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1.561 Motion Based Design (MIT) 1.561 Motion Based Design (MIT)

Description

This course presents a rational basis for the preliminary design of motion-sensitive structures. Topics covered include: analytical and numerical techniques for establishing the optimal stiffness distribution, the role of damping in controlling motion, tuned mass dampers, base isolation systems, and active structural control. Examples illustrating the application of the motion-based design paradigm to building structures subjected to seismic excitation are discussed. This course presents a rational basis for the preliminary design of motion-sensitive structures. Topics covered include: analytical and numerical techniques for establishing the optimal stiffness distribution, the role of damping in controlling motion, tuned mass dampers, base isolation systems, and active structural control. Examples illustrating the application of the motion-based design paradigm to building structures subjected to seismic excitation are discussed.

Subjects

preliminary design | preliminary design | motion-sensitive structures | motion-sensitive structures | analytical techniques | analytical techniques | numerical techniques | numerical techniques | optimal stiffness distribution | optimal stiffness distribution | damping | damping | controlling motion | controlling motion | tuned mass dampers | tuned mass dampers | base isolation systems | base isolation systems | active structural control | active structural control | building structures | building structures | wind excitation | wind excitation | seismic excitation | seismic excitation | building design | building design | numerical analysis | numerical analysis | motion control | motion control | motion-based design | motion-based design | safety | safety | serviceability | serviceability | loadings | loadings | optimal stiffness | optimal stiffness | optimal damping | optimal damping | base isolation | base isolation

License

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18.03 Differential Equations (MIT) 18.03 Differential Equations (MIT)

Description

Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time. Topics include: Solution of first-order ODE's by analytical, graphical and numerical methods; Linear ODE's, especially second order with constant coefficients; Undetermined coefficients and variation of parameters; Sinusoidal and exponential signals: oscillations, damping, resonance; Complex numbers and exponentials; Fourier series, periodic solutions; Delta functions, convolution, and Laplace transform methods; Matrix and first order linear systems: eigenvalues and Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time. Topics include: Solution of first-order ODE's by analytical, graphical and numerical methods; Linear ODE's, especially second order with constant coefficients; Undetermined coefficients and variation of parameters; Sinusoidal and exponential signals: oscillations, damping, resonance; Complex numbers and exponentials; Fourier series, periodic solutions; Delta functions, convolution, and Laplace transform methods; Matrix and first order linear systems: eigenvalues and

Subjects

Ordinary Differential Equations | Ordinary Differential Equations | ODE | ODE | modeling physical systems | modeling physical systems | first-order ODE's | first-order ODE's | Linear ODE's | Linear ODE's | second order ODE's | second order ODE's | second order ODE's with constant coefficients | second order ODE's with constant coefficients | Undetermined coefficients | Undetermined coefficients | variation of parameters | variation of parameters | Sinusoidal signals | Sinusoidal signals | exponential signals | exponential signals | oscillations | oscillations | damping | damping | resonance | resonance | Complex numbers and exponentials | Complex numbers and exponentials | Fourier series | Fourier series | periodic solutions | periodic solutions | Delta functions | Delta functions | convolution | convolution | Laplace transform methods Matrix systems | Laplace transform methods Matrix systems | first order linear systems | first order linear systems | eigenvalues and eigenvectors | eigenvalues and eigenvectors | Non-linear autonomous systems | Non-linear autonomous systems | critical point analysis | critical point analysis | phase plane diagrams | phase plane diagrams

License

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22.611J Introduction To Plasma Physics I (MIT) 22.611J Introduction To Plasma Physics I (MIT)

Description

Introduces plasma phenomena relevant to energy generation by controlled thermonuclear fusion and to astrophysics. Basic plasma properties and collective behavior. Coulomb collisions and transport processes. Motion of charged particles in magnetic fields; plasma confinement schemes. MHD models; simple equilibrium and stability analysis. Two-fluid hydrodynamic plasma models; wave propagation in a magnetic field.Introduces kinetic theory; Vlasov plasma model; electron plasma waves and Landau damping; ion-acoustic waves; streaming instabilities. A subject description tailored to fit the background and interests of the attending students distributed shortly before and at the beginning of the subject. Introduces plasma phenomena relevant to energy generation by controlled thermonuclear fusion and to astrophysics. Basic plasma properties and collective behavior. Coulomb collisions and transport processes. Motion of charged particles in magnetic fields; plasma confinement schemes. MHD models; simple equilibrium and stability analysis. Two-fluid hydrodynamic plasma models; wave propagation in a magnetic field.Introduces kinetic theory; Vlasov plasma model; electron plasma waves and Landau damping; ion-acoustic waves; streaming instabilities. A subject description tailored to fit the background and interests of the attending students distributed shortly before and at the beginning of the subject.

Subjects

plasma phenomena | plasma phenomena | energy generation | energy generation | thermonuclear fusion | thermonuclear fusion | astrophysics | astrophysics | Coulomb collisions | Coulomb collisions | transport processes | transport processes | plasma confinement schemes | | plasma confinement schemes | | MHD models | MHD models | kinetic theory | kinetic theory | Vlasov plasma model | Vlasov plasma model | electron plasma waves | electron plasma waves | Landau damping | Landau damping | ion-acoustic waves | ion-acoustic waves | streaming instabilities | streaming instabilities | 22.611 | 22.611 | 6.651 | 6.651 | 8.613 | 8.613

License

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18.03 Differential Equations (MIT) 18.03 Differential Equations (MIT)

Description

Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time. Topics include: Solution of first-order ODE's by analytical, graphical and numerical methods; Linear ODE's, especially second order with constant coefficients; Undetermined coefficients and variation of parameters; Sinusoidal and exponential signals: oscillations, damping, resonance; Complex numbers and exponentials; Fourier series, periodic solutions; Delta functions, convolution, and Laplace transform methods; Matrix and first order linear systems: eigenvalues and Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time. Topics include: Solution of first-order ODE's by analytical, graphical and numerical methods; Linear ODE's, especially second order with constant coefficients; Undetermined coefficients and variation of parameters; Sinusoidal and exponential signals: oscillations, damping, resonance; Complex numbers and exponentials; Fourier series, periodic solutions; Delta functions, convolution, and Laplace transform methods; Matrix and first order linear systems: eigenvalues and

Subjects

Ordinary Differential Equations | Ordinary Differential Equations | ODE | ODE | modeling physical systems | modeling physical systems | first-order ODE's | first-order ODE's | Linear ODE's | Linear ODE's | second order ODE's | second order ODE's | second order ODE's with constant coefficients | second order ODE's with constant coefficients | Undetermined coefficients | Undetermined coefficients | variation of parameters | variation of parameters | Sinusoidal signals | Sinusoidal signals | exponential signals | exponential signals | oscillations | oscillations | damping | damping | resonance | resonance | Complex numbers and exponentials | Complex numbers and exponentials | Fourier series | Fourier series | periodic solutions | periodic solutions | Delta functions | Delta functions | convolution | convolution | Laplace transform methods | Laplace transform methods | Matrix systems | Matrix systems | first order linear systems | first order linear systems | eigenvalues and eigenvectors | eigenvalues and eigenvectors | Non-linear autonomous systems | Non-linear autonomous systems | critical point analysis | critical point analysis | phase plane diagrams | phase plane diagrams | constant coefficients | constant coefficients | complex numbers | complex numbers | exponentials | exponentials | eigenvalues | eigenvalues | eigenvectors | eigenvectors

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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18.03SC Differential Equations (MIT) 18.03SC Differential Equations (MIT)

Description

Includes audio/video content: AV lectures. The laws of nature are expressed as differential equations. Scientists and engineers must know how to model the world in terms of differential equations, and how to solve those equations and interpret the solutions. This course focuses on the equations and techniques most useful in science and engineering. Includes audio/video content: AV lectures. The laws of nature are expressed as differential equations. Scientists and engineers must know how to model the world in terms of differential equations, and how to solve those equations and interpret the solutions. This course focuses on the equations and techniques most useful in science and engineering.

Subjects

Ordinary Differential Equations | Ordinary Differential Equations | ODE | ODE | modeling physical systems | modeling physical systems | first-order ODE's | first-order ODE's | Linear ODE's | Linear ODE's | second order ODE's | second order ODE's | second order ODE's with constant coefficients | second order ODE's with constant coefficients | Undetermined coefficients | Undetermined coefficients | variation of parameters | variation of parameters | Sinusoidal signals | Sinusoidal signals | exponential signals | exponential signals | oscillations | oscillations | damping | damping | resonance | resonance | Complex numbers and exponentials | Complex numbers and exponentials | Fourier series | Fourier series | periodic solutions | periodic solutions | Delta functions | Delta functions | convolution | convolution | Laplace transform methods | Laplace transform methods | Matrix systems | Matrix systems | first order linear systems | first order linear systems | eigenvalues and eigenvectors | eigenvalues and eigenvectors | Non-linear autonomous systems | Non-linear autonomous systems | critical point analysis | critical point analysis | phase plane diagrams | phase plane diagrams

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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18.03 Differential Equations (MIT) 18.03 Differential Equations (MIT)

Description

Includes audio/video content: AV lectures. Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time. Includes audio/video content: AV lectures. Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time.

Subjects

Ordinary Differential Equations | Ordinary Differential Equations | ODE | ODE | modeling physical systems | modeling physical systems | first-order ODE's | first-order ODE's | Linear ODE's | Linear ODE's | second order ODE's | second order ODE's | second order ODE's with constant coefficients | second order ODE's with constant coefficients | Undetermined coefficients | Undetermined coefficients | variation of parameters | variation of parameters | Sinusoidal signals | Sinusoidal signals | exponential signals | exponential signals | oscillations | oscillations | damping | damping | resonance | resonance | Complex numbers and exponentials | Complex numbers and exponentials | Fourier series | Fourier series | periodic solutions | periodic solutions | Delta functions | Delta functions | convolution | convolution | Laplace transform methods | Laplace transform methods | Matrix systems | Matrix systems | first order linear systems | first order linear systems | eigenvalues and eigenvectors | eigenvalues and eigenvectors | Non-linear autonomous systems | Non-linear autonomous systems | critical point analysis | critical point analysis | phase plane diagrams | phase plane diagrams

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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22.611J Introduction to Plasma Physics I (MIT) 22.611J Introduction to Plasma Physics I (MIT)

Description

The plasma state dominates the visible universe, and is important in fields as diverse as Astrophysics and Controlled Fusion. Plasma is often referred to as "the fourth state of matter." This course introduces the study of the nature and behavior of plasma. A variety of models to describe plasma behavior are presented. The plasma state dominates the visible universe, and is important in fields as diverse as Astrophysics and Controlled Fusion. Plasma is often referred to as "the fourth state of matter." This course introduces the study of the nature and behavior of plasma. A variety of models to describe plasma behavior are presented.

Subjects

plasma phenomena | plasma phenomena | energy generation | energy generation | controlled thermonuclear fusion | controlled thermonuclear fusion | astrophysics | astrophysics | Coulomb collisions | Coulomb collisions | transport processes | transport processes | charged particles | charged particles | magnetic fields | magnetic fields | plasma confinement schemes | plasma confinement schemes | MHD models | MHD models | simple equilibrium | simple equilibrium | stability analysis | stability analysis | Two-fluid hydrodynamic plasma models | Two-fluid hydrodynamic plasma models | wave propagation | wave propagation | kinetic theory | kinetic theory | Vlasov plasma model | Vlasov plasma model | electron plasma waves | electron plasma waves | Landau damping | Landau damping | ion-acoustic waves | ion-acoustic waves | streaming instabilities | streaming instabilities

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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22.611J Introduction to Plasma Physics I (MIT) 22.611J Introduction to Plasma Physics I (MIT)

Description

In this course, students will learn about plasmas, the fourth state of matter. The plasma state dominates the visible universe, and is of increasing economic importance. Plasmas behave in lots of interesting and sometimes unexpected ways. The course is intended only as a first plasma physics course, but includes critical concepts needed for a foundation for further study. A solid undergraduate background in classical physics, electromagnetic theory including Maxwell's equations, and mathematical familiarity with partial differential equations and complex analysis are prerequisites. The course introduces plasma phenomena relevant to energy generation by controlled thermonuclear fusion and to astrophysics, coulomb collisions and transport processes, motion of charged particles in magne In this course, students will learn about plasmas, the fourth state of matter. The plasma state dominates the visible universe, and is of increasing economic importance. Plasmas behave in lots of interesting and sometimes unexpected ways. The course is intended only as a first plasma physics course, but includes critical concepts needed for a foundation for further study. A solid undergraduate background in classical physics, electromagnetic theory including Maxwell's equations, and mathematical familiarity with partial differential equations and complex analysis are prerequisites. The course introduces plasma phenomena relevant to energy generation by controlled thermonuclear fusion and to astrophysics, coulomb collisions and transport processes, motion of charged particles in magne

Subjects

plasma phenomena | plasma phenomena | energy generation | energy generation | controlled thermonuclear fusion | controlled thermonuclear fusion | astrophysics | astrophysics | Coulomb collisions | Coulomb collisions | transport processes | transport processes | charged particles | charged particles | magnetic fields | magnetic fields | plasma confinement schemes | plasma confinement schemes | MHD models | MHD models | simple equilibrium | simple equilibrium | stability analysis | stability analysis | Two-fluid hydrodynamic plasma models | Two-fluid hydrodynamic plasma models | wave propagation | wave propagation | kinetic theory | kinetic theory | Vlasov plasma model | Vlasov plasma model | electron plasma waves | electron plasma waves | Landau damping | Landau damping | ion-acoustic waves | ion-acoustic waves | streaming instabilities | streaming instabilities | fourth state of matter | fourth state of matter | plasma state | plasma state | visible universe | visible universe | economics | economics | plasmas | plasmas | motion of charged particles | motion of charged particles | two-fluid hydrodynamic plasma models | two-fluid hydrodynamic plasma models | Debye Shielding | Debye Shielding | collective effects | collective effects | charged particle motion | charged particle motion | EM Fields | EM Fields | cross-sections | cross-sections | relaxation | relaxation | fluid plasma descriptions | fluid plasma descriptions | MHD equilibrium | MHD equilibrium | MHD dynamics | MHD dynamics | dynamics in two-fluid plasmas | dynamics in two-fluid plasmas | cold plasma waves | cold plasma waves | magnetic field | magnetic field | microscopic to fluid plasma descriptions | microscopic to fluid plasma descriptions | Vlasov-Maxwell kinetic theory.linear Landau growth | Vlasov-Maxwell kinetic theory.linear Landau growth | kinetic description of waves | kinetic description of waves | instabilities | instabilities | Vlasov-Maxwell kinetic theory | Vlasov-Maxwell kinetic theory | linear Landau growth | linear Landau growth | 22.611 | 22.611 | 6.651 | 6.651 | 8.613 | 8.613

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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1.561 Motion Based Design (MIT)

Description

This course presents a rational basis for the preliminary design of motion-sensitive structures. Topics covered include: analytical and numerical techniques for establishing the optimal stiffness distribution, the role of damping in controlling motion, tuned mass dampers, base isolation systems, and active structural control. Examples illustrating the application of the motion-based design paradigm to building structures subjected to seismic excitation are discussed.

Subjects

preliminary design | motion-sensitive structures | analytical techniques | numerical techniques | optimal stiffness distribution | damping | controlling motion | tuned mass dampers | base isolation systems | active structural control | building structures | wind excitation | seismic excitation | building design | numerical analysis | motion control | motion-based design | safety | serviceability | loadings | optimal stiffness | optimal damping | base isolation

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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RES.8-005 Vibrations and Waves Problem Solving (MIT) RES.8-005 Vibrations and Waves Problem Solving (MIT)

Description

Includes audio/video content: AV lectures. 8.03 Physics III: Vibrations and Waves is the third course in the core physics curriculum at MIT, following 8.01 Physics I: Classical Mechanics and 8.02 Physics II: Electricity and Magnetism. Topics include mechanical vibrations and waves, electromagnetic waves, and optics. These Problem Solving Help Videos provide step-by-step solutions to sample problems. Also included is information about how Physics III is typically taught on the MIT campus. Instructor Insights are shared by Professor Wit Busza who has taught Physics III and its associated recitation sessions many times. Professor Busza's insights focus on his approach to problem solving, strategies for supporting students as they solve problems, and common sources of confusion for students i Includes audio/video content: AV lectures. 8.03 Physics III: Vibrations and Waves is the third course in the core physics curriculum at MIT, following 8.01 Physics I: Classical Mechanics and 8.02 Physics II: Electricity and Magnetism. Topics include mechanical vibrations and waves, electromagnetic waves, and optics. These Problem Solving Help Videos provide step-by-step solutions to sample problems. Also included is information about how Physics III is typically taught on the MIT campus. Instructor Insights are shared by Professor Wit Busza who has taught Physics III and its associated recitation sessions many times. Professor Busza's insights focus on his approach to problem solving, strategies for supporting students as they solve problems, and common sources of confusion for students i

Subjects

vibrations | vibrations | waves | waves | mass on a spring | mass on a spring | LC circuit | LC circuit | simple harmonic motion | simple harmonic motion | harmonic oscillators | harmonic oscillators | damping | damping | coupled oscillators | coupled oscillators | traveling waves | traveling waves | standing waves | standing waves | electromagnetic waves | electromagnetic waves | interference | interference | radiating electromagnetic waves | radiating electromagnetic waves | Quality Factor Q | Quality Factor Q

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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1.561 Motion Based Design (MIT)

Description

This course presents a rational basis for the preliminary design of motion-sensitive structures. Topics covered include: analytical and numerical techniques for establishing the optimal stiffness distribution, the role of damping in controlling motion, tuned mass dampers, base isolation systems, and active structural control. Examples illustrating the application of the motion-based design paradigm to building structures subjected to seismic excitation are discussed.

Subjects

preliminary design | motion-sensitive structures | analytical techniques | numerical techniques | optimal stiffness distribution | damping | controlling motion | tuned mass dampers | base isolation systems | active structural control | building structures | wind excitation | seismic excitation | building design | numerical analysis | motion control | motion-based design | safety | serviceability | loadings | optimal stiffness | optimal damping | base isolation

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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18.03 Differential Equations (MIT)

Description

Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time.

Subjects

Ordinary Differential Equations | ODE | modeling physical systems | first-order ODE's | Linear ODE's | second order ODE's | second order ODE's with constant coefficients | Undetermined coefficients | variation of parameters | Sinusoidal signals | exponential signals | oscillations | damping | resonance | Complex numbers and exponentials | Fourier series | periodic solutions | Delta functions | convolution | Laplace transform methods | Matrix systems | first order linear systems | eigenvalues and eigenvectors | Non-linear autonomous systems | critical point analysis | phase plane diagrams

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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22.611J Introduction to Plasma Physics I (MIT)

Description

In this course, students will learn about plasmas, the fourth state of matter. The plasma state dominates the visible universe, and is of increasing economic importance. Plasmas behave in lots of interesting and sometimes unexpected ways. The course is intended only as a first plasma physics course, but includes critical concepts needed for a foundation for further study. A solid undergraduate background in classical physics, electromagnetic theory including Maxwell's equations, and mathematical familiarity with partial differential equations and complex analysis are prerequisites. The course introduces plasma phenomena relevant to energy generation by controlled thermonuclear fusion and to astrophysics, coulomb collisions and transport processes, motion of charged particles in magne

Subjects

plasma phenomena | energy generation | controlled thermonuclear fusion | astrophysics | Coulomb collisions | transport processes | charged particles | magnetic fields | plasma confinement schemes | MHD models | simple equilibrium | stability analysis | Two-fluid hydrodynamic plasma models | wave propagation | kinetic theory | Vlasov plasma model | electron plasma waves | Landau damping | ion-acoustic waves | streaming instabilities | fourth state of matter | plasma state | visible universe | economics | plasmas | motion of charged particles | two-fluid hydrodynamic plasma models | Debye Shielding | collective effects | charged particle motion | EM Fields | cross-sections | relaxation | fluid plasma descriptions | MHD equilibrium | MHD dynamics | dynamics in two-fluid plasmas | cold plasma waves | magnetic field | microscopic to fluid plasma descriptions | Vlasov-Maxwell kinetic theory.linear Landau growth | kinetic description of waves | instabilities | Vlasov-Maxwell kinetic theory | linear Landau growth | 22.611 | 6.651 | 8.613

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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22.611J Introduction to Plasma Physics I (MIT)

Description

In this course, students will learn about plasmas, the fourth state of matter. The plasma state dominates the visible universe, and is of increasing economic importance. Plasmas behave in lots of interesting and sometimes unexpected ways. The course is intended only as a first plasma physics course, but includes critical concepts needed for a foundation for further study. A solid undergraduate background in classical physics, electromagnetic theory including Maxwell's equations, and mathematical familiarity with partial differential equations and complex analysis are prerequisites. The course introduces plasma phenomena relevant to energy generation by controlled thermonuclear fusion and to astrophysics, coulomb collisions and transport processes, motion of charged particles in magne

Subjects

plasma phenomena | energy generation | controlled thermonuclear fusion | astrophysics | Coulomb collisions | transport processes | charged particles | magnetic fields | plasma confinement schemes | MHD models | simple equilibrium | stability analysis | Two-fluid hydrodynamic plasma models | wave propagation | kinetic theory | Vlasov plasma model | electron plasma waves | Landau damping | ion-acoustic waves | streaming instabilities | fourth state of matter | plasma state | visible universe | economics | plasmas | motion of charged particles | two-fluid hydrodynamic plasma models | Debye Shielding | collective effects | charged particle motion | EM Fields | cross-sections | relaxation | fluid plasma descriptions | MHD equilibrium | MHD dynamics | dynamics in two-fluid plasmas | cold plasma waves | magnetic field | microscopic to fluid plasma descriptions | Vlasov-Maxwell kinetic theory.linear Landau growth | kinetic description of waves | instabilities | Vlasov-Maxwell kinetic theory | linear Landau growth | 22.611 | 6.651 | 8.613

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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18.03 Differential Equations (MIT)

Description

Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time. Topics include: Solution of first-order ODE's by analytical, graphical and numerical methods; Linear ODE's, especially second order with constant coefficients; Undetermined coefficients and variation of parameters; Sinusoidal and exponential signals: oscillations, damping, resonance; Complex numbers and exponentials; Fourier series, periodic solutions; Delta functions, convolution, and Laplace transform methods; Matrix and first order linear systems: eigenvalues and

Subjects

Ordinary Differential Equations | ODE | modeling physical systems | first-order ODE's | Linear ODE's | second order ODE's | second order ODE's with constant coefficients | Undetermined coefficients | variation of parameters | Sinusoidal signals | exponential signals | oscillations | damping | resonance | Complex numbers and exponentials | Fourier series | periodic solutions | Delta functions | convolution | Laplace transform methods Matrix systems | first order linear systems | eigenvalues and eigenvectors | Non-linear autonomous systems | critical point analysis | phase plane diagrams

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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22.611J Introduction To Plasma Physics I (MIT)

Description

Introduces plasma phenomena relevant to energy generation by controlled thermonuclear fusion and to astrophysics. Basic plasma properties and collective behavior. Coulomb collisions and transport processes. Motion of charged particles in magnetic fields; plasma confinement schemes. MHD models; simple equilibrium and stability analysis. Two-fluid hydrodynamic plasma models; wave propagation in a magnetic field.Introduces kinetic theory; Vlasov plasma model; electron plasma waves and Landau damping; ion-acoustic waves; streaming instabilities. A subject description tailored to fit the background and interests of the attending students distributed shortly before and at the beginning of the subject.

Subjects

plasma phenomena | energy generation | thermonuclear fusion | astrophysics | Coulomb collisions | transport processes | plasma confinement schemes | | MHD models | kinetic theory | Vlasov plasma model | electron plasma waves | Landau damping | ion-acoustic waves | streaming instabilities | 22.611 | 6.651 | 8.613

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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18.03 Differential Equations (MIT)

Description

Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time. Topics include: Solution of first-order ODE's by analytical, graphical and numerical methods; Linear ODE's, especially second order with constant coefficients; Undetermined coefficients and variation of parameters; Sinusoidal and exponential signals: oscillations, damping, resonance; Complex numbers and exponentials; Fourier series, periodic solutions; Delta functions, convolution, and Laplace transform methods; Matrix and first order linear systems: eigenvalues and

Subjects

Ordinary Differential Equations | ODE | modeling physical systems | first-order ODE's | Linear ODE's | second order ODE's | second order ODE's with constant coefficients | Undetermined coefficients | variation of parameters | Sinusoidal signals | exponential signals | oscillations | damping | resonance | Complex numbers and exponentials | Fourier series | periodic solutions | Delta functions | convolution | Laplace transform methods | Matrix systems | first order linear systems | eigenvalues and eigenvectors | Non-linear autonomous systems | critical point analysis | phase plane diagrams | constant coefficients | complex numbers | exponentials | eigenvalues | eigenvectors

License

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18.03SC Differential Equations (MIT)

Description

The laws of nature are expressed as differential equations. Scientists and engineers must know how to model the world in terms of differential equations, and how to solve those equations and interpret the solutions. This course focuses on the equations and techniques most useful in science and engineering.

Subjects

Ordinary Differential Equations | ODE | modeling physical systems | first-order ODE's | Linear ODE's | second order ODE's | second order ODE's with constant coefficients | Undetermined coefficients | variation of parameters | Sinusoidal signals | exponential signals | oscillations | damping | resonance | Complex numbers and exponentials | Fourier series | periodic solutions | Delta functions | convolution | Laplace transform methods | Matrix systems | first order linear systems | eigenvalues and eigenvectors | Non-linear autonomous systems | critical point analysis | phase plane diagrams

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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18.03 Differential Equations (MIT)

Description

Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time.

Subjects

Ordinary Differential Equations | ODE | modeling physical systems | first-order ODE's | Linear ODE's | second order ODE's | second order ODE's with constant coefficients | Undetermined coefficients | variation of parameters | Sinusoidal signals | exponential signals | oscillations | damping | resonance | Complex numbers and exponentials | Fourier series | periodic solutions | Delta functions | convolution | Laplace transform methods | Matrix systems | first order linear systems | eigenvalues and eigenvectors | Non-linear autonomous systems | critical point analysis | phase plane diagrams

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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22.611J Introduction to Plasma Physics I (MIT)

Description

The plasma state dominates the visible universe, and is important in fields as diverse as Astrophysics and Controlled Fusion. Plasma is often referred to as "the fourth state of matter." This course introduces the study of the nature and behavior of plasma. A variety of models to describe plasma behavior are presented.

Subjects

plasma phenomena | energy generation | controlled thermonuclear fusion | astrophysics | Coulomb collisions | transport processes | charged particles | magnetic fields | plasma confinement schemes | MHD models | simple equilibrium | stability analysis | Two-fluid hydrodynamic plasma models | wave propagation | kinetic theory | Vlasov plasma model | electron plasma waves | Landau damping | ion-acoustic waves | streaming instabilities

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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22.611J Introduction to Plasma Physics I (MIT)

Description

In this course, students will learn about plasmas, the fourth state of matter. The plasma state dominates the visible universe, and is of increasing economic importance. Plasmas behave in lots of interesting and sometimes unexpected ways. The course is intended only as a first plasma physics course, but includes critical concepts needed for a foundation for further study. A solid undergraduate background in classical physics, electromagnetic theory including Maxwell's equations, and mathematical familiarity with partial differential equations and complex analysis are prerequisites. The course introduces plasma phenomena relevant to energy generation by controlled thermonuclear fusion and to astrophysics, coulomb collisions and transport processes, motion of charged particles in magne

Subjects

plasma phenomena | energy generation | controlled thermonuclear fusion | astrophysics | Coulomb collisions | transport processes | charged particles | magnetic fields | plasma confinement schemes | MHD models | simple equilibrium | stability analysis | Two-fluid hydrodynamic plasma models | wave propagation | kinetic theory | Vlasov plasma model | electron plasma waves | Landau damping | ion-acoustic waves | streaming instabilities | fourth state of matter | plasma state | visible universe | economics | plasmas | motion of charged particles | two-fluid hydrodynamic plasma models | Debye Shielding | collective effects | charged particle motion | EM Fields | cross-sections | relaxation | fluid plasma descriptions | MHD equilibrium | MHD dynamics | dynamics in two-fluid plasmas | cold plasma waves | magnetic field | microscopic to fluid plasma descriptions | Vlasov-Maxwell kinetic theory.linear Landau growth | kinetic description of waves | instabilities | Vlasov-Maxwell kinetic theory | linear Landau growth | 22.611 | 6.651 | 8.613

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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RES.8-005 Vibrations and Waves Problem Solving (MIT)

Description

8.03 Physics III: Vibrations and Waves is the third course in the core physics curriculum at MIT, following 8.01 Physics I: Classical Mechanics and 8.02 Physics II: Electricity and Magnetism. Topics include mechanical vibrations and waves, electromagnetic waves, and optics. These Problem Solving Help Videos provide step-by-step solutions to sample problems. Also included is information about how Physics III is typically taught on the MIT campus. Instructor Insights are shared by Professor Wit Busza who has taught Physics III and its associated recitation sessions many times. Professor Busza's insights focus on his approach to problem solving, strategies for supporting students as they solve problems, and common sources of confusion for students in the process of problem solving. Note: The

Subjects

vibrations | waves | mass on a spring | LC circuit | simple harmonic motion | harmonic oscillators | damping | coupled oscillators | traveling waves | standing waves | electromagnetic waves | interference | radiating electromagnetic waves | Quality Factor Q

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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