3.1.4. Damped Oscillations

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Where to Move

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• ☰ 1. Mathematical Foundations of Physics
  • ☰ 1.1. Physical Quantities and Units
    • ☰ 1.1.1. Physical Quantities
    • ☰ 1.1.2. SI Base Units
    • ☰ 1.1.3. Derived Units
    • ☰ 1.1.4. Unit Conversions
    • ☰ 1.1.5. Scientific Notation
    • ☰ 1.1.6. Orders of Magnitude
    • ☰ 1.1.7. Dimensional Analysis
    • ☰ 1.1.8. Significant Figures
    • ☰ 1.1.9. Measurement Uncertainty
  • ☰ 1.2. Scalars and Vectors
    • ☰ 1.2.1. Scalars and Vectors
    • ☰ 1.2.2. Vector Notation
    • ☰ 1.2.3. Vector Addition and Subtraction
    • ☰ 1.2.4. Vector Components
    • ☰ 1.2.5. Unit Vectors
    • ☰ 1.2.6. Dot Product
    • ☰ 1.2.7. Cross Product
    • ☰ 1.2.8. Applications of Vectors in Physics
  • ☰ 1.3. Coordinate Systems
    • ☰ 1.3.1. Cartesian Coordinates
    • ☰ 1.3.2. Polar Coordinates
    • ☰ 1.3.3. Cylindrical Coordinates
    • ☰ 1.3.4. Spherical Coordinates
    • ☰ 1.3.5. Coordinate Transformations
  • ☰ 1.4. Calculus for Physics
    • ☰ 1.4.1. Functions and Graphs
    • ☰ 1.4.2. Derivatives
    • ☰ 1.4.3. Physical Meaning of Derivatives
    • ☰ 1.4.4. Partial Derivatives
    • ☰ 1.4.5. Integrals
    • ☰ 1.4.6. Physical Meaning of Integrals
    • ☰ 1.4.7. Differential Equations
    • ☰ 1.4.8. Taylor Series and Approximations
• ☰ 2. Part I: Classical Mechanics
  • ☰ 2.1. Kinematics
    • ☰ 2.1.1. Motion in One Dimension
      • ☰ 2.1.1.1. Position
      • ☰ 2.1.1.2. Distance and Displacement
      • ☰ 2.1.1.3. Speed and Velocity
      • ☰ 2.1.1.4. Average Velocity
      • ☰ 2.1.1.5. Instantaneous Velocity
      • ☰ 2.1.1.6. Acceleration
    • ☰ 2.1.2. Motion with Constant Acceleration
      • ☰ 2.1.2.1. Kinematic Equations
      • ☰ 2.1.2.2. Free Fall
      • ☰ 2.1.2.3. Vertical Motion
      • ☰ 2.1.2.4. Position-Time Graphs
      • ☰ 2.1.2.5. Velocity-Time Graphs
      • ☰ 2.1.2.6. Acceleration-Time Graphs
    • ☰ 2.1.3. Motion in Two and Three Dimensions
      • ☰ 2.1.3.1. Position Vectors
      • ☰ 2.1.3.2. Velocity Vectors
      • ☰ 2.1.3.3. Acceleration Vectors
      • ☰ 2.1.3.4. Relative Motion
    • ☰ 2.1.4. Projectile Motion
      • ☰ 2.1.4.1. Horizontal Projection
      • ☰ 2.1.4.2. Oblique Projection
      • ☰ 2.1.4.3. Maximum Height
      • ☰ 2.1.4.4. Time of Flight
      • ☰ 2.1.4.5. Projectile Range
      • ☰ 2.1.4.6. Trajectory Equation
    • ☰ 2.1.5. Circular Motion
      • ☰ 2.1.5.1. Angular Position
      • ☰ 2.1.5.2. Angular Velocity
      • ☰ 2.1.5.3. Angular Acceleration
      • ☰ 2.1.5.4. Uniform Circular Motion
      • ☰ 2.1.5.5. Centripetal Acceleration
  • ☰ 2.2. Newton's Laws of Motion
    • ☰ 2.2.1. Force
      • ☰ 2.2.1.1. Concept of Force
      • ☰ 2.2.1.2. Fundamental Forces
      • ☰ 2.2.1.3. Contact Forces
      • ☰ 2.2.1.4. Free-Body Diagrams
    • ☰ 2.2.2. Newton's First Law
      • ☰ 2.2.2.1. Inertia
      • ☰ 2.2.2.2. Inertial Reference Frames
      • ☰ 2.2.2.3. Equilibrium
    • ☰ 2.2.3. Newton's Second Law
      • ☰ 2.2.3.1. Force, Mass, and Acceleration
      • ☰ 2.2.3.2. Net Force
      • ☰ 2.2.3.3. Applications of F = ma
    • ☰ 2.2.4. Newton's Third Law
      • ☰ 2.2.4.1. Action-Reaction Pairs
      • ☰ 2.2.4.2. Interaction Forces
    • ☰ 2.2.5. Common Forces
      • ☰ 2.2.5.1. Weight
      • ☰ 2.2.5.2. Normal Force
      • ☰ 2.2.5.3. Tension
      • ☰ 2.2.5.4. Spring Force
      • ☰ 2.2.5.5. Static Friction
      • ☰ 2.2.5.6. Kinetic Friction
      • ☰ 2.2.5.7. Drag Force
    • ☰ 2.2.6. Applications of Newton's Laws
      • ☰ 2.2.6.1. Connected Objects
      • ☰ 2.2.6.2. Pulley Systems
      • ☰ 2.2.6.3. Inclined Planes
      • ☰ 2.2.6.4. Elevators
      • ☰ 2.2.6.5. Circular Motion
  • ☰ 2.3. Work and Energy
    • ☰ 2.3.1. Work
      • ☰ 2.3.1.1. Work Done by a Constant Force
      • ☰ 2.3.1.2. Work Done by a Variable Force
      • ☰ 2.3.1.3. Work from Force-Position Graphs
    • ☰ 2.3.2. Kinetic Energy
      • ☰ 2.3.2.1. Translational Kinetic Energy
      • ☰ 2.3.2.2. Work-Energy Theorem
    • ☰ 2.3.3. Potential Energy
      • ☰ 2.3.3.1. Gravitational Potential Energy
      • ☰ 2.3.3.2. Elastic Potential Energy
      • ☰ 2.3.3.3. Potential-Energy Curves
    • ☰ 2.3.4. Conservation of Energy
      • ☰ 2.3.4.1. Mechanical Energy
      • ☰ 2.3.4.2. Conservative Forces
      • ☰ 2.3.4.3. Non-Conservative Forces
      • ☰ 2.3.4.4. Conservation of Mechanical Energy
      • ☰ 2.3.4.5. Energy Dissipation
    • ☰ 2.3.5. Power
      • ☰ 2.3.5.1. Average Power
      • ☰ 2.3.5.2. Instantaneous Power
      • ☰ 2.3.5.3. Efficiency
  • ☰ 2.4. Momentum and Collisions
    • ☰ 2.4.1. Linear Momentum
      • ☰ 2.4.1.1. Momentum
      • ☰ 2.4.1.2. Momentum and Force
    • ☰ 2.4.2. Impulse
      • ☰ 2.4.2.1. Impulse
      • ☰ 2.4.2.2. Impulse-Momentum Theorem
      • ☰ 2.4.2.3. Force-Time Graphs
    • ☰ 2.4.3. Conservation of Momentum
      • ☰ 2.4.3.1. Isolated Systems
      • ☰ 2.4.3.2. Center-of-Mass Motion
    • ☰ 2.4.4. Collisions
      • ☰ 2.4.4.1. Elastic Collisions
      • ☰ 2.4.4.2. Inelastic Collisions
      • ☰ 2.4.4.3. Perfectly Inelastic Collisions
      • ☰ 2.4.4.4. One-Dimensional Collisions
      • ☰ 2.4.4.5. Two-Dimensional Collisions
    • ☰ 2.4.5. Center of Mass
      • ☰ 2.4.5.1. Center of Mass of Particles
      • ☰ 2.4.5.2. Center of Mass of Continuous Objects
    • ☰ 2.4.6. Rocket Motion
      • ☰ 2.4.6.1. Variable-Mass Systems
      • ☰ 2.4.6.2. Rocket Equation
  • ☰ 2.5. Rotational Motion
    • ☰ 2.5.1. Rotational Kinematics
      • ☰ 2.5.1.1. Angular Displacement
      • ☰ 2.5.1.2. Angular Velocity
      • ☰ 2.5.1.3. Angular Acceleration
    • ☰ 2.5.2. Torque
      • ☰ 2.5.2.1. Torque
      • ☰ 2.5.2.2. Lever Arm
      • ☰ 2.5.2.3. Vector Definition of Torque
    • ☰ 2.5.3. Moment of Inertia
      • ☰ 2.5.3.1. Rotational Inertia
      • ☰ 2.5.3.2. Common Moments of Inertia
      • ☰ 2.5.3.3. Parallel-Axis Theorem
    • ☰ 2.5.4. Rotational Dynamics
      • ☰ 2.5.4.1. Newton's Second Law for Rotation
      • ☰ 2.5.4.2. Rotational Kinetic Energy
      • ☰ 2.5.4.3. Work and Power in Rotation
    • ☰ 2.5.5. Angular Momentum
      • ☰ 2.5.5.1. Angular Momentum
      • ☰ 2.5.5.2. Conservation of Angular Momentum
    • ☰ 2.5.6. Rolling Motion
      • ☰ 2.5.6.1. Rolling Without Slipping
      • ☰ 2.5.6.2. Translational and Rotational Energy
    • ☰ 2.5.7. Static Equilibrium
      • ☰ 2.5.7.1. Conditions for Equilibrium
      • ☰ 2.5.7.2. Center of Gravity
      • ☰ 2.5.7.3. Stability
  • ☰ 2.6. Gravitation
    • ☰ 2.6.1. Newton's Law of Gravitation
      • ☰ 2.6.1.1. Universal Gravitation
      • ☰ 2.6.1.2. Gravitational Constant
      • ☰ 2.6.1.3. Superposition
    • ☰ 2.6.2. Gravitational Field
      • ☰ 2.6.2.1. Gravitational Field Strength
      • ☰ 2.6.2.2. Field of Spherical Bodies
    • ☰ 2.6.3. Gravitational Potential
      • ☰ 2.6.3.1. Gravitational Potential Energy
      • ☰ 2.6.3.2. Gravitational Potential
    • ☰ 2.6.4. Planetary Motion
      • ☰ 2.6.4.1. Kepler's Laws
      • ☰ 2.6.4.2. Circular Orbits
      • ☰ 2.6.4.3. Orbital Velocity
      • ☰ 2.6.4.4. Orbital Period
    • ☰ 2.6.5. Satellites and Spaceflight
      • ☰ 2.6.5.1. Geostationary Satellites
      • ☰ 2.6.5.2. Escape Velocity
      • ☰ 2.6.5.3. Orbital Energy
• ☰ 3. Part II: Oscillations, Waves, and Fluids
  • ☰ 3.1. Oscillations
    • ☰ 3.1.1. Simple Harmonic Motion
      • ☰ 3.1.1.1. Periodic Motion
      • ☰ 3.1.1.2. Amplitude
      • ☰ 3.1.1.3. Frequency and Period
      • ☰ 3.1.1.4. Angular Frequency
      • ☰ 3.1.1.5. SHM Equation
    • ☰ 3.1.2. Mass-Spring Systems
      • ☰ 3.1.2.1. Hooke's Law
      • ☰ 3.1.2.2. Spring Oscillations
      • ☰ 3.1.2.3. Energy in SHM
    • ☰ 3.1.3. Pendulums
      • ☰ 3.1.3.1. Simple Pendulum
      • ☰ 3.1.3.2. Physical Pendulum
    • ☰ 3.1.4. Damped Oscillations
      • ☰ 3.1.4.1. Damping
      • ☰ 3.1.4.2. Critical Damping
    • ☰ 3.1.5. Forced Oscillations and Resonance
      • ☰ 3.1.5.1. Driving Force
      • ☰ 3.1.5.2. Resonance
      • ☰ 3.1.5.3. Natural Frequency
  • ☰ 3.2. Mechanical Waves
    • ☰ 3.2.1. Fundamentals of Waves
      • ☰ 3.2.1.1. Transverse Waves
      • ☰ 3.2.1.2. Longitudinal Waves
      • ☰ 3.2.1.3. Wavelength
      • ☰ 3.2.1.4. Frequency
      • ☰ 3.2.1.5. Wave Speed
      • ☰ 3.2.1.6. Amplitude
    • ☰ 3.2.2. Mathematical Description of Waves
      • ☰ 3.2.2.1. Wave Function
      • ☰ 3.2.2.2. Phase
      • ☰ 3.2.2.3. Wave Equation
    • ☰ 3.2.3. Superposition
      • ☰ 3.2.3.1. Interference
      • ☰ 3.2.3.2. Constructive Interference
      • ☰ 3.2.3.3. Destructive Interference
    • ☰ 3.2.4. Standing Waves
      • ☰ 3.2.4.1. Nodes and Antinodes
      • ☰ 3.2.4.2. Strings
      • ☰ 3.2.4.3. Pipes
      • ☰ 3.2.4.4. Harmonics
    • ☰ 3.2.5. Sound Waves
      • ☰ 3.2.5.1. Speed of Sound
      • ☰ 3.2.5.2. Sound Intensity
      • ☰ 3.2.5.3. Decibels
      • ☰ 3.2.5.4. Beats
      • ☰ 3.2.5.5. Doppler Effect
  • ☰ 3.3. Fluid Mechanics
    • ☰ 3.3.1. Properties of Fluids
      • ☰ 3.3.1.1. Density
      • ☰ 3.3.1.2. Pressure
      • ☰ 3.3.1.3. Compressibility
    • ☰ 3.3.2. Fluid Statics
      • ☰ 3.3.2.1. Hydrostatic Pressure
      • ☰ 3.3.2.2. Pascal's Principle
    • ☰ 3.3.3. Buoyancy
      • ☰ 3.3.3.1. Archimedes' Principle
      • ☰ 3.3.3.2. Floating and Sinking
    • ☰ 3.3.4. Fluid Dynamics
      • ☰ 3.3.4.1. Flow Rate
      • ☰ 3.3.4.2. Continuity Equation
      • ☰ 3.3.4.3. Bernoulli's Equation
    • ☰ 3.3.5. Viscosity
      • ☰ 3.3.5.1. Laminar Flow
      • ☰ 3.3.5.2. Turbulent Flow
      • ☰ 3.3.5.3. Poiseuille's Law
      • ☰ 3.3.5.4. Reynolds Number
• ☰ 4. Part III: Thermodynamics
  • ☰ 4.1. Temperature and Heat
    • ☰ 4.1.1. Temperature and Thermal Equilibrium
    • ☰ 4.1.2. Zeroth Law of Thermodynamics
    • ☰ 4.1.3. Temperature Scales
    • ☰ 4.1.4. Thermal Expansion
    • ☰ 4.1.5. Heat and Internal Energy
    • ☰ 4.1.6. Specific Heat Capacity
    • ☰ 4.1.7. Calorimetry
    • ☰ 4.1.8. Phase Changes
    • ☰ 4.1.9. Latent Heat
    • ☰ 4.1.10. Heat Transfer
  • ☰ 4.2. Kinetic Theory of Gases
    • ☰ 4.2.1. Ideal Gas Law
    • ☰ 4.2.2. Molecular Interpretation of Pressure
    • ☰ 4.2.3. Temperature and Molecular Kinetic Energy
    • ☰ 4.2.4. RMS Molecular Speed
    • ☰ 4.2.5. Maxwell-Boltzmann Distribution
    • ☰ 4.2.6. Mean Free Path
  • ☰ 4.3. Thermodynamics
    • ☰ 4.3.1. Thermodynamic Systems
    • ☰ 4.3.2. First Law of Thermodynamics
    • ☰ 4.3.3. Isothermal Processes
    • ☰ 4.3.4. Isobaric Processes
    • ☰ 4.3.5. Isochoric Processes
    • ☰ 4.3.6. Adiabatic Processes
    • ☰ 4.3.7. Heat Engines
    • ☰ 4.3.8. Carnot Cycle
    • ☰ 4.3.9. Refrigerators
    • ☰ 4.3.10. Second Law of Thermodynamics
    • ☰ 4.3.11. Entropy
    • ☰ 4.3.12. Reversible and Irreversible Processes
• ☰ 5. Part IV: Electricity and Magnetism
  • ☰ 5.1. Electric Charge and Electric Field
    • ☰ 5.1.1. Electric Charge
    • ☰ 5.1.2. Conductors and Insulators
    • ☰ 5.1.3. Coulomb's Law
    • ☰ 5.1.4. Superposition
    • ☰ 5.1.5. Electric Field
    • ☰ 5.1.6. Electric Field Lines
    • ☰ 5.1.7. Electric Dipoles
    • ☰ 5.1.8. Electric Flux
    • ☰ 5.1.9. Gauss's Law
  • ☰ 5.2. Electric Potential
    • ☰ 5.2.1. Electric Potential Energy
    • ☰ 5.2.2. Electric Potential
    • ☰ 5.2.3. Equipotential Surfaces
    • ☰ 5.2.4. Relationship Between Potential and Field
    • ☰ 5.2.5. Potential of Continuous Charge Distributions
  • ☰ 5.3. Capacitance
    • ☰ 5.3.1. Capacitors
    • ☰ 5.3.2. Parallel-Plate Capacitor
    • ☰ 5.3.3. Series and Parallel Capacitors
    • ☰ 5.3.4. Energy Stored in Capacitors
    • ☰ 5.3.5. Dielectrics
    • ☰ 5.3.6. Polarization
  • ☰ 5.4. Electric Current and Resistance
    • ☰ 5.4.1. Electric Current
    • ☰ 5.4.2. Current Density
    • ☰ 5.4.3. Drift Velocity
    • ☰ 5.4.4. Resistance
    • ☰ 5.4.5. Ohm's Law
    • ☰ 5.4.6. Resistivity
    • ☰ 5.4.7. Electrical Energy
    • ☰ 5.4.8. Electric Power
    • ☰ 5.4.9. Electromotive Force
  • ☰ 5.5. DC Circuits
    • ☰ 5.5.1. Kirchhoff's Laws
    • ☰ 5.5.2. Multi-Loop Circuits
    • ☰ 5.5.3. RC Circuits
    • ☰ 5.5.4. Measuring Instruments
  • ☰ 5.6. Magnetism
    • ☰ 5.6.1. Magnetic Fields
    • ☰ 5.6.2. Lorentz Force
    • ☰ 5.6.3. Motion of Charged Particles
    • ☰ 5.6.4. Force on Current-Carrying Wires
    • ☰ 5.6.5. Torque on Current Loops
    • ☰ 5.6.6. Biot-Savart Law
    • ☰ 5.6.7. Ampère's Law
    • ☰ 5.6.8. Solenoids
    • ☰ 5.6.9. Magnetic Materials
  • ☰ 5.7. Electromagnetic Induction
    • ☰ 5.7.1. Magnetic Flux
    • ☰ 5.7.2. Faraday's Law
    • ☰ 5.7.3. Lenz's Law
    • ☰ 5.7.4. Motional EMF
    • ☰ 5.7.5. Self-Inductance
    • ☰ 5.7.6. Mutual Inductance
    • ☰ 5.7.7. RL Circuits
    • ☰ 5.7.8. LC Oscillations
  • ☰ 5.8. Alternating Current
    • ☰ 5.8.1. AC Voltage and Current
    • ☰ 5.8.2. RMS Quantities
    • ☰ 5.8.3. Resistors in AC Circuits
    • ☰ 5.8.4. Capacitors in AC Circuits
    • ☰ 5.8.5. Inductors in AC Circuits
    • ☰ 5.8.6. RLC Circuits
    • ☰ 5.8.7. Impedance
    • ☰ 5.8.8. Resonance
    • ☰ 5.8.9. Transformers
  • ☰ 5.9. Maxwell's Equations and Electromagnetic Waves
    • ☰ 5.9.1. Gauss's Law for Electricity
    • ☰ 5.9.2. Gauss's Law for Magnetism
    • ☰ 5.9.3. Faraday's Law
    • ☰ 5.9.4. Ampère-Maxwell Law
    • ☰ 5.9.5. Electromagnetic Waves
    • ☰ 5.9.6. Speed of Light
    • ☰ 5.9.7. Electromagnetic Spectrum
    • ☰ 5.9.8. Poynting Vector
    • ☰ 5.9.9. Radiation Pressure
• ☰ 6. Part V: Optics
  • ☰ 6.1. Geometrical Optics
    • ☰ 6.1.1. Nature of Light
    • ☰ 6.1.2. Reflection
    • ☰ 6.1.3. Plane Mirrors
    • ☰ 6.1.4. Refraction
    • ☰ 6.1.5. Snell's Law
    • ☰ 6.1.6. Total Internal Reflection
    • ☰ 6.1.7. Spherical Mirrors
    • ☰ 6.1.8. Thin Lenses
    • ☰ 6.1.9. Mirror Equation
    • ☰ 6.1.10. Lens Equation
    • ☰ 6.1.11. Magnification
    • ☰ 6.1.12. Ray Diagrams
    • ☰ 6.1.13. Optical Instruments
  • ☰ 6.2. Wave Optics
    • ☰ 6.2.1. Interference
    • ☰ 6.2.2. Young's Double-Slit Experiment
    • ☰ 6.2.3. Diffraction
    • ☰ 6.2.4. Single-Slit Diffraction
    • ☰ 6.2.5. Diffraction Gratings
    • ☰ 6.2.6. Polarization
    • ☰ 6.2.7. Malus's Law
    • ☰ 6.2.8. Brewster's Angle
    • ☰ 6.2.9. Rayleigh Criterion
    • ☰ 6.2.10. Optical Resolution
• ☰ 7. Part VI: Modern Physics
  • ☰ 7.1. Special Relativity
    • ☰ 7.1.1. Galilean Relativity
    • ☰ 7.1.2. Michelson-Morley Experiment
    • ☰ 7.1.3. Einstein's Postulates
    • ☰ 7.1.4. Lorentz Transformations
    • ☰ 7.1.5. Relativity of Simultaneity
    • ☰ 7.1.6. Time Dilation
    • ☰ 7.1.7. Length Contraction
    • ☰ 7.1.8. Relativistic Velocity Addition
    • ☰ 7.1.9. Relativistic Momentum
    • ☰ 7.1.10. Relativistic Energy
    • ☰ 7.1.11. Mass-Energy Equivalence
    • ☰ 7.1.12. Energy-Momentum Relation
    • ☰ 7.1.13. Spacetime Diagrams
    • ☰ 7.1.14. Light Cones
  • ☰ 7.2. Introduction to Quantum Physics
    • ☰ 7.2.1. Blackbody Radiation
    • ☰ 7.2.2. Planck's Hypothesis
    • ☰ 7.2.3. Photoelectric Effect
    • ☰ 7.2.4. Photon Energy
    • ☰ 7.2.5. Photon Momentum
    • ☰ 7.2.6. Compton Scattering
    • ☰ 7.2.7. de Broglie Wavelength
    • ☰ 7.2.8. Matter Waves
    • ☰ 7.2.9. Wave-Particle Duality
    • ☰ 7.2.10. Double-Slit Experiment
    • ☰ 7.2.11. Heisenberg Uncertainty Principle
  • ☰ 7.3. Quantum Mechanics
    • ☰ 7.3.1. Wave Function
    • ☰ 7.3.2. Probability Interpretation
    • ☰ 7.3.3. Normalization
    • ☰ 7.3.4. Schrödinger Equation
    • ☰ 7.3.5. Operators and Observables
    • ☰ 7.3.6. Expectation Values
    • ☰ 7.3.7. Particle in a Box
    • ☰ 7.3.8. Finite Potential Wells
    • ☰ 7.3.9. Quantum Tunneling
    • ☰ 7.3.10. Quantum Harmonic Oscillator
    • ☰ 7.3.11. Hydrogen Atom
    • ☰ 7.3.12. Quantum Numbers
    • ☰ 7.3.13. Angular Momentum
    • ☰ 7.3.14. Spin
    • ☰ 7.3.15. Stern-Gerlach Experiment
    • ☰ 7.3.16. Pauli Exclusion Principle
  • ☰ 7.4. Atomic Physics
    • ☰ 7.4.1. Thomson Atomic Model
    • ☰ 7.4.2. Rutherford Atomic Model
    • ☰ 7.4.3. Bohr Model
    • ☰ 7.4.4. Atomic Spectra
    • ☰ 7.4.5. Hydrogen Spectrum
    • ☰ 7.4.6. Electron Shells
    • ☰ 7.4.7. Orbitals
    • ☰ 7.4.8. Electron Configurations
    • ☰ 7.4.9. X-Ray Spectra
    • ☰ 7.4.10. Atomic Transitions
    • ☰ 7.4.11. Lasers
    • ☰ 7.4.12. Stimulated Emission
• ☰ 8. Part VII: Nuclear and Particle Physics
  • ☰ 8.1. Nuclear Structure
    • ☰ 8.1.1. The Atomic Nucleus
      • ☰ 8.1.1.1. Protons and Neutrons
      • ☰ 8.1.1.2. Atomic Number
      • ☰ 8.1.1.3. Mass Number
      • ☰ 8.1.1.4. Isotopes
      • ☰ 8.1.1.5. Isotones
      • ☰ 8.1.1.6. Isobars
    • ☰ 8.1.2. Nuclear Size and Density
      • ☰ 8.1.2.1. Nuclear Radius
      • ☰ 8.1.2.2. Nuclear Density
      • ☰ 8.1.2.3. Nuclear Charge Distribution
    • ☰ 8.1.3. Nuclear Forces
      • ☰ 8.1.3.1. Strong Nuclear Force
      • ☰ 8.1.3.2. Properties of Nuclear Forces
      • ☰ 8.1.3.3. Proton-Neutron Interaction
      • ☰ 8.1.3.4. Nuclear Stability
    • ☰ 8.1.4. Mass and Binding Energy
      • ☰ 8.1.4.1. Atomic Mass Units
      • ☰ 8.1.4.2. Mass Defect
      • ☰ 8.1.4.3. Binding Energy
      • ☰ 8.1.4.4. Binding Energy per Nucleon
      • ☰ 8.1.4.5. Binding-Energy Curve
    • ☰ 8.1.5. Nuclear Models
      • ☰ 8.1.5.1. Liquid-Drop Model
      • ☰ 8.1.5.2. Semi-Empirical Mass Formula
      • ☰ 8.1.5.3. Nuclear Shell Model
      • ☰ 8.1.5.4. Magic Numbers
      • ☰ 8.1.5.5. Collective Model
    • ☰ 8.1.6. Nuclear Spin and Magnetic Moments
      • ☰ 8.1.6.1. Nuclear Angular Momentum
      • ☰ 8.1.6.2. Nuclear Spin
      • ☰ 8.1.6.3. Nuclear Magnetic Moment
  • ☰ 8.2. Radioactivity and Nuclear Decay
    • ☰ 8.2.1. Radioactive Decay
      • ☰ 8.2.1.1. Nuclear Instability
      • ☰ 8.2.1.2. Random Nature of Decay
      • ☰ 8.2.1.3. Decay Constant
    • ☰ 8.2.2. Radioactive Decay Law
      • ☰ 8.2.2.1. Exponential Decay
      • ☰ 8.2.2.2. Activity
      • ☰ 8.2.2.3. Half-Life
      • ☰ 8.2.2.4. Mean Lifetime
    • ☰ 8.2.3. Alpha Decay
      • ☰ 8.2.3.1. Alpha Particles
      • ☰ 8.2.3.2. Energy of Alpha Decay
    • ☰ 8.2.4. Beta Decay
      • ☰ 8.2.4.1. Beta-Minus Decay
      • ☰ 8.2.4.2. Beta-Plus Decay
      • ☰ 8.2.4.3. Electron Capture
      • ☰ 8.2.4.4. Neutrinos
      • ☰ 8.2.4.5. Energy Spectrum
    • ☰ 8.2.5. Gamma Decay
      • ☰ 8.2.5.1. Nuclear Excited States
      • ☰ 8.2.5.2. Gamma-Ray Emission
      • ☰ 8.2.5.3. Internal Conversion
    • ☰ 8.2.6. Decay Chains
      • ☰ 8.2.6.1. Parent and Daughter Nuclei
      • ☰ 8.2.6.2. Secular Equilibrium
      • ☰ 8.2.6.3. Natural Radioactive Series
  • ☰ 8.3. Interaction of Radiation with Matter
    • ☰ 8.3.1. Charged Particle Interactions
      • ☰ 8.3.1.1. Ionization
      • ☰ 8.3.1.2. Excitation
      • ☰ 8.3.1.3. Energy Loss
      • ☰ 8.3.1.4. Stopping Power
      • ☰ 8.3.1.5. Range
    • ☰ 8.3.2. Heavy Charged Particles
      • ☰ 8.3.2.1. Alpha Particles
      • ☰ 8.3.2.2. Bragg Curve
      • ☰ 8.3.2.3. Bragg Peak
    • ☰ 8.3.3. Electron Interactions
      • ☰ 8.3.3.1. Collisional Energy Loss
      • ☰ 8.3.3.2. Bremsstrahlung
      • ☰ 8.3.3.3. Electron Range
    • ☰ 8.3.4. Photon Interactions
      • ☰ 8.3.4.1. Pair Production
      • ☰ 8.3.4.2. Rayleigh Scattering
    • ☰ 8.3.5. Attenuation of Radiation
      • ☰ 8.3.5.1. Linear Attenuation Coefficient
      • ☰ 8.3.5.2. Mass Attenuation Coefficient
      • ☰ 8.3.5.3. Exponential Attenuation
      • ☰ 8.3.5.4. Half-Value Layer
    • ☰ 8.3.6. Neutron Interactions
      • ☰ 8.3.6.1. Elastic Scattering
      • ☰ 8.3.6.2. Inelastic Scattering
      • ☰ 8.3.6.3. Neutron Capture
      • ☰ 8.3.6.4. Neutron Moderation
  • ☰ 8.4. Radiation Detection and Measurement
    • ☰ 8.4.1. Principles of Radiation Detection
      • ☰ 8.4.1.1. Energy Deposition
      • ☰ 8.4.1.2. Detector Efficiency
      • ☰ 8.4.1.3. Energy Resolution
      • ☰ 8.4.1.4. Timing Resolution
      • ☰ 8.4.1.5. Dead Time
    • ☰ 8.4.2. Gas-Filled Detectors
      • ☰ 8.4.2.1. Ionization Chambers
      • ☰ 8.4.2.2. Proportional Counters
      • ☰ 8.4.2.3. Geiger-Müller Counters
    • ☰ 8.4.3. Scintillation Detectors
      • ☰ 8.4.3.1. Scintillation Process
      • ☰ 8.4.3.2. Organic Scintillators
      • ☰ 8.4.3.3. Inorganic Scintillators
      • ☰ 8.4.3.4. Photomultiplier Tubes
      • ☰ 8.4.3.5. Silicon Photomultipliers
    • ☰ 8.4.4. Semiconductor Detectors
      • ☰ 8.4.4.1. Silicon Detectors
      • ☰ 8.4.4.2. Germanium Detectors
      • ☰ 8.4.4.3. Electron-Hole Pair Creation
    • ☰ 8.4.5. Gamma-Ray Spectroscopy
      • ☰ 8.4.5.1. Photopeak
      • ☰ 8.4.5.2. Compton Continuum
      • ☰ 8.4.5.3. Compton Edge
      • ☰ 8.4.5.4. Escape Peaks
    • ☰ 8.4.6. Coincidence Measurements
      • ☰ 8.4.6.1. Coincidence Detection
      • ☰ 8.4.6.2. Timing Windows
      • ☰ 8.4.6.3. True Coincidences
      • ☰ 8.4.6.4. Random Coincidences
  • ☰ 8.5. Nuclear Reactions
    • ☰ 8.5.1. Principles of Nuclear Reactions
      • ☰ 8.5.1.1. Reaction Notation
      • ☰ 8.5.1.2. Conservation Laws
      • ☰ 8.5.1.3. Reaction Energetics
    • ☰ 8.5.2. Q-Value
      • ☰ 8.5.2.1. Exothermic Reactions
      • ☰ 8.5.2.2. Endothermic Reactions
      • ☰ 8.5.2.3. Reaction Thresholds
    • ☰ 8.5.3. Reaction Cross Section
      • ☰ 8.5.3.1. Cross Section
      • ☰ 8.5.3.2. Reaction Probability
      • ☰ 8.5.3.3. Energy Dependence
    • ☰ 8.5.4. Types of Nuclear Reactions
      • ☰ 8.5.4.1. Elastic Scattering
      • ☰ 8.5.4.2. Inelastic Scattering
      • ☰ 8.5.4.3. Capture Reactions
      • ☰ 8.5.4.4. Transfer Reactions
      • ☰ 8.5.4.5. Charge-Exchange Reactions
    • ☰ 8.5.5. Compound Nucleus
      • ☰ 8.5.5.1. Formation
      • ☰ 8.5.5.2. Decay Channels
      • ☰ 8.5.5.3. Resonances
  • ☰ 8.6. Nuclear Fission and Fusion
    • ☰ 8.6.1. Nuclear Fission
      • ☰ 8.6.1.1. Fission Process
      • ☰ 8.6.1.2. Fission Fragments
      • ☰ 8.6.1.3. Energy Release
      • ☰ 8.6.1.4. Neutron Production
    • ☰ 8.6.2. Chain Reactions
      • ☰ 8.6.2.1. Criticality
      • ☰ 8.6.2.2. Multiplication Factor
      • ☰ 8.6.2.3. Critical Mass
    • ☰ 8.6.3. Nuclear Reactors
      • ☰ 8.6.3.1. Reactor Components
      • ☰ 8.6.3.2. Fuel
      • ☰ 8.6.3.3. Moderator
      • ☰ 8.6.3.4. Control Rods
      • ☰ 8.6.3.5. Coolant
    • ☰ 8.6.4. Nuclear Fusion
      • ☰ 8.6.4.1. Fusion Reactions
      • ☰ 8.6.4.2. Coulomb Barrier
    • ☰ 8.6.5. Stellar Fusion
      • ☰ 8.6.5.1. Proton-Proton Chain
      • ☰ 8.6.5.2. CNO Cycle
      • ☰ 8.6.5.3. Nucleosynthesis
    • ☰ 8.6.6. Controlled Fusion
      • ☰ 8.6.6.1. Magnetic Confinement
      • ☰ 8.6.6.2. Tokamaks
      • ☰ 8.6.6.3. Inertial Confinement
  • ☰ 8.7. Particle Physics Foundations
    • ☰ 8.7.1. From Atoms to Elementary Particles
      • ☰ 8.7.1.1. Discovery of the Electron
      • ☰ 8.7.1.2. Discovery of the Nucleus
      • ☰ 8.7.1.3. Discovery of the Neutron
      • ☰ 8.7.1.4. Discovery of Antimatter
    • ☰ 8.7.2. Classification of Particles
      • ☰ 8.7.2.1. Elementary Particles
      • ☰ 8.7.2.2. Composite Particles
      • ☰ 8.7.2.3. Fermions
      • ☰ 8.7.2.4. Bosons
    • ☰ 8.7.3. Antiparticles
      • ☰ 8.7.3.1. Matter and Antimatter
      • ☰ 8.7.3.2. Pair Production
      • ☰ 8.7.3.3. Annihilation
    • ☰ 8.7.4. Relativistic Particle Kinematics
      • ☰ 8.7.4.1. Four-Momentum
      • ☰ 8.7.4.2. Invariant Mass
    • ☰ 8.7.5. Particle Decays
      • ☰ 8.7.5.1. Decay Width
      • ☰ 8.7.5.2. Lifetime
      • ☰ 8.7.5.3. Branching Ratio
      • ☰ 8.7.5.4. Conservation Laws
  • ☰ 8.8. Quarks and Hadrons
    • ☰ 8.8.1. Quarks
      • ☰ 8.8.1.1. Up Quark
      • ☰ 8.8.1.2. Down Quark
      • ☰ 8.8.1.3. Strange Quark
      • ☰ 8.8.1.4. Charm Quark
      • ☰ 8.8.1.5. Top Quark
      • ☰ 8.8.1.6. Bottom Quark
    • ☰ 8.8.2. Quark Properties
      • ☰ 8.8.2.1. Mass
      • ☰ 8.8.2.2. Flavor
      • ☰ 8.8.2.3. Color Charge
    • ☰ 8.8.3. Hadrons
      • ☰ 8.8.3.1. Baryons
      • ☰ 8.8.3.2. Mesons
    • ☰ 8.8.4. Baryon Structure
      • ☰ 8.8.4.1. Proton Quark Structure
      • ☰ 8.8.4.2. Neutron Quark Structure
      • ☰ 8.8.4.3. Other Baryons
    • ☰ 8.8.5. Meson Structure
      • ☰ 8.8.5.1. Pions
      • ☰ 8.8.5.2. Kaons
      • ☰ 8.8.5.3. Heavy Mesons
    • ☰ 8.8.6. Confinement
      • ☰ 8.8.6.1. Color Confinement
      • ☰ 8.8.6.2. Hadronization
      • ☰ 8.8.6.3. Jets
  • ☰ 8.9. Leptons and Neutrinos
    • ☰ 8.9.1. Charged Leptons
      • ☰ 8.9.1.1. Electron
      • ☰ 8.9.1.2. Muon
      • ☰ 8.9.1.3. Tau
    • ☰ 8.9.2. Neutrinos
      • ☰ 8.9.2.1. Electron Neutrino
      • ☰ 8.9.2.2. Muon Neutrino
      • ☰ 8.9.2.3. Tau Neutrino
    • ☰ 8.9.3. Neutrino Interactions
      • ☰ 8.9.3.1. Weak Interactions
      • ☰ 8.9.3.2. Neutrino Detection
    • ☰ 8.9.4. Neutrino Oscillations
      • ☰ 8.9.4.1. Neutrino Flavor
      • ☰ 8.9.4.2. Flavor Oscillation
      • ☰ 8.9.4.3. Neutrino Mass
  • ☰ 8.10. Fundamental Interactions
    • ☰ 8.10.1. Four Fundamental Interactions
      • ☰ 8.10.1.1. Electromagnetism
      • ☰ 8.10.1.2. Strong Interaction
      • ☰ 8.10.1.3. Weak Interaction
    • ☰ 8.10.2. Exchange Particles
      • ☰ 8.10.2.1. Photons
      • ☰ 8.10.2.2. Gluons
      • ☰ 8.10.2.3. W Bosons
      • ☰ 8.10.2.4. Z Boson
    • ☰ 8.10.3. Electromagnetic Interaction
      • ☰ 8.10.3.1. Photon Exchange
    • ☰ 8.10.4. Strong Interaction
      • ☰ 8.10.4.1. Color Charge
      • ☰ 8.10.4.2. Gluons
      • ☰ 8.10.4.3. Quantum Chromodynamics
    • ☰ 8.10.5. Weak Interaction
      • ☰ 8.10.5.1. Beta Decay
      • ☰ 8.10.5.2. W and Z Bosons
      • ☰ 8.10.5.3. Flavor-Changing Processes
  • ☰ 8.11. The Standard Model
    • ☰ 8.11.1. Overview of the Standard Model
      • ☰ 8.11.1.1. Matter Particles
      • ☰ 8.11.1.2. Force Carriers
      • ☰ 8.11.1.3. Particle Generations
    • ☰ 8.11.2. Fermions
      • ☰ 8.11.2.1. Quarks
      • ☰ 8.11.2.2. Leptons
    • ☰ 8.11.3. Gauge Bosons
      • ☰ 8.11.3.1. Photon
      • ☰ 8.11.3.2. Gluons
      • ☰ 8.11.3.3. W Bosons
      • ☰ 8.11.3.4. Z Boson
    • ☰ 8.11.4. Higgs Field and Higgs Boson
      • ☰ 8.11.4.1. Higgs Field
      • ☰ 8.11.4.2. Spontaneous Symmetry Breaking
      • ☰ 8.11.4.3. Particle Masses
      • ☰ 8.11.4.4. Higgs Boson
    • ☰ 8.11.5. Standard Model Interactions
      • ☰ 8.11.5.1. Electroweak Theory
      • ☰ 8.11.5.2. Quantum Chromodynamics
    • ☰ 8.11.6. Limitations of the Standard Model
      • ☰ 8.11.6.1. Gravity
      • ☰ 8.11.6.2. Dark Matter
      • ☰ 8.11.6.3. Neutrino Masses
      • ☰ 8.11.6.4. Matter-Antimatter Asymmetry
  • ☰ 8.12. Symmetries and Conservation Laws
    • ☰ 8.12.1. Conservation Laws
      • ☰ 8.12.1.1. Energy
    • ☰ 8.12.2. Particle Quantum Numbers
      • ☰ 8.12.2.1. Baryon Number
      • ☰ 8.12.2.2. Lepton Number
      • ☰ 8.12.2.3. Strangeness
      • ☰ 8.12.2.4. Charm
      • ☰ 8.12.2.5. Isospin
    • ☰ 8.12.3. Symmetries
      • ☰ 8.12.3.1. Charge Conjugation
      • ☰ 8.12.3.2. Parity
      • ☰ 8.12.3.3. Time Reversal
    • ☰ 8.12.4. CP Symmetry
      • ☰ 8.12.4.1. CP Conservation
      • ☰ 8.12.4.2. CP Violation
      • ☰ 8.12.4.3. Matter-Antimatter Asymmetry
  • ☰ 8.13. Particle Accelerators
    • ☰ 8.13.1. Principles of Acceleration
      • ☰ 8.13.1.1. Electric-Field Acceleration
      • ☰ 8.13.1.2. Magnetic-Field Steering
    • ☰ 8.13.2. Linear Accelerators
      • ☰ 8.13.2.1. LINACs
      • ☰ 8.13.2.2. Radio-Frequency Acceleration
    • ☰ 8.13.3. Cyclotrons
      • ☰ 8.13.3.1. Cyclotron Principle
      • ☰ 8.13.3.2. Cyclotron Frequency
      • ☰ 8.13.3.3. Limitations
    • ☰ 8.13.4. Synchrotrons
      • ☰ 8.13.4.1. Circular Accelerators
      • ☰ 8.13.4.2. Magnetic Focusing
      • ☰ 8.13.4.3. RF Cavities
    • ☰ 8.13.5. Colliders
      • ☰ 8.13.5.1. Fixed-Target Experiments
      • ☰ 8.13.5.2. Collider Experiments
      • ☰ 8.13.5.3. Center-of-Mass Energy
    • ☰ 8.13.6. Major Particle Accelerators
      • ☰ 8.13.6.1. Large Hadron Collider
      • ☰ 8.13.6.2. Electron-Positron Colliders
      • ☰ 8.13.6.3. Heavy-Ion Colliders
  • ☰ 8.14. Particle Detectors
    • ☰ 8.14.1. Principles of Particle Detection
      • ☰ 8.14.1.1. Ionization
      • ☰ 8.14.1.2. Excitation
      • ☰ 8.14.1.3. Energy Deposition
      • ☰ 8.14.1.4. Particle Identification
    • ☰ 8.14.2. Tracking Detectors
      • ☰ 8.14.2.1. Cloud Chambers
      • ☰ 8.14.2.2. Bubble Chambers
      • ☰ 8.14.2.3. Wire Chambers
      • ☰ 8.14.2.4. Silicon Trackers
    • ☰ 8.14.3. Calorimeters
      • ☰ 8.14.3.1. Electromagnetic Calorimeters
      • ☰ 8.14.3.2. Hadronic Calorimeters
      • ☰ 8.14.3.3. Shower Development
    • ☰ 8.14.4. Cherenkov Detectors
      • ☰ 8.14.4.1. Cherenkov Radiation
      • ☰ 8.14.4.2. Particle Velocity Measurement
    • ☰ 8.14.5. Time-of-Flight Detectors
      • ☰ 8.14.5.1. Timing Measurements
      • ☰ 8.14.5.2. Particle Identification
    • ☰ 8.14.6. Modern Detector Systems
      • ☰ 8.14.6.1. Tracking
      • ☰ 8.14.6.2. Muon Systems
      • ☰ 8.14.6.3. Trigger Systems
• ☰ 9. Part VIII: Condensed Matter and Applied Physics
  • ☰ 9.1. Solid-State Physics
    • ☰ 9.1.1. Crystal Structure
      • ☰ 9.1.1.1. Crystal Lattices
      • ☰ 9.1.1.2. Unit Cells
      • ☰ 9.1.1.3. Bravais Lattices
    • ☰ 9.1.2. Electronic Properties
      • ☰ 9.1.2.1. Energy Bands
      • ☰ 9.1.2.2. Conductors
      • ☰ 9.1.2.3. Insulators
      • ☰ 9.1.2.4. Semiconductors
    • ☰ 9.1.3. Semiconductor Physics
      • ☰ 9.1.3.1. Intrinsic Semiconductors
      • ☰ 9.1.3.2. Doping
      • ☰ 9.1.3.3. p-Type Materials
      • ☰ 9.1.3.4. n-Type Materials
      • ☰ 9.1.3.5. p-n Junctions
    • ☰ 9.1.4. Superconductivity
      • ☰ 9.1.4.1. Zero Resistance
      • ☰ 9.1.4.2. Meissner Effect
      • ☰ 9.1.4.3. Critical Temperature
  • ☰ 9.2. Electronics
    • ☰ 9.2.1. Semiconductor Diodes
      • ☰ 9.2.1.1. p-n Junction
      • ☰ 9.2.1.2. Diode Characteristics
      • ☰ 9.2.1.3. Rectifiers
    • ☰ 9.2.2. Transistors
      • ☰ 9.2.2.1. Bipolar Junction Transistors
      • ☰ 9.2.2.2. Field-Effect Transistors
    • ☰ 9.2.3. Operational Amplifiers
      • ☰ 9.2.3.1. Ideal Op-Amp
      • ☰ 9.2.3.2. Amplifiers
      • ☰ 9.2.3.3. Comparators
    • ☰ 9.2.4. Digital Electronics
      • ☰ 9.2.4.1. Binary Numbers
      • ☰ 9.2.4.2. Logic Gates
      • ☰ 9.2.4.3. Boolean Algebra
      • ☰ 9.2.4.4. Basic Digital Circuits
• ☰ 10. Part IX: Astrophysics and Cosmology
  • ☰ 10.1. Astrophysics
    • ☰ 10.1.1. Measuring the Universe
      • ☰ 10.1.1.1. Astronomical Distances
      • ☰ 10.1.1.2. Parallax
      • ☰ 10.1.1.3. Luminosity
      • ☰ 10.1.1.4. Apparent Brightness
    • ☰ 10.1.2. Stars
      • ☰ 10.1.2.1. Stellar Spectra
      • ☰ 10.1.2.2. Hertzsprung-Russell Diagram
      • ☰ 10.1.2.3. Stellar Evolution
    • ☰ 10.1.3. Stellar Remnants
      • ☰ 10.1.3.1. White Dwarfs
      • ☰ 10.1.3.2. Neutron Stars
      • ☰ 10.1.3.3. Black Holes
    • ☰ 10.1.4. Galaxies
      • ☰ 10.1.4.1. Structure of Galaxies
      • ☰ 10.1.4.2. Milky Way
      • ☰ 10.1.4.3. Galaxy Classification
  • ☰ 10.2. Cosmology
    • ☰ 10.2.1. Expanding Universe
      • ☰ 10.2.1.1. Hubble's Law
      • ☰ 10.2.1.2. Cosmological Redshift
    • ☰ 10.2.2. Big Bang Cosmology
      • ☰ 10.2.2.1. Early Universe
      • ☰ 10.2.2.2. Cosmic Microwave Background
      • ☰ 10.2.2.3. Primordial Nucleosynthesis
    • ☰ 10.2.3. Dark Matter
      • ☰ 10.2.3.1. Evidence for Dark Matter