Time is the indefinite continued progress of existence and events that occur in irreversible succession through the past, in the present, the future. Time is a component quantity of various measurements used to sequence events, to compare the duration of events or the intervals between them, to quantify rates of change of quantities in material reality or in the conscious experience. Time is referred to as a fourth dimension, along with three spatial dimensions. Time has long been an important subject of study in religion and science, but defining it in a manner applicable to all fields without circularity has eluded scholars. Diverse fields such as business, sports, the sciences, the performing arts all incorporate some notion of time into their respective measuring systems. Time in physics is unambiguously operationally defined as "what a clock reads". See Units of Time. Time is one of the seven fundamental physical quantities in both the International System of Units and International System of Quantities.
Time is used to define other quantities – such as velocity – so defining time in terms of such quantities would result in circularity of definition. An operational definition of time, wherein one says that observing a certain number of repetitions of one or another standard cyclical event constitutes one standard unit such as the second, is useful in the conduct of both advanced experiments and everyday affairs of life; the operational definition leaves aside the question whether there is something called time, apart from the counting activity just mentioned, that flows and that can be measured. Investigations of a single continuum called spacetime bring questions about space into questions about time, questions that have their roots in the works of early students of natural philosophy. Temporal measurement has occupied scientists and technologists, was a prime motivation in navigation and astronomy. Periodic events and periodic motion have long served as standards for units of time. Examples include the apparent motion of the sun across the sky, the phases of the moon, the swing of a pendulum, the beat of a heart.
The international unit of time, the second, is defined by measuring the electronic transition frequency of caesium atoms. Time is of significant social importance, having economic value as well as personal value, due to an awareness of the limited time in each day and in human life spans. Speaking, methods of temporal measurement, or chronometry, take two distinct forms: the calendar, a mathematical tool for organising intervals of time, the clock, a physical mechanism that counts the passage of time. In day-to-day life, the clock is consulted for periods less than a day whereas the calendar is consulted for periods longer than a day. Personal electronic devices display both calendars and clocks simultaneously; the number that marks the occurrence of a specified event as to hour or date is obtained by counting from a fiducial epoch – a central reference point. Artifacts from the Paleolithic suggest that the moon was used to reckon time as early as 6,000 years ago. Lunar calendars were among the first to appear, with years of either 13 lunar months.
Without intercalation to add days or months to some years, seasons drift in a calendar based on twelve lunar months. Lunisolar calendars have a thirteenth month added to some years to make up for the difference between a full year and a year of just twelve lunar months; the numbers twelve and thirteen came to feature prominently in many cultures, at least due to this relationship of months to years. Other early forms of calendars originated in Mesoamerica in ancient Mayan civilization; these calendars were religiously and astronomically based, with 18 months in a year and 20 days in a month, plus five epagomenal days at the end of the year. The reforms of Julius Caesar in 45 BC put the Roman world on a solar calendar; this Julian calendar was faulty in that its intercalation still allowed the astronomical solstices and equinoxes to advance against it by about 11 minutes per year. Pope Gregory XIII introduced a correction in 1582. During the French Revolution, a new clock and calendar were invented in attempt to de-Christianize time and create a more rational system in order to replace the Gregorian calendar.
The French Republican Calendar's days consisted of ten hours of a hundred minutes of a hundred seconds, which marked a deviation from the 12-based duodecimal system used in many other devices by many cultures. The system was abolished in 1806. A large variety of devices have been invented to measure time; the study of these devices is called horology. An Egyptian device that dates to c. 1500 BC, similar in shape to a bent T-square, measured the passage of time from the shadow cast by its crossbar on a nonlinear rule. The T was oriented eastward in the mornings. At noon, the device was turned around so. A sundial uses a gnomon to cast a shadow on a set of markings calibrated to the hour; the position of the shadow marks the hour in local time. The idea to separate the day into smaller parts is credited to Egyptians because of their sundials, which operated on a duodecimal system; the importance of the number 12 is due to the number of lunar cycles in a year and the number of stars used to count the passage of night.
The most precise timekeeping device of the ancient
Virtual work arises in the application of the principle of least action to the study of forces and movement of a mechanical system. The work of a force acting on a particle as it moves along a displacement is different for different displacements. Among all the possible displacements that a particle may follow, called virtual displacements, one will minimize the action; this displacement is therefore the displacement followed by the particle according to the principle of least action. The work of a force on a particle along a virtual displacement is known as the virtual work. Virtual work and the associated calculus of variations were formulated to analyze systems of rigid bodies, but they have been developed for the study of the mechanics of deformable bodies; the principle of virtual work had always been used in some form since antiquity in the study of statics. It was used by the Greeks, medieval Arabs and Latins, Renaissance Italians as "the law of lever"; the idea of virtual work was invoked by many notable physicists of the 17th century, such as Galileo, Torricelli and Huygens, in varying degrees of generality, when solving problems in statics.
Working with Leibnizian concepts, Johann Bernoulli systematized the virtual work principle and made explicit the concept of infinitesimal displacement. He was able to solve problems for both rigid bodies as well as fluids. Bernoulli's version of virtual work law appeared in his letter to Pierre Varignon in 1715, published in Varignon's second volume of Nouvelle mécanique ou Statique in 1725; this formulation of the principle is today known as the principle of virtual velocities and is considered as the prototype of the contemporary virtual work principles. In 1743 D'Alembert published his Traité de Dynamique where he applied the principle of virtual work, based on Bernoulli's work, to solve various problems in dynamics, his idea was to convert a dynamical problem into static problem by introducing inertial force. In 1768, Lagrange presented the virtual work principle in a more efficient form by introducing generalized coordinates and presented it as an alternative principle of mechanics by which all problems of equilibrium could be solved.
A systematic exposition of Lagrange's program of applying this approach to all of mechanics, both static and dynamic D'Alembert's principle, was given in his Mécanique Analytique of 1788. Although Lagrange had presented his version of least action principle prior to this work, he recognized the virtual work principle to be more fundamental because it could be assumed alone as the foundation for all mechanics, unlike the modern understanding that least action does not account for non-conservative forces. If a force acts on a particle as it moves from point A to point B for each possible trajectory that the particle may take, it is possible to compute the total work done by the force along the path; the principle of virtual work, the form of the principle of least action applied to these systems, states that the path followed by the particle is the one for which the difference between the work along this path and other nearby paths is zero. The formal procedure for computing the difference of functions evaluated on nearby paths is a generalization of the derivative known from differential calculus, is termed the calculus of variations.
Consider a point particle that moves along a path, described by a function r from point A, where r, to point B, where r. It is possible that the particle moves from A to B along a nearby path described by r + δr, where δr is called the variation of r; the variation δr satisfies the requirement δr = δr = 0. The components of the variation, δr1, δr2 and δr3, are called virtual displacements; this can be generalized to an arbitrary mechanical system defined by the generalized coordinates qi, i = 1... n. In which case, the variation of the trajectory qi is defined by the virtual displacements δqi, i = 1... n. Virtual work is the total work done by the applied forces and the inertial forces of a mechanical system as it moves through a set of virtual displacements; when considering forces applied to a body in static equilibrium, the principle of least action requires the virtual work of these forces to be zero. Consider a particle P that moves from a point A to a point B along a trajectory r, while a force F is applied to it.
The work done by the force F is given by the integral W = ∫ r = A r = B F ⋅ d r = ∫ t 0 t 1 F ⋅ d r d t d t = ∫ t 0 t 1 F ⋅ v d t, where dr is the differential element along the curve, the trajectory of P, v is its velocity. It is important to notice. Now consider particle P that moves from point A to point B again, but this time it moves along the nearby trajectory that differs from r by the variation δr=εh, where ε is a scaling constant that can be made as small as desired and h(
In physics, angular momentum is the rotational equivalent of linear momentum. It is an important quantity in physics because it is a conserved quantity—the total angular momentum of a closed system remains constant. In three dimensions, the angular momentum for a point particle is a pseudovector r × p, the cross product of the particle's position vector r and its momentum vector p = mv; this definition can be applied to each point in physical fields. Unlike momentum, angular momentum does depend on where the origin is chosen, since the particle's position is measured from it. Just like for angular velocity, there are two special types of angular momentum: the spin angular momentum and the orbital angular momentum; the spin angular momentum of an object is defined as the angular momentum about its centre of mass coordinate. The orbital angular momentum of an object about a chosen origin is defined as the angular momentum of the centre of mass about the origin; the total angular momentum of an object is the sum of orbital angular momenta.
The orbital angular momentum vector of a particle is always parallel and directly proportional to the orbital angular velocity vector ω of the particle, where the constant of proportionality depends on both the mass of the particle and its distance from origin. However, the spin angular momentum of the object is proportional but not always parallel to the spin angular velocity Ω, making the constant of proportionality a second-rank tensor rather than a scalar. Angular momentum is additive. For a continuous rigid body, the total angular momentum is the volume integral of angular momentum density over the entire body. Torque can be defined as the rate of change of angular momentum, analogous to force; the net external torque on any system is always equal to the total torque on the system. Therefore, for a closed system, the total torque on the system must be 0, which means that the total angular momentum of the system is constant; the conservation of angular momentum helps explain many observed phenomena, for example the increase in rotational speed of a spinning figure skater as the skater's arms are contracted, the high rotational rates of neutron stars, the Coriolis effect, the precession of gyroscopes.
In general, conservation does limit the possible motion of a system, but does not uniquely determine what the exact motion is. In quantum mechanics, angular momentum is an operator with quantized eigenvalues. Angular momentum is subject to the Heisenberg uncertainty principle, meaning that at any time, only one component can be measured with definite precision; because of this, it turns out that the notion of an elementary particle "spinning" about an axis does not exist. For technical reasons, elementary particles still possess a spin angular momentum, but this angular momentum does not correspond to spinning motion in the ordinary sense. Angular momentum is a vector quantity that represents the product of a body's rotational inertia and rotational velocity about a particular axis. However, if the particle's trajectory lies in a single plane, it is sufficient to discard the vector nature of angular momentum, treat it as a scalar. Angular momentum can be considered a rotational analog of linear momentum.
Thus, where linear momentum p is proportional to mass m and linear speed v, p = m v, angular momentum L is proportional to moment of inertia I and angular speed ω, L = I ω. Unlike mass, which depends only on amount of matter, moment of inertia is dependent on the position of the axis of rotation and the shape of the matter. Unlike linear speed, which does not depend upon the choice of origin, angular velocity is always measured with respect to a fixed origin; therefore speaking, L should be referred to as the angular momentum relative to that center. Because I = r 2 m for a single particle and ω = v r for circular motion, angular momentum can be expanded, L = r 2 m ⋅ v r, reduced to, L = r m v, the product of the radius of rotation r and the linear momentum of the particle p = m v, where v in this case is the equivalent linear speed at the radius; this simple analysis can apply to non-circular motion if only the component of the motion, perpendicular to the radius vector is considered. In that case, L
In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes; the same amount of work is done by the body when decelerating from its current speed to a state of rest. In classical mechanics, the kinetic energy of a non-rotating object of mass m traveling at a speed v is 1 2 m v 2. In relativistic mechanics, this is a good approximation only when v is much less than the speed of light; the standard unit of kinetic energy is the joule. The imperial unit of kinetic energy is the foot-pound; the adjective kinetic has its roots in the Greek word κίνησις kinesis, meaning "motion". The dichotomy between kinetic energy and potential energy can be traced back to Aristotle's concepts of actuality and potentiality; the principle in classical mechanics that E ∝ mv2 was first developed by Gottfried Leibniz and Johann Bernoulli, who described kinetic energy as the living force, vis viva.
Willem's Gravesande of the Netherlands provided experimental evidence of this relationship. By dropping weights from different heights into a block of clay, Willem's Gravesande determined that their penetration depth was proportional to the square of their impact speed. Émilie du Châtelet published an explanation. The terms kinetic energy and work in their present scientific meanings date back to the mid-19th century. Early understandings of these ideas can be attributed to Gaspard-Gustave Coriolis, who in 1829 published the paper titled Du Calcul de l'Effet des Machines outlining the mathematics of kinetic energy. William Thomson Lord Kelvin, is given the credit for coining the term "kinetic energy" c. 1849–51. Energy occurs in many forms, including chemical energy, thermal energy, electromagnetic radiation, gravitational energy, electric energy, elastic energy, nuclear energy, rest energy; these can be categorized in two main classes: kinetic energy. Kinetic energy is the movement energy of an object.
Kinetic energy can be transformed into other kinds of energy. Kinetic energy may be best understood by examples that demonstrate how it is transformed to and from other forms of energy. For example, a cyclist uses chemical energy provided by food to accelerate a bicycle to a chosen speed. On a level surface, this speed can be maintained without further work, except to overcome air resistance and friction; the chemical energy has been converted into kinetic energy, the energy of motion, but the process is not efficient and produces heat within the cyclist. The kinetic energy in the moving cyclist and the bicycle can be converted to other forms. For example, the cyclist could encounter a hill just high enough to coast up, so that the bicycle comes to a complete halt at the top; the kinetic energy has now been converted to gravitational potential energy that can be released by freewheeling down the other side of the hill. Since the bicycle lost some of its energy to friction, it never regains all of its speed without additional pedaling.
The energy is not destroyed. Alternatively, the cyclist could connect a dynamo to one of the wheels and generate some electrical energy on the descent; the bicycle would be traveling slower at the bottom of the hill than without the generator because some of the energy has been diverted into electrical energy. Another possibility would be for the cyclist to apply the brakes, in which case the kinetic energy would be dissipated through friction as heat. Like any physical quantity, a function of velocity, the kinetic energy of an object depends on the relationship between the object and the observer's frame of reference. Thus, the kinetic energy of an object is not invariant. Spacecraft use chemical energy to launch and gain considerable kinetic energy to reach orbital velocity. In an circular orbit, this kinetic energy remains constant because there is no friction in near-earth space. However, it becomes apparent at re-entry. If the orbit is elliptical or hyperbolic throughout the orbit kinetic and potential energy are exchanged.
Without loss or gain, the sum of the kinetic and potential energy remains constant. Kinetic energy can be passed from one object to another. In the game of billiards, the player imposes kinetic energy on the cue ball by striking it with the cue stick. If the cue ball collides with another ball, it slows down and the ball it hit accelerates its speed as the kinetic energy is passed on to it. Collisions in billiards are elastic collisions, in which kinetic energy is preserved. In inelastic collisions, kinetic energy is dissipated in various forms of energy, such as heat, binding energy. Flywheels have been developed as a method of energy storage; this illustrates that kinetic energy is stored in rotational motion. Several mathematical descriptions of kinetic energy exist that describe it in the appropriate physical situation. For objects and processes in common human experience, the formula ½mv² given by Newtonian mechanics is suitable. However, if the speed of the object is comparabl
Lagrangian mechanics is a reformulation of classical mechanics, introduced by the Italian-French mathematician and astronomer Joseph-Louis Lagrange in 1788. In Lagrangian mechanics, the trajectory of a system of particles is derived by solving the Lagrange equations in one of two forms, either the Lagrange equations of the first kind, which treat constraints explicitly as extra equations using Lagrange multipliers. In each case, a mathematical function called the Lagrangian is a function of the generalized coordinates, their time derivatives, time, contains the information about the dynamics of the system. No new physics are introduced in applying Lagrangian mechanics compared to Newtonian mechanics, it is, more mathematically sophisticated and systematic. Newton's laws can include non-conservative forces like friction. Lagrangian mechanics is ideal for systems with conservative forces and for bypassing constraint forces in any coordinate system. Dissipative and driven forces can be accounted for by splitting the external forces into a sum of potential and non-potential forces, leading to a set of modified Euler–Lagrange equations.
Generalized coordinates can be chosen by convenience, to exploit symmetries in the system or the geometry of the constraints, which may simplify solving for the motion of the system. Lagrangian mechanics reveals conserved quantities and their symmetries in a direct way, as a special case of Noether's theorem. Lagrangian mechanics is important not just for its broad applications, but for its role in advancing deep understanding of physics. Although Lagrange only sought to describe classical mechanics in his treatise Mécanique analytique, William Rowan Hamilton developed Hamilton's principle that can be used to derive the Lagrange equation and was recognized to be applicable to much of fundamental theoretical physics as well quantum mechanics and the theory of relativity, it can be applied to other systems by analogy, for instance to coupled electric circuits with inductances and capacitances. Lagrangian mechanics is used to solve mechanical problems in physics and when Newton's formulation of classical mechanics is not convenient.
Lagrangian mechanics applies to the dynamics of particles, while fields are described using a Lagrangian density. Lagrange's equations are used in optimization problems of dynamic systems. In mechanics, Lagrange's equations of the second kind are used much more than those of the first kind. Suppose we have a bead sliding around on a wire, or a swinging simple pendulum, etc. If one tracks each of the massive objects as a particle, calculation of the motion of the particle using Newtonian mechanics would require solving for the time-varying constraint force required to keep the particle in the constrained motion. For the same problem using Lagrangian mechanics, one looks at the path the particle can take and chooses a convenient set of independent generalized coordinates that characterize the possible motion of the particle; this choice eliminates the need for the constraint force to enter into the resultant system of equations. There are fewer equations since one is not directly calculating the influence of the constraint on the particle at a given moment.
For a wide variety of physical systems, if the size and shape of a massive object are negligible, it is a useful simplification to treat it as a point particle. For a system of N point particles with masses m1, m2... mN, each particle has a position vector, denoted r1, r2... rN. Cartesian coordinates are sufficient, so r1 =, r2 = and so on. In three dimensional space, each position vector requires three coordinates to uniquely define the location of a point, so there are 3N coordinates to uniquely define the configuration of the system; these are all specific points in space to locate the particles. The velocity of each particle is how fast the particle moves along its path of motion, is the time derivative of its position, thusIn Newtonian mechanics, the equations of motion are given by Newton's laws; the second law "net force equals mass times acceleration",applies to each particle. For an N particle system in 3 dimensions, there are 3N second order ordinary differential equations in the positions of the particles to solve for.
Instead of forces, Lagrangian mechanics uses the energies in the system. The central quantity of Lagrangian mechanics is the Lagrangian, a function which summarizes the dynamics of the entire system. Overall, the Lagrangian has no single expression for all physical systems. Any function which generates the correct equations of motion, in agreement with physical laws, can be taken as a Lagrangian, it is possible to construct general expressions for large classes of applications. The non-relativistic Lagrangian for a system of particles can be defined by L = T − V where T = 1 2 ∑ k = 1 N m k v k 2 is the total kinetic energy of the system, equalling the sum Σ of the kinetic energies of the particles, V is the potential energy of the system. Kinetic energy is the energy of the system's motion, vk2 = vk
Friction is the force resisting the relative motion of solid surfaces, fluid layers, material elements sliding against each other. There are several types of friction: Dry friction is a force that opposes the relative lateral motion of two solid surfaces in contact. Dry friction is subdivided into static friction between non-moving surfaces, kinetic friction between moving surfaces. With the exception of atomic or molecular friction, dry friction arises from the interaction of surface features, known as asperities Fluid friction describes the friction between layers of a viscous fluid that are moving relative to each other. Lubricated friction is a case of fluid friction where a lubricant fluid separates two solid surfaces. Skin friction is a component of drag, the force resisting the motion of a fluid across the surface of a body. Internal friction is the force resisting motion between the elements making up a solid material while it undergoes deformation; when surfaces in contact move relative to each other, the friction between the two surfaces converts kinetic energy into thermal energy.
This property can have dramatic consequences, as illustrated by the use of friction created by rubbing pieces of wood together to start a fire. Kinetic energy is converted to thermal energy whenever motion with friction occurs, for example when a viscous fluid is stirred. Another important consequence of many types of friction can be wear, which may lead to performance degradation or damage to components. Friction is a component of the science of tribology. Friction is important in supplying traction to facilitate motion on land. Most land vehicles rely on friction for acceleration and changing direction. Sudden reductions in traction can cause loss of control and accidents. Friction is not itself a fundamental force. Dry friction arises from a combination of inter-surface adhesion, surface roughness, surface deformation, surface contamination; the complexity of these interactions makes the calculation of friction from first principles impractical and necessitates the use of empirical methods for analysis and the development of theory.
Friction is a non-conservative force - work done against friction is path dependent. In the presence of friction, some energy is always lost in the form of heat, thus mechanical energy is not conserved. The Greeks, including Aristotle and Pliny the Elder, were interested in the cause and mitigation of friction, they were aware of differences between static and kinetic friction with Themistius stating in 350 A. D. that "it is easier to further the motion of a moving body than to move a body at rest". The classic laws of sliding friction were discovered by Leonardo da Vinci in 1493, a pioneer in tribology, but the laws documented in his notebooks, were not published and remained unknown; these laws were rediscovered by Guillaume Amontons in 1699 and became known as Amonton's three laws of dry friction. Amontons presented the nature of friction in terms of surface irregularities and the force required to raise the weight pressing the surfaces together; this view was further elaborated by Bernard Forest de Bélidor and Leonhard Euler, who derived the angle of repose of a weight on an inclined plane and first distinguished between static and kinetic friction.
John Theophilus Desaguliers first recognized the role of adhesion in friction. Microscopic forces cause surfaces to stick together; the understanding of friction was further developed by Charles-Augustin de Coulomb. Coulomb investigated the influence of four main factors on friction: the nature of the materials in contact and their surface coatings. Coulomb further considered the influence of sliding velocity and humidity, in order to decide between the different explanations on the nature of friction, proposed; the distinction between static and dynamic friction is made in Coulomb's friction law, although this distinction was drawn by Johann Andreas von Segner in 1758. The effect of the time of repose was explained by Pieter van Musschenbroek by considering the surfaces of fibrous materials, with fibers meshing together, which takes a finite time in which the friction increases. John Leslie noted a weakness in the views of Amontons and Coulomb: If friction arises from a weight being drawn up the inclined plane of successive asperities, why isn't it balanced through descending the opposite slope?
Leslie was skeptical about the role of adhesion proposed by Desaguliers, which should on the whole have the same tendency to accelerate as to retard the motion. In Leslie's view, friction should be seen as a time-dependent process of flattening, pressing down asperities, which creates new obstacles in what were cavities before. Arthur Jules Morin developed the concept of sliding versus rolling friction. Osborne Reynolds derived the equation of viscous flow; this completed the classic empirical model of friction used today in engineering. In 1877, Fleeming Jenkin and J. A. Ewing investigated the continuity between static and kinetic friction; the focus of research during the 20th century has been to understand the physical mechanisms behind friction. Frank Philip Bowden and David Tabor showed that, at a microscopic level, the actual area of contact between surfaces is a small fraction of the apparent area; this actual area of contact, caused by asperities increases with pressure. The development of the atomic force microscope
Vibration is a mechanical phenomenon whereby oscillations occur about an equilibrium point. The word comes from Latin vibrationem; the oscillations may be periodic, such as the motion of a pendulum—or random, such as the movement of a tire on a gravel road. Vibration can be desirable: for example, the motion of a tuning fork, the reed in a woodwind instrument or harmonica, a mobile phone, or the cone of a loudspeaker. In many cases, vibration is undesirable, wasting energy and creating unwanted sound. For example, the vibrational motions of engines, electric motors, or any mechanical device in operation are unwanted; such vibrations could be caused by imbalances in the rotating parts, uneven friction, or the meshing of gear teeth. Careful designs minimize unwanted vibrations; the studies of sound and vibration are related. Sound, or pressure waves, are generated by vibrating structures. Hence, attempts to reduce noise are related to issues of vibration. Free vibration occurs when a mechanical system is set in motion with an initial input and allowed to vibrate freely.
Examples of this type of vibration are pulling a child back on a swing and letting it go, or hitting a tuning fork and letting it ring. The mechanical system vibrates at one or more of its natural frequencies and damps down to motionlessness. Forced vibration is; the disturbance can be a transient input, or a random input. The periodic input can be a non-harmonic disturbance. Examples of these types of vibration include a washing machine shaking due to an imbalance, transportation vibration caused by an engine or uneven road, or the vibration of a building during an earthquake. For linear systems, the frequency of the steady-state vibration response resulting from the application of a periodic, harmonic input is equal to the frequency of the applied force or motion, with the response magnitude being dependent on the actual mechanical system. Damped vibration: When the energy of a vibrating system is dissipated by friction and other resistances, the vibrations are said to be damped; the vibrations reduce or change in frequency or intensity or cease and the system rests in its equilibrium position.
An example of this type of vibration is the vehicular suspension. Vibration testing is accomplished by introducing a forcing function into a structure with some type of shaker. Alternately, a DUT is attached to the "table" of a shaker. Vibration testing is performed to examine the response of a device under test to a defined vibration environment; the measured response may rattle sound output. Squeak and rattle testing is performed with a special type of quiet shaker that produces low sound levels while under operation. For low frequency forcing, servohydraulic shakers are used. For higher frequencies, electrodynamic shakers are used. One or more "input" or "control" points located on the DUT-side of a fixture is kept at a specified acceleration. Other "response" points experience maximum vibration level or minimum vibration level, it is desirable to achieve anti-resonance to keep a system from becoming too noisy, or to reduce strain on certain parts due to vibration modes caused by specific vibration frequencies.
The most common types of vibration testing services conducted by vibration test labs are Sinusoidal and Random. Sine tests are performed to survey the structural response of the device under test. A random test is considered to more replicate a real world environment, such as road inputs to a moving automobile. Most vibration testing is conducted in a'single DUT axis' at a time though most real-world vibration occurs in various axes simultaneously. MIL-STD-810G, released in late 2008, Test Method 527, calls for multiple exciter testing; the vibration test fixture used to attach the DUT to the shaker table must be designed for the frequency range of the vibration test spectrum. For smaller fixtures and lower frequency ranges, the designer targets a fixture design, free of resonances in the test frequency range; this becomes more difficult as the test frequency increases. In these cases multi-point control strategies can mitigate some of the resonances that may be present in the future. Devices designed to trace or record vibrations are called vibroscopes.
Vibration Analysis, applied in an industrial or maintenance environment aims to reduce maintenance costs and equipment downtime by detecting equipment faults. VA is a key component of a Condition Monitoring program, is referred to as Predictive Maintenance. Most VA is used to detect faults in rotating equipment such as Unbalance, rolling element bearing faults and resonance conditions. VA can use the units of Displacement and Acceleration displayed as a time waveform, but most the spectrum is used, derived from a fast Fourier transform of the TWF; the vibration spectrum provides important frequency information that can pinpoint the faulty component. The fundamentals of vibration analysis can be understood by studying the simple Mass-spring-damper model. Indeed a complex structure such as an automobile body can be modeled as a "summation" of simple mass–spring–damper models. T