CHAPTER III - THE FLEXIBLE STRING8.

CHAPTER III - THE FLEXIBLE STRING
8. Waves on a String
The Wave Velocity. The General Solution for Wave
Motion. Initial Conditions. Boundary Conditions.
Reflection at a Boundary. Strings of Finite Length.
9. Simple Harmonic Oscillations
The Wave Equation. Standing Waves. Normal Modes.
Fourier Series. Initial Conditions. The Series
Coefficients. Plucked String, Struck String, Energy of
Vibration
10. Forced Vibrations
Wave Impedance and Admittance. General Driving
Force. String of Finite Length. Driving Force Applied
Anywhere. Alternative Series Form. Distributed Driving
Force. Transient Driving Force. The Piano String. The
Effect of Friction. Characteristic Impedances and
Admittances.
11. Strings of Variable Density and Tension
General Equation of Motion. Orthogonality of
Characteristic Functions. Driven Motion. Nonuniform
Mass. The Sequence of Characteristic Functions. The
Allowed Frequencies. Vibrations of a Whirling String.
The Allowed Frequencies. The Shape of the String.
Driven Motion of the Whirling String.
12. Perturbation Calculations
The Equation of Motion. First-order Corrections.
Examples of the Method. Characteristic Impedances.
Forced Oscillation. Transient Motion
13. Effect of Motion of the End Supports
Impedance of the Support. Reflection of Waves.
Hyperbolic Functions. String Driven from One End.
Shape of the String. Standing Wave and Position of
Minima. Characteristic Functions. Transient Response.
Recapitulati