| |
| |
| 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 | |