| |
| |
Learning Tools Used in This Book | |
| |
| |
| |
Simple Harmonic Motion | |
| |
| |
| |
Sinusoidal oscillations are everywhere | |
| |
| |
| |
The physics and mathematics behind simple sinusoidal motion | |
| |
| |
| |
Important parameters and adjustable constants of simple harmonic motion | |
| |
| |
| |
Mass on a spring | |
| |
| |
| |
Electrical oscillators | |
| |
| |
| |
Review of Taylor series approximations | |
| |
| |
| |
Euler's equation | |
| |
| |
| |
Review of complex numbers | |
| |
| |
| |
Complex exponential notation for oscillatory motion | |
| |
| |
| |
The complex representation for AC circuits | |
| |
| |
| |
Another important complex function: The quantum mechanical wavefunction | |
| |
| |
| |
Pure sinusoidal oscillations and uncertainty principles | |
| |
| |
Concept and skill inventory | |
| |
| |
Problems | |
| |
| |
| |
Examples of Simple Harmonic Motion | |
| |
| |
| |
Requirements for harmonic oscillation | |
| |
| |
| |
Pendulums | |
| |
| |
| |
Elastic deformations and Young's modulus | |
| |
| |
| |
Shear | |
| |
| |
| |
Torsion and torsional oscillators | |
| |
| |
| |
Bending and Cantilevers | |
| |
| |
Concept and skill inventory | |
| |
| |
Problems | |
| |
| |
| |
Damped Oscillations | |
| |
| |
| |
Damped mechanical oscillators | |
| |
| |
| |
Damped electrical oscillators | |
| |
| |
| |
Exponential decay of energy | |
| |
| |
| |
The quality factor | |
| |
| |
| |
Underdamped, overdamped, and critically damped behavior | |
| |
| |
| |
Types of damping | |
| |
| |
Concept and skill inventory | |
| |
| |
Problems | |
| |
| |
| |
Driven Oscillations and Resonance | |
| |
| |
| |
Resonance | |
| |
| |
| |
Effects of damping | |
| |
| |
| |
Energy flow | |
| |
| |
| |
Linear differential equations the superposition principle for driven systems, and the response to multiple drive forces | |
| |
| |
| |
Transients | |
| |
| |
| |
Electrical resonance | |
| |
| |
| |
Other examples of resonance: MRT and other spectroscopies | |
| |
| |
| |
Nonlinear oscillators and chaos | |
| |
| |
Concept and skill inventory | |
| |
| |
Problems | |
| |
| |
| |
Symmetric Coupled Oscillators and Hilbert Space | |
| |
| |
| |
Beats: An aside? | |
| |
| |
| |
Two symmetric coupled oscillators: Equations of motion | |
| |
| |
| |
Normal modes | |
| |
| |
| |
Superposing normal modes | |
| |
| |
| |
Normal mode analysis, and normal modes as an alternate description of reality | |
| |
| |
| |
Hilbert space and bra-ket notation | |
| |
| |
| |
The analogy between coupled oscillators and molecular energy levels | |
| |
| |
| |
Nonzero initial velocities | |
| |
| |
| |
Damped, driven coupled oscillators | |
| |
| |
Concept and skill inventory | |
| |
| |
Problems | |
| |
| |
| |
Asymmetric Coupled Oscillators and the Eigenvalue Equation | |
| |
| |
| |
Matrix math | |
| |
| |
| |
Equations of motion and the eigenvalue equation | |
| |
| |
| |
Procedure for solving the eigenvalue equation | |
| |
| |
| |
Systems with more than two objects | |
| |
| |
| |
Normal mode analysis for multi-object, asymmetrical systems | |
| |
| |
| |
More matrix math | |
| |
| |
| |
Orthogonality of normal modes, normal mode coordinates, degeneracy, and scaling of Hilbert space for unequal masses | |
| |
| |
Concept and skill inventory | |
| |
| |
Problems | |
| |
| |
| |
String Theory | |
| |
| |
| |
The beaded string | |
| |
| |
| |
Standing wave guess: Boundary conditions quantize the allowed frequencies | |
| |
| |
| |
The highest possible frequency; connection to waves in a crystalline solid | |
| |
| |
| |
Normal mode analysis for the beaded string | |
| |
| |
| |
Longitudinal oscillations | |
| |
| |
| |
The continuous string | |
| |
| |
| |
Normal mode analysis for continuous systems | |
| |
| |
| |
k-space | |
| |
| |
Concept and skill inventor | |
| |
| |
Problems | |
| |
| |
| |
Fourier Analysis | |
| |
| |
| |
Introduction | |
| |
| |
| |
The Fourier Expansion | |
| |
| |
| |
Expansions using nonnormalized orthogonal basis functions | |
| |
| |
| |
Finding the coefficients in the Fourier series expansion | |
| |
| |
| |
Fourier Transforms and the meaning of negative frequency | |
| |
| |
| |
The Discrete Fourier Transform (DFT) | |
| |
| |
| |
Some applications of Fourier Analysis | |
| |
| |
Concept and skill inventory | |
| |
| |
Problems | |
| |
| |
| |
Traveling Waves | |
| |
| |
| |
Introduction | |
| |
| |
| |
The wave equation | |
| |
| |
| |
Traveling sinusoidal waves | |
| |
| |
| |
The superposition principle for traveling waves | |
| |
| |
| |
Electromagnetic waves in vacuum | |
| |
| |
| |
Electromagnetic waves in matter | |
| |
| |
| |
Waves on transmission lines | |
| |
| |
| |
Sound waves | |
| |
| |
| |
Musical instruments based on tubes | |
| |
| |
| |
Power carried by rope and electromagnetic waves; RMS amplitudes | |
| |
| |
| |
Intensity of sound waves; decibels | |
| |
| |
| |
Dispersion relations and group velocity | |
| |
| |
Concept and skill inventory | |
| |
| |
Problems | |
| |
| |
| |
Waves at Interfaces | |
| |
| |
| |
Reflections and the idea of boundary conditions | |
| |
| |
| |
Transmitted waves | |
| |
| |
| |
Characteristic impedances for mechanical systems | |
| |
| |
| |
�Universal� expressions for transmission and reflection | |
| |
| |
| |
Reflected and transmitted waves for transmission lines | |
| |
| |
| |
Reflection and transmission for electromagnetic waves in matter: Normal incidence | |
| |
| |
| |
Reflection and transmission for sound waves, and summary of isomorphisms | |
| |
| |
| |
Snell's Law | |
| |
| |
| |
Total internal reflection and evanescent waves | |
| |
| |
Concept and skill inventory | |
| |
| |
Problems | |
| |
| |
| |
Group Velocity for an Arbitrary Envelope Function | |
| |
| |
Index | |