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Normal Mode
A normal mode of a dynamical system is a pattern of motion in which all parts of the system move sinusoidally with the same frequency and with a fixed phase relation. The free motion described by the normal modes takes place at fixed frequencies. These fixed frequencies of the normal modes of a system are known as its natural frequencies or resonant frequencies. A physical object, such as a building, bridge, or molecule, has a set of normal modes and their natural frequencies that depend on its structure, materials and boundary conditions. The most general motion of a linear system is a superposition of its normal modes. The modes are normal in the sense that they can move independently, that is to say that an excitation of one mode will never cause motion of a different mode. In mathematical terms, normal modes are orthogonal to each other. General definitions Mode In the wave theory of physics and engineering, a mode in a dynamical system is a standing wave st ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dynamical System
In mathematics, a dynamical system is a system in which a Function (mathematics), function describes the time dependence of a Point (geometry), point in an ambient space, such as in a parametric curve. Examples include the mathematical models that describe the swinging of a clock pendulum, fluid dynamics, the flow of water in a pipe, the Brownian motion, random motion of particles in the air, and population dynamics, the number of fish each springtime in a lake. The most general definition unifies several concepts in mathematics such as ordinary differential equations and ergodic theory by allowing different choices of the space and how time is measured. Time can be measured by integers, by real number, real or complex numbers or can be a more general algebraic object, losing the memory of its physical origin, and the space may be a manifold or simply a Set (mathematics), set, without the need of a Differentiability, smooth space-time structure defined on it. At any given time, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Mechanics
Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is the foundation of all quantum physics, which includes quantum chemistry, quantum field theory, quantum technology, and quantum information science. Quantum mechanics can describe many systems that classical physics cannot. Classical physics can describe many aspects of nature at an ordinary (macroscopic and Microscopic scale, (optical) microscopic) scale, but is not sufficient for describing them at very small submicroscopic (atomic and subatomic) scales. Classical mechanics can be derived from quantum mechanics as an approximation that is valid at ordinary scales. Quantum systems have Bound state, bound states that are Quantization (physics), quantized to Discrete mathematics, discrete values of energy, momentum, angular momentum, and ot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Displacement (distance)
In geometry and mechanics, a displacement is a vector whose length is the shortest distance from the initial to the final position of a point P undergoing motion. It quantifies both the distance and direction of the net or total motion along a straight line from the initial position to the final position of the point trajectory. A displacement may be identified with the translation that maps the initial position to the final position. Displacement is the shift in location when an object in motion changes from one position to another. For motion over a given interval of time, the displacement divided by the length of the time interval defines the average velocity (a vector), whose magnitude is the average speed (a scalar quantity). Formulation A displacement may be formulated as a '' relative position'' (resulting from the motion), that is, as the final position of a point relative to its initial position . The corresponding displacement vector can be defined as the differenc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coupled Harmonic Oscillator
''Coupled'' is an American dating game show that aired on Fox from May 17 to August 2, 2016. It was hosted by television personality, Terrence J and created by Mark Burnett, of ''Survivor'', '' The Apprentice'', '' Are You Smarter than a 5th Grader?'', ''Shark Tank'', and '' The Voice'', as well as Ben Newmark, Dan Newmark and Larry Barron. Filming took place in Anguilla. The cast included Miss Arizona USA 2009, Alicia-Monique Blanco; Miss Colorado USA 2015, Talyah Polee; host, Domonique Price, and American singer-songwriter, TV personality, and former collegiate athlete; Alex Lagemann. Tyler Gattuso was in the running to be a cast member on '' Big Brother 17'', but was ultimately not chosen due to the news being leaked by online media and his Instagram hinting at the news suggesting he wasn't going to be active for quite a while. A few days later, after the cast for Big Brother was announced, he was ranting on Twitter, shortly deleting them and deactivating his account. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spring Constant
In physics, Hooke's law is an empirical law which states that the force () needed to extend or compress a spring (device), spring by some distance () Proportionality (mathematics)#Direct_proportionality, scales linearly with respect to that distance—that is, where is a constant factor characteristic of the spring (i.e., its stiffness), and is small compared to the total possible deformation of the spring. The law is named after 17th-century British physicist Robert Hooke. He first stated the law in 1676 as a Latin anagram. He published the solution of his anagram in 1678 as: ("as the extension, so the force" or "the extension is proportional to the force"). Hooke states in the 1678 work that he was aware of the law since 1660. Hooke's equation holds (to some extent) in many other situations where an elasticity (physics), elastic body is Deformation (physics), deformed, such as wind blowing on a tall building, and a musician plucking a string (music), string of a guitar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mass
Mass is an Intrinsic and extrinsic properties, intrinsic property of a physical body, body. It was traditionally believed to be related to the physical quantity, quantity of matter in a body, until the discovery of the atom and particle physics. It was found that different atoms and different elementary particle, elementary particles, theoretically with the same amount of matter, have nonetheless different masses. Mass in modern physics has multiple Mass in special relativity, definitions which are conceptually distinct, but physically equivalent. Mass can be experimentally defined as a measure (mathematics), measure of the body's inertia, meaning the resistance to acceleration (change of velocity) when a net force is applied. The object's mass also determines the Force, strength of its gravitational attraction to other bodies. The SI base unit of mass is the kilogram (kg). In physics, mass is Mass versus weight, not the same as weight, even though mass is often determined by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electrical Circuit
An electrical network is an interconnection of electrical components (e.g., battery (electricity), batteries, resistors, inductors, capacitors, switches, transistors) or a model of such an interconnection, consisting of electrical elements (e.g., voltage sources, current sources, Electrical resistance and conductance, resistances, inductances, capacitances). An electrical circuit is a network consisting of a closed loop, giving a return path for the current. Thus all circuits are networks, but not all networks are circuits (although networks without a closed loop are often referred to as "open circuits"). A resistive network is a network containing only resistors and ideal current and voltage sources. Network analysis (electrical circuits), Analysis of resistive networks is less complicated than analysis of networks containing capacitors and inductors. If the sources are constant (Direct current, DC) sources, the result is a DC network. The effective resistance and current dist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Molecular Spectra
The emission spectrum of a chemical element or chemical compound is the Spectrum (physical sciences), spectrum of frequencies of electromagnetic radiation emitted due to electrons making a atomic electron transition, transition from a high energy state to a lower energy state. The photon energy of the emitted photons is equal to the energy difference between the two states. There are many possible electron transitions for each atom, and each transition has a specific energy difference. This collection of different transitions, leading to different radiated wavelengths, make up an emission spectrum. Each element's emission spectrum is unique. Therefore, spectroscopy can be used to identify elements in matter of unknown composition. Similarly, the emission spectra of molecules can be used in chemical analysis of substances. Emission In physics, emission is the process by which a higher energy quantum mechanical state of a particle becomes converted to a lower one through the emis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Acoustics
Acoustics is a branch of physics that deals with the study of mechanical waves in gases, liquids, and solids including topics such as vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician while someone working in the field of acoustics technology may be called an Acoustical engineering, acoustical engineer. The application of acoustics is present in almost all aspects of modern society with the most obvious being the audio and noise control industries. Hearing (sense), Hearing is one of the most crucial means of survival in the animal world and speech is one of the most distinctive characteristics of human development and culture. Accordingly, the science of acoustics spreads across many facets of human society—music, medicine, architecture, industrial production, warfare and more. Likewise, animal species such as songbirds and frogs use sound and hearing as a key element of mating rituals or for marking territories. Art, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conservative System
In mathematics, a conservative system is a dynamical system which stands in contrast to a dissipative system. Roughly speaking, such systems have no friction or other mechanism to dissipate the dynamics, and thus, their phase space does not shrink over time. Precisely speaking, they are those dynamical systems that have a null wandering set: under time evolution, no portion of the phase space ever "wanders away", never to be returned to or revisited. Alternately, conservative systems are those to which the Poincaré recurrence theorem applies. An important special case of conservative systems are the measure-preserving dynamical systems. Informal introduction Informally, dynamical systems describe the time evolution of the phase space of some mechanical system. Commonly, such evolution is given by some differential equations, or quite often in terms of discrete time steps. However, in the present case, instead of focusing on the time evolution of discrete points, one shifts atte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mode Shape Of A Round Plate With Node Lines
Mode ( meaning "manner, tune, measure, due measure, rhythm, melody") may refer to: Arts and entertainment * MO''D''E (magazine), a defunct U.S. women's fashion magazine * ''Mode'' magazine, a fictional fashion magazine which is the setting for the ABC series ''Ugly Betty'' * ''Mode'' (video game), a 1996 video game * Mode Records, a record label * Mode Media, a defunct digital media company * ''Mode'' (book series), a quartet of novels by Piers Anthony * Modern Organization for Dance Evolvement, known as MODE, a 1970s modern dance organisation in New York * ''Mode'', a defunct Indonesian women's magazine Music * Mode (music), a system of musical tonality involving a type of scale coupled with a set of characteristic melodic behaviors ** Modus (medieval music) *** Gregorian mode, a system of modes used in Gregorian chant (as opposed to ancient Greek modes or Byzantine octoechos) * "Mode", a song by PRhyme from the 2015 soundtrack '' Southpaw: Music from and Inspired by t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symmetry In Mathematics
Symmetry occurs not only in geometry, but also in other branches of mathematics. Symmetry is a type of invariance: the property that a mathematical object remains unchanged under a set of operations or transformations. Given a structured object ''X'' of any sort, a symmetry is a mapping of the object onto itself which preserves the structure. This can occur in many ways; for example, if ''X'' is a set with no additional structure, a symmetry is a bijective map from the set to itself, giving rise to permutation groups. If the object ''X'' is a set of points in the plane with its metric structure or any other metric space, a symmetry is a bijection of the set to itself which preserves the distance between each pair of points (i.e., an isometry). In general, every kind of structure in mathematics will have its own kind of symmetry, many of which are listed in the given points mentioned above. Symmetry in geometry The types of symmetry considered in basic geometry include ref ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
