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Tensile Membrane Structures
Tension is the pulling or stretching force transmitted axially along an object such as a string, rope, chain, rod, truss member, or other object, so as to stretch or pull apart the object. In terms of force, it is the opposite of ''compression''. Tension might also be described as the action-reaction pair of forces acting at each end of an object. At the atomic level, when atoms or molecules are pulled apart from each other and gain potential energy with a restoring force still existing, the restoring force might create what is also called tension. Each end of a string or rod under such tension could pull on the object it is attached to, in order to restore the string/rod to its relaxed length. Tension (as a transmitted force, as an action-reaction pair of forces, or as a restoring force) is measured in newtons in the International System of Units (or pounds-force in Imperial units). The ends of a string or other object transmitting tension will exert forces on the objects to ...
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Tug Of War Tension
A tugboat or tug is a marine vessel that manoeuvres other vessels by pushing or pulling them, with direct contact or a tow line. These boats typically tug ships in circumstances where they cannot or should not move under their own power, such as in crowded harbor, harbors or narrow canals, or cannot move at all, such as barges, disabled ships, log rafts, or oil platforms. Some are ocean-going, and some are icebreakers or salvage tugs. Early models were powered by steam engines, which were later superseded by diesel engines. Many have deluge gun water jets, which help in firefighting, especially in harbours. Types Seagoing Seagoing tugs (deep-sea tugs or ocean tugboats) fall into four basic categories: #The standard seagoing tug with model bow that tows almost exclusively by way of a wire cable. In some rare cases, such as some USN fleet tugs, a synthetic rope hawser may be used for the tow in the belief that the line can be pulled aboard a disabled ship by the crew owing t ...
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Newton's Third Law
Newton's laws of motion are three physical laws that describe the relationship between the motion of an object and the forces acting on it. These laws, which provide the basis for Newtonian mechanics, can be paraphrased as follows: # A body remains at rest, or in motion at a constant speed in a straight line, unless it is acted upon by a force. # At any instant of time, the net force on a body is equal to the body's acceleration multiplied by its mass or, equivalently, the rate at which the body's momentum is changing with time. # If two bodies exert forces on each other, these forces have the same magnitude but opposite directions. The three laws of motion were first stated by Isaac Newton in his ''Philosophiæ Naturalis Principia Mathematica'' (''Mathematical Principles of Natural Philosophy''), originally published in 1687. Newton used them to investigate and explain the motion of many physical objects and systems. In the time since Newton, new insights, especially around t ...
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Structural Load
A structural load or structural action is a mechanical load (more generally a force) applied to Structural engineering#Structural elements, structural elements. A load causes stress (physics), stress, deformation (engineering), deformation, displacement (vector), displacement or acceleration in a structure. Structural analysis, a discipline in engineering, analyzes the effects of loads on structures and structural elements. Excess load may cause structural failure, so this should be considered and controlled during the design of a structure. Particular mechanical structures—such as aircraft, satellites, rockets, space stations, ships, and submarines—are subject to their own particular structural loads and actions. Engineers often evaluate structural loads based upon published regulations, contracts, or specifications. Accepted technical standards are used for acceptance testing and inspection. Types In civil engineering, specified loads are the best estimate of the actual l ...
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Elongation (mechanics)
In physics and continuum mechanics, deformation is the change in the shape or size of an object. It has dimension of length with SI unit of metre (m). It is quantified as the residual displacement of particles in a non- rigid body, from an configuration to a configuration, excluding the body's average translation and rotation (its rigid transformation). A ''configuration'' is a set containing the positions of all particles of the body. A deformation can occur because of external loads, intrinsic activity (e.g. muscle contraction), body forces (such as gravity or electromagnetic forces), or changes in temperature, moisture content, or chemical reactions, etc. In a continuous body, a ''deformation field'' results from a stress field due to applied forces or because of some changes in the conditions of the body. The relation between stress and strain (relative deformation) is expressed by constitutive equations, e.g., Hooke's law for linear elastic materials. Defor ...
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Pressure
Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and even by industry. Further, both spellings are often used ''within'' a particular industry or country. Industries in British English-speaking countries typically use the "gauge" spelling. is the pressure relative to the ambient pressure. Various #Units, units are used to express pressure. Some of these derive from a unit of force divided by a unit of area; the International System of Units, SI unit of pressure, the Pascal (unit), pascal (Pa), for example, is one newton (unit), newton per square metre (N/m2); similarly, the Pound (force), pound-force per square inch (Pound per square inch, psi, symbol lbf/in2) is the traditional unit of pressure in the imperial units, imperial and United States customary units, US customary systems. Pressure ma ...
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Stringed Instrument
In musical instrument classification, string instruments, or chordophones, are musical instruments that produce sound from vibrating strings when a performer strums, plucks, strikes or sounds the strings in varying manners. Musicians play some string instruments, like guitars, by plucking the strings with their fingers or a plectrum (pick), and others by hitting the strings with a light wooden hammer or by rubbing the strings with a bow, like violins. In some keyboard instruments, such as the harpsichord, the musician presses a key that plucks the string. Other musical instruments generate sound by striking the string. With bowed instruments, the player pulls a rosined horsehair bow across the strings, causing them to vibrate. With a hurdy-gurdy, the musician cranks a wheel whose rosined edge touches the strings. Bowed instruments include the string section instruments of the orchestra in Western classical music (violin, viola, cello and double bass) and a number of ...
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Scale Of Harmonics
The scale of harmonics is a musical scale based on the noded positions of the natural harmonics existing on a string. This musical scale is present on the guqin, regarded as one of the first string instruments with a musical scale.Yin, Wei. ''Zhongguo Qinshi Yanyi'' 【中国琴史演义】 (Chinese). Pages 1-10. Most fret positions appearing on Non-Western string instruments (lutes) are equal to positions of this scale. Unexpectedly, these fret positions are actually the corresponding undertones of the overtones from the harmonic series. The distance from the nut to the fret is an integer number lower than the distance from the fret to the bridge (see: superparticular number). Origin On the guqin, the left end of the dotted scale is a mirror image of the right end. The instrument is played with flageolet tones (harmonics) as well as pressing the strings on the wood. The flageolets appear on the harmonic positions of the overtone series, therefore these positions are marked a ...
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Eigenvalue
In linear algebra, an eigenvector ( ) or characteristic vector is a vector that has its direction unchanged (or reversed) by a given linear transformation. More precisely, an eigenvector \mathbf v of a linear transformation T is scaled by a constant factor \lambda when the linear transformation is applied to it: T\mathbf v=\lambda \mathbf v. The corresponding eigenvalue, characteristic value, or characteristic root is the multiplying factor \lambda (possibly a negative or complex number). Geometrically, vectors are multi-dimensional quantities with magnitude and direction, often pictured as arrows. A linear transformation rotates, stretches, or shears the vectors upon which it acts. A linear transformation's eigenvectors are those vectors that are only stretched or shrunk, with neither rotation nor shear. The corresponding eigenvalue is the factor by which an eigenvector is stretched or shrunk. If the eigenvalue is negative, the eigenvector's direction is reversed. Th ...
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Sturm–Liouville Theory
In mathematics and its applications, a Sturm–Liouville problem is a second-order linear ordinary differential equation of the form \frac \left (x) \frac\right+ q(x)y = -\lambda w(x) y for given functions p(x), q(x) and w(x), together with some boundary conditions at extreme values of x. The goals of a given Sturm–Liouville problem are: * To find the for which there exists a non-trivial solution to the problem. Such values are called the ''eigenvalues'' of the problem. * For each eigenvalue , to find the corresponding solution y = y(x) of the problem. Such functions y are called the '' eigenfunctions'' associated to each . Sturm–Liouville theory is the general study of Sturm–Liouville problems. In particular, for a "regular" Sturm–Liouville problem, it can be shown that there are an infinite number of eigenvalues each with a unique eigenfunction, and that these eigenfunctions form an orthonormal basis of a certain Hilbert space of functions. This theory is important ...
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Transverse Wave
In physics, a transverse wave is a wave that oscillates perpendicularly to the direction of the wave's advance. In contrast, a longitudinal wave travels in the direction of its oscillations. All waves move energy from place to place without transporting the matter in the transmission medium if there is one. Electromagnetic waves are transverse without requiring a medium. The designation “transverse” indicates the direction of the wave is perpendicular to the displacement of the particles of the medium through which it passes, or in the case of EM waves, the oscillation is perpendicular to the direction of the wave. A simple example is given by the waves that can be created on a horizontal length of string by anchoring one end and moving the other end up and down. Another example is the waves that are created on the membrane of a drum. The waves propagate in directions that are parallel to the membrane plane, but each point in the membrane itself gets displaced up and dow ...
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Newton's Laws Of Motion
Newton's laws of motion are three physical laws that describe the relationship between the motion of an object and the forces acting on it. These laws, which provide the basis for Newtonian mechanics, can be paraphrased as follows: # A body remains at rest, or in motion at a constant speed in a straight line, unless it is acted upon by a force. # At any instant of time, the net force on a body is equal to the body's acceleration multiplied by its mass or, equivalently, the rate at which the body's momentum is changing with time. # If two bodies exert forces on each other, these forces have the same magnitude but opposite directions. The three laws of motion were first stated by Isaac Newton in his ''Philosophiæ Naturalis Principia Mathematica'' (''Mathematical Principles of Natural Philosophy''), originally published in 1687. Newton used them to investigate and explain the motion of many physical objects and systems. In the time since Newton, new insights, especially around t ...
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Frequencies
Frequency is the number of occurrences of a repeating event per unit of time. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio signals (sound), radio waves, and light. The interval of time between events is called the period. It is the reciprocal of the frequency. For example, if a heart beats at a frequency of 120 times per minute (2 hertz), its period is one half of a second. Special definitions of frequency are used in certain contexts, such as the angular frequency in rotational or cyclical properties, when the rate of angular progress is measured. Spatial frequency is defined for properties that vary or cccur repeatedly in geometry or space. The unit of measurement of frequency in the International System of Units (SI) is the hertz, having the symbol Hz. Definitions and units For cyclical phenomena such as oscillations, waves, or for examples ...
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