harmonic Analysis 101 



CHAPTER IV 



BARS 



40. Elementary Theory of Elasticity. Strains . . . . 106 



41. Stresses 108 



42. Elastic Constants. Potential Energy of Deformation . . 110 



43. Longitudinal Vibrations of Bars . . ... . . 114 



44. Plane Waves in an Elastic Medium . . . . . 118 



45. Flexural Vibrations of a Bar . . . . . .120 



46. Free-free Bar . . . . . . . .... 124 



47. Clamped-free Bar 127 



48. Summary of Results. Forced Vibrations . . ... 130 



49. Applications . 131 



50. Effect of Permanent Tension . ... . . . . 132 



51. Vibrations of a Ring. Flexural and Extensional Modes . 133 



