Trial ends in

### 15.13: Types of Damping TABLE OFCONTENTS X ## Chapter 1: Units, Dimensions, and Measurements 301.1: The Scope of Physics301.2: Orders of Magnitude301.3: Models, Theories, and Laws301.4: Units and Standards of Measurement301.5: Estimation of the Physical Quantities301.6: Base Quantities and Derived Quantities301.7: Conversion of Units301.8: Accuracy and Precision301.9: Random and Systematic Errors301.10: Rules for Significant Figures301.11: Significant Figures in Calculations301.12: Dimensional Analysis301.13: Problem Solving: Dimensional Analysis301.14: Solving Problems in Physics ## Chapter 2: Vectors and Scalars 302.1: Introduction to Scalars302.2: Introduction to Vectors302.3: Vector Components in the Cartesian Coordinate System302.4: Polar and Cylindrical Coordinates302.5: Spherical Coordinates302.6: Vector Algebra: Graphical Method302.7: Vector Algebra: Method of Components302.8: Scalar Product (Dot Product)302.9: Vector Product (Cross Product)302.10: Scalar and Vector Triple Products302.11: Gradient and Del Operator302.12: Divergence and Curl302.13: Second Derivatives and Laplace Operator302.14: Line, Surface, and Volume Integrals302.15: Divergence and Stokes' Theorems ## Chapter 3: Motion Along a Straight Line 303.1: Position and Displacement303.2: Average Velocity303.3: Instantaneous Velocity - I303.4: Instantaneous Velocity - II303.5: Average Acceleration303.6: Instantaneous Acceleration303.7: Kinematic Equations - I303.8: Kinematic Equations - II303.9: Kinematic Equations - III303.10: Kinematic Equations: Problem Solving303.11: Free-falling Bodies: Introduction303.12: Free-falling Bodies: Example303.13: Velocity and Position by Graphical Method303.14: Velocity and Position by Integral Method ## Chapter 4: Motion in Two or Three Dimensions 304.1: Position and Displacement Vectors304.2: Average and Instantaneous Velocity Vectors304.3: Acceleration Vectors304.4: Direction of Acceleration Vectors304.5: Projectile Motion304.6: Projectile Motion: Equations304.7: Projectile Motion: Example304.8: Uniform Circular Motion304.9: Non-uniform Circular Motion304.10: Relative Velocity in One Dimension304.11: Relative Velocity in Two Dimensions ## Chapter 5: Newton's Laws of Motion 305.1: Force305.2: Types of Forces305.3: Newton's First Law: Introduction305.4: Newton's First Law: Application305.5: Internal and External Forces305.6: Newton's Second Law305.7: Mass and Weight305.8: Weightlessness305.9: Apparent Weight305.10: Newton's Third Law: Introduction305.11: Newton's Third Law: Examples305.12: Drawing Free-body Diagrams: Rules305.13: Free Body Diagrams: Examples305.14: Inertial Frames of Reference305.15: Non-inertial Frames of Reference305.16: Centrifugal Force ## Chapter 6: Application of Newton's Laws of Motion 306.1: First Law: Particles in One-dimensional Equilibrium306.2: First Law: Particles in Two-dimensional Equilibrium306.3: Second Law: Motion under Same Force306.4: Second Law: Motion under Same Acceleration306.5: Frictional Force306.6: Static and Kinetic Frictional Force306.7: Dynamics of Circular Motion306.8: Dynamics Of Circular Motion: Applications306.9: Drag Force and Terminal Speed306.10: Tension ## Chapter 7: Work and Kinetic Energy 307.1: Work307.2: Positive, Negative, and Zero Work307.3: Energy307.4: Types of Potential Energy307.5: Types of Kinetic Energy307.6: Kinetic Energy - I307.7: Kinetic Energy - II307.8: Work-energy Theorem307.9: Work and Energy for Variable Forces307.10: Work-Energy Theorem for Motion Along a Curve307.11: Work Done Over an Inclined Plane307.12: Work Done by Many Forces307.13: Work Done by Gravity307.14: Power307.15: Power Expended by a Constant Force ## Chapter 8: Potential Energy and Energy Conservation 308.1: Gravitational Potential Energy308.2: Elastic Potential Energy308.3: Conservation of Mechanical Energy308.4: Work Done on a System by External Force308.5: Conservative Forces308.6: Non-conservative Forces308.7: Conservation of Energy308.8: Conservation of Energy: Application308.9: Force and Potential Energy in One Dimension308.10: Force and Potential Energy in Three Dimensions308.11: Energy Diagrams - I308.12: Energy Diagrams - II ## Chapter 9: Linear Momentum, Impulse and Collisions 309.1: Linear Momentum309.2: Force and Momentum309.3: Impulse309.4: Impulse-Momentum Theorem309.5: Conservation of Momentum: Introduction309.6: Conservation of Momentum: Problem Solving309.7: Types Of Collisions - I309.8: Types of Collisions - II309.9: Elastic Collisions: Introduction309.10: Elastic Collisions: Case Study309.11: Collisions in Multiple Dimensions: Introduction309.12: Collisions in Multiple Dimensions: Problem Solving309.13: Center of Mass: Introduction309.14: Significance of Center of Mass309.15: Gravitational Potential Energy for Extended Objects309.16: Rocket Propulsion in Empty Space - I309.17: Rocket Propulsion In Empty Space - II309.18: Rocket Propulsion in Gravitational Field - I309.19: Rocket Propulsion in Gravitational Field - II ## Chapter 10: Rotation and Rigid Bodies 3010.1: Angular Velocity and Displacement3010.2: Angular Velocity and Acceleration3010.3: Rotation with Constant Angular Acceleration - I3010.4: Rotation with Constant Angular Acceleration - II3010.5: Relating Angular And Linear Quantities - I3010.6: Relating Angular And Linear Quantities - II3010.7: Moment of Inertia3010.8: Moment of Inertia and Rotational Kinetic Energy3010.9: Moment of Inertia: Calculations3010.10: Moment of Inertia of Compound Objects3010.11: Parallel-axis Theorem3010.12: Perpendicular-Axis Theorem3010.13: Vector Transformation in Rotating Coordinate Systems3010.14: Coriolis Force ## Chapter 11: Dynamics of Rotational Motions 3011.1: Torque3011.2: Net Torque Calculations3011.3: Equation of Rotational Dynamics3011.4: Rolling Without Slipping3011.5: Rolling With Slipping3011.6: Work and Power for Rotational Motion3011.7: Work-Energy Theorem for Rotational Motion3011.8: Angular Momentum: Single Particle3011.9: Angular Momentum: Rigid Body3011.10: Conservation of Angular Momentum3011.11: Conservation of Angular Momentum: Application3011.12: Rotation of Asymmetric Top3011.13: Gyroscope3011.14: Gyroscope: Precession ## Chapter 12: Equilibrium and Elasticity 3012.1: Static Equilibrium - I3012.2: Static Equilibrium - II3012.3: Center of Gravity3012.4: Finding the Center of Gravity3012.5: Rigid Body Equilibrium Problems - I3012.6: Rigid Body Equilibrium Problems - II3012.7: Stress3012.8: Strain and Elastic Modulus3012.9: Problem Solving on Stress and Strain3012.10: Indeterminate Structure3012.11: Elasticity3012.12: Plasticity ## Chapter 13: Fluid Mechanics 3013.1: Characteristics of Fluids3013.2: Density3013.3: Pressure of Fluids3013.4: Variation of Atmospheric Pressure3013.5: Pascal's Law3013.6: Application of Pascal's Law3013.7: Pressure Gauges3013.8: Buoyancy3013.9: Archimedes' Principle3013.10: Density and Archimedes' Principle3013.11: Accelerating Fluids3013.12: Surface Tension and Surface Energy3013.13: Excess Pressure Inside a Drop and a Bubble3013.14: Contact Angle3013.15: Rise of Liquid in a Capillary Tube3013.16: Laminar and Turbulent Flow3013.17: Equation of Continuity3013.18: Bernoulli's Equation3013.19: Bernoulli's Principle3013.20: Bernoulli's Principle: Applications3013.21: Energy Conservation and Bernoulli's Equation3013.22: Viscosity3013.23: Poiseuille's Law and Reynolds Number3013.24: Stokes' Law ## Chapter 14: Gravitation 3014.1: Gravitation3014.2: Newton's Law of Gravitation3014.3: Gravitation Between Spherically Symmetric Masses3014.4: Gravity between Spherical Bodies3014.5: Reduced Mass Coordinates: Isolated Two-body Problem3014.6: Acceleration due to Gravity on Earth3014.7: Acceleration due to Gravity on Other Planets3014.8: Apparent Weight and the Earth's Rotation3014.9: Variation in Acceleration due to Gravity near the Earth's Surface3014.10: Potential Energy due to Gravitation3014.11: The Principle of Superposition and the Gravitational Field3014.12: Escape Velocity3014.13: Circular Orbits and Critical Velocity for Satellites3014.14: Energy of a Satellite in a Circular Orbit3014.15: Kepler's First Law of Planetary Motion3014.16: Kepler's Second Law of Planetary Motion3014.17: Kepler's Third Law of Planetary Motion3014.18: Tidal Forces3014.19: Schwarzschild Radius and Event Horizon3014.20: Detection of Black Holes3014.21: Principle of Equivalence3014.22: Space-Time Curvature and the General Theory of Relativity ## Chapter 15: Oscillations 3015.1: Simple Harmonic Motion3015.2: Characteristics of Simple Harmonic Motion3015.3: Oscillations about an Equilibrium Position3015.4: Energy in Simple Harmonic Motion3015.5: Frequency of Spring-Mass System3015.6: Simple Harmonic Motion and Uniform Circular Motion3015.7: Problem Solving: Energy in Simple Harmonic Motion3015.8: Simple Pendulum3015.9: Torsional Pendulum3015.10: Physical Pendulum3015.11: Measuring Acceleration Due to Gravity3015.12: Damped Oscillations3015.13: Types of Damping3015.14: Forced Oscillations3015.15: Concept of Resonance and its Characteristics ## Chapter 16: Waves 3016.1: Travelling Waves3016.2: Wave Parameters3016.3: Equations of Wave Motion3016.4: Graphing the Wave Function3016.5: Velocity and Acceleration of a Wave3016.6: Speed of a Transverse Wave3016.7: Problem-Solving: Tuning of a Guitar String3016.8: Kinetic and Potential Energy of a Wave3016.9: Energy and Power of a Wave3016.10: Interference and Superposition of Waves3016.11: Reflection of Waves3016.12: Propagation of Waves3016.13: Standing Waves3016.14: Modes of Standing Waves - I3016.15: Modes of Standing Waves: II ## Chapter 17: Sound 3017.1: Sound Waves3017.2: Sound as Pressure Waves3017.3: Perception of Sound Waves3017.4: Speed of Sound in Solids and Liquids3017.5: Speed of Sound in Gases3017.6: Deriving the Speed of Sound in a Liquid3017.7: Sound Intensity3017.8: Sound Intensity Level3017.9: Intensity and Pressure of Sound Waves3017.10: Sound Waves: Interference3017.11: Interference: Path Lengths3017.12: Sound Waves: Resonance3017.13: Beats3017.14: Doppler Effect - I3017.15: Doppler Effect - II3017.16: Shock Waves3017.17: Echo ## Chapter 18: Temperature and Heat 3018.1: Temperature and Thermal Equilibrium3018.2: Zeroth Law of Thermodynamics3018.3: Thermometers and Temperature Scales3018.4: Gas Thermometers and the Kelvin Scale3018.5: Thermal Expansion3018.6: Thermal Stress3018.7: Heat Flow and Specific Heat3018.8: Phase Changes3018.9: Mechanisms of Heat Transfer I3018.10: Mechanisms of Heat Transfer II ## Chapter 19: The Kinetic Theory of Gases 3019.1: Ideal Gas Equation3019.2: Van der Waals Equation3019.3: pV-Diagrams3019.4: Kinetic Theory of an Ideal Gas3019.5: Molecular Kinetic Energy3019.6: Distribution of Molecular Speeds3019.7: Phase Diagram ## Chapter 20: The First Law of Thermodynamics 3020.1: Thermodynamic Systems3020.2: Work Done During Volume Change3020.3: Path Between Thermodynamics States3020.4: Internal Energy3020.5: First Law of Thermodynamics3020.6: Cyclic Processes And Isolated Systems3020.7: Isothermal Processes3020.8: Isochoric and Isobaric Processes3020.9: Heat Capacities of an Ideal Gas I3020.10: Heat Capacities of an Ideal Gas II3020.11: Heat Capacities of an Ideal Gas III3020.12: Adiabatic Processes for an Ideal Gas3020.13: Pressure and Volume in an Adiabatic Process3020.14: Work Done in an Adiabatic Process ## Chapter 21: The Second Law of Thermodynamics 3021.1: Reversible and Irreversible Processes3021.2: Heat Engines3021.3: Refrigerators and Heat Pumps3021.4: Statements of the Second Law of Thermodynamics3021.5: The Carnot Cycle3021.6: Efficiency of The Carnot Cycle3021.7: The Carnot Cycle and the Second Law of Thermodynamics3021.8: Entropy3021.9: Entropy Change in Reversible Processes3021.10: Entropy and the Second Law of Thermodynamics ## Chapter 22: Electric Charges and Fields 3022.1: Electric Charges3022.2: Sources and Properties of Electric Charge3022.3: Conductors and Insulators3022.4: Charging Conductors By Induction3022.5: Coulomb's Law3022.6: Coulomb's Law and The Principle of Superposition3022.7: Electric Field3022.8: Electric Field of Two Equal and Opposite Charges3022.9: Continuous Charge Distributions3022.10: Electric Field Lines3022.11: Properties of Electric Field Lines3022.12: Electric Dipoles and Dipole Moment3022.13: Induced Electric Dipoles ## Chapter 23: Gauss's Law 3023.1: Electric Flux3023.2: Gauss's Law3023.3: Gauss's Law: Spherical Symmetry3023.4: Gauss's Law: Cylindrical Symmetry3023.5: Gauss's Law: Planar Symmetry3023.6: Electric Field Inside a Conductor3023.7: Charge on a Conductor3023.8: Electric Field at the Surface of a Conductor ## Chapter 24: Electric Potential 3024.1: Electric Potential Energy3024.2: Electric Potential Energy in a Uniform Electric Field3024.3: Electric Potential Energy of Two Point Charges3024.4: Electric Potential and Potential Difference3024.5: Finding Electric Potential From Electric Field3024.6: Equipotential Surfaces and Field Lines3024.7: Equipotential Surfaces and Conductors3024.8: Determining Electric Field From Electric Potential ## Chapter 25: Capacitance 3025.1: Capacitors and Capacitance3025.2: Spherical and Cylindrical Capacitor3025.3: Capacitors in Series and Parallel3025.4: Energy Stored in a Capacitor3025.5: Capacitor With A Dielectric3025.6: Dielectric Polarization in a Capacitor ## Chapter 26: Current and Resistance 3026.1: Electrical Current3026.2: Drift Velocity3026.3: Current Density3026.4: Resistivity3026.5: Resistance3026.6: Ohm's Law3026.7: Electrical Power ## Chapter 27: Direct-Current Circuits 3027.1: Electromotive Force3027.2: Resistors In Series3027.3: Resistors In Parallel3027.4: Kirchhoff's Rules3027.5: Galvanometer3027.6: Ammeter3027.7: RC Circuits: Charging A Capacitor3027.8: RC Circuits: Discharging A Capacitor ## Chapter 28: Magnetic Forces and Fields 3028.1: Magnetism3028.2: Magnetic Fields3028.3: Magnetic Field Lines3028.4: Magnetic Flux3028.5: Motion Of A Charged Particle In A Magnetic Field3028.6: Magnetic Force On A Current-Carrying Conductor3028.7: Force On A Current Loop In A Magnetic Field3028.8: Torque On A Current Loop In A Magnetic Field ## Chapter 29: Sources of Magnetic Fields 3029.1: Magnetic Field due to Moving Charges3029.2: Biot-Savart Law3029.3: Magnetic Field Due To A Thin Straight Wire3029.4: Magnetic Force Between Two Parallel Currents3029.5: Magnetic Field Of A Current Loop3029.6: Ampere's Law3029.7: Ampere's Law: Problem-Solving3029.8: Solenoids3029.9: Magnetic Field of a Solenoid3029.10: Toroids3029.11: Diamagnetism3029.12: Paramagnetism3029.13: Ferromagnetism ## Chapter 30: Electromagnetic Induction 3030.1: Induction3030.2: Faraday's Law3030.3: Lenz's Law3030.4: Motional Emf3030.5: Induced Electric Fields3030.6: Displacement Current3030.7: Significance of Displacement Current3030.8: Electromagnetic Fields3030.9: Maxwell's Equation Of Electromagnetism3030.10: Symmetry in Maxwell's Equations3030.11: Electric Generator: Alternator3030.12: Back EMF ## Chapter 31: Inductance 3031.1: Mutual Inductance3031.2: Self-Inductance3031.3: Inductors3031.4: Energy In A Magnetic Field3031.5: RL Circuits3031.6: Current Growth And Decay In RL Circuits3031.7: LC Circuits3031.8: Oscillations In An LC Circuit3031.9: RLC Series Circuits ## Chapter 32: Alternating-Current Circuits 3032.1: AC Sources3032.2: Resistor in an AC Circuit3032.3: Capacitor in an AC Circuit3032.4: Inductor in an AC Circuit3032.5: RLC Series Circuits: Introduction3032.6: RLC Series Circuits: Impedance3032.7: Power in an AC Circuit3032.8: Resonance in an AC Circuit ## Chapter 33: Electromagnetic Waves 3033.1: Electromagnetic Waves3033.2: The Electromagnetic Spectrum3033.3: Plane Electromagnetic Waves I3033.4: Plane Electromagnetic Waves II3033.5: Propagation Speed of Electromagnetic Waves3033.6: Electromagnetic Waves in Matter3033.7: Energy Carried By Electromagnetic Waves3033.8: Intensity Of Electromagnetic Waves3033.9: Momentum And Radiation Pressure Full Table of Contents

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Types of Damping

### 15.13: Types of Damping

If the amount of damping in a system is gradually increased, the period and frequency start to become affected because damping opposes, and hence slows, the back and forth motion (the net force is smaller in both directions). If there is a very large amount of damping, the system does not even oscillate; instead, it slowly moves toward equilibrium. In brief, an overdamped system moves slowly towards equilibrium, whereas an underdamped system moves quickly to equilibrium but will oscillate about the equilibrium point as it does so. In contrast, a critically damped system moves as quickly as possible towards equilibrium without oscillating about the equilibrium point.

Generally, critical damping is often desired because such a system not only returns to equilibrium rapidly, but remains at equilibrium too. In addition, a constant force applied to a critically damped system moves the system to a new equilibrium position in the shortest time possible, without overshooting or oscillating about the new position. For example, when a person stands on a bathroom scale that has a needle gauge, the needle moves to its equilibrium position without oscillating. It would be quite inconvenient if the needle oscillated about the new equilibrium position for a long time before settling. Damping forces can vary greatly in character. Friction, for example, is sometimes independent of velocity. However, many damping forces depend on velocity—sometimes in complex ways and sometimes simply being proportional to velocity.

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