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 fork, the reed in a woodwind instrument or harmonica. In many cases, vibration is undesirable, wasting energy, for example, the vibrational motions of engines, electric motors, or any mechanical device in operation are typically unwanted. Such vibrations could be caused by imbalances in the parts, uneven friction. Careful designs usually minimize unwanted vibrations, the studies of sound and vibration are closely related. Sound, or pressure waves, are generated by vibrating structures, attempts to reduce noise are often related to issues of vibration. Free vibration occurs when a system is set in motion with an initial input. Examples of this type of vibration are pulling a child back on a swing and letting go, or hitting a tuning fork, the mechanical system vibrates at one or more of its natural frequencies and damps down to motionlessness.
Forced vibration is when a disturbance is applied to a mechanical system. The disturbance can be a periodic and steady-state input, a transient input, the periodic input can be a harmonic or a non-harmonic disturbance. Damped vibration, When the energy of a system is gradually dissipated by friction and other resistances. The vibrations gradually reduce or change in frequency or intensity or cease, Vibration testing is accomplished by introducing a forcing function into a structure, usually 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 be life, resonant frequencies or squeak. Squeak and rattle testing is performed with a type of quiet shaker that produces very low sound levels while under operation. For relatively low frequency forcing, servohydraulic shakers are used, for higher frequencies, electrodynamic shakers are used.
Generally, 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
Angular displacement of a body is the angle in radians through which a point or line has been rotated in a specified sense about a specified axis. When an object rotates about its axis, the motion cannot simply be analyzed as a particle, since in circular motion it undergoes a changing velocity, when dealing with the rotation of an object, it becomes simpler to consider the body itself rigid. A body is generally considered rigid when the separations between all the particles remains constant throughout the motion, so for example parts of its mass are not flying off. In a realistic sense, all things can be deformable, however this impact is minimal, Thus the rotation of a rigid body over a fixed axis is referred to as rotational motion. In the example illustrated to the right, a particle on object P is at a distance r from the origin, O. It becomes important to represent the position of particle P in terms of its polar coordinates. In this particular example, the value of θ is changing, if using radians, it provides a very simple relationship between distance traveled around the circle and the distance r from the centre.
Therefore,1 revolution is 2 π radians, when object travels from point P to point Q, as it does in the illustration to the left, over δ t the radius of the circle goes around a change in angle. Δ θ = θ2 − θ1 which equals the Angular Displacement, in three dimensions, angular displacement is an entity with a direction and a magnitude. The direction specifies the axis of rotation, which exists by virtue of the Eulers rotation theorem. This entity is called an axis-angle, despite having direction and magnitude, angular displacement is not a vector because it does not obey the commutative law for addition. Nevertheless, when dealing with infinitesimal rotations, second order infinitesimals can be discarded, several ways to describe angular displacement exist, like rotation matrices or Euler angles. See charts on SO for others, given that any frame in the space can be described by a rotation matrix, the displacement among them can be described by a rotation matrix. Being A0 and A f two matrices, the angular displacement matrix between them can be obtained as Δ A = A f, when this product is performed having a very small difference between both frames we will obtain a matrix close to the identity.
In the limit, we will have a rotation matrix. An infinitesimal angular displacement is a rotation matrix, As any rotation matrix has a single real eigenvalue, which is +1. Its module can be deduced from the value of the infinitesimal rotation, when it is divided by the time, this will yield the angular velocity vector. Suppose we specify an axis of rotation by a unit vector, expanding the rotation matrix as an infinite addition, and taking the first order approach, the rotation matrix ΔR is represented as, Δ R = + Δ θ = I + A Δ θ
International System of Units
The International System of Units is the modern form of the metric system, and is the most widely used system of measurement. It comprises a coherent system of units of measurement built on seven base units, the system establishes a set of twenty prefixes to the unit names and unit symbols that may be used when specifying multiples and fractions of the units. The system was published in 1960 as the result of an initiative began in 1948. It is based on the system of units rather than any variant of the centimetre-gram-second system. The motivation for the development of the SI was the diversity of units that had sprung up within the CGS systems, the International System of Units has been adopted by most developed countries, the adoption has not been universal in all English-speaking countries. The metric system was first implemented during the French Revolution with just the metre and kilogram as standards of length, in the 1830s Carl Friedrich Gauss laid the foundations for a coherent system based on length and time.
In the 1860s a group working under the auspices of the British Association for the Advancement of Science formulated the requirement for a coherent system of units with base units and derived units. Meanwhile, in 1875, the Treaty of the Metre passed responsibility for verification of the kilogram, in 1921, the Treaty was extended to include all physical quantities including electrical units originally defined in 1893. The units associated with these quantities were the metre, second, kelvin, in 1971, a seventh base quantity, amount of substance represented by the mole, was added to the definition of SI. On 11 July 1792, the proposed the names metre, are and grave for the units of length, capacity. The committee proposed that multiples and submultiples of these units were to be denoted by decimal-based prefixes such as centi for a hundredth, on 10 December 1799, the law by which the metric system was to be definitively adopted in France was passed. Prior to this, the strength of the magnetic field had only been described in relative terms.
The technique used by Gauss was to equate the torque induced on a magnet of known mass by the earth’s magnetic field with the torque induced on an equivalent system under gravity. The resultant calculations enabled him to assign dimensions based on mass, length, a French-inspired initiative for international cooperation in metrology led to the signing in 1875 of the Metre Convention. Initially the convention only covered standards for the metre and the kilogram, one of each was selected at random to become the International prototype metre and International prototype kilogram that replaced the mètre des Archives and kilogramme des Archives respectively. Each member state was entitled to one of each of the prototypes to serve as the national prototype for that country. Initially its prime purpose was a periodic recalibration of national prototype metres. The official language of the Metre Convention is French and the version of all official documents published by or on behalf of the CGPM is the French-language version
Physics is the natural science that involves the study of matter and its motion and behavior through space and time, along with related concepts such as energy and force. One of the most fundamental disciplines, the main goal of physics is to understand how the universe behaves. Physics is one of the oldest academic disciplines, perhaps the oldest through its inclusion of astronomy, Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the mechanisms of other sciences while opening new avenues of research in areas such as mathematics. Physics makes significant contributions through advances in new technologies that arise from theoretical breakthroughs, the United Nations named 2005 the World Year of Physics. Astronomy is the oldest of the natural sciences, the stars and planets were often a target of worship, believed to represent their gods. While the explanations for these phenomena were often unscientific and lacking in evidence, according to Asger Aaboe, the origins of Western astronomy can be found in Mesopotamia, and all Western efforts in the exact sciences are descended from late Babylonian astronomy.
The most notable innovations were in the field of optics and vision, which came from the works of many scientists like Ibn Sahl, Al-Kindi, Ibn al-Haytham, Al-Farisi and Avicenna. The most notable work was The Book of Optics, written by Ibn Al-Haitham, in which he was not only the first to disprove the ancient Greek idea about vision, but came up with a new theory. In the book, he was the first to study the phenomenon of the pinhole camera, many European scholars and fellow polymaths, from Robert Grosseteste and Leonardo da Vinci to René Descartes, Johannes Kepler and Isaac Newton, were in his debt. Indeed, the influence of Ibn al-Haythams Optics ranks alongside that of Newtons work of the same title, the translation of The Book of Optics had a huge impact on Europe. From it, European scholars were able to build the devices as what Ibn al-Haytham did. From this, such important things as eyeglasses, magnifying glasses, Physics became a separate science when early modern Europeans used experimental and quantitative methods to discover what are now considered to be the laws of physics.
Newton developed calculus, the study of change, which provided new mathematical methods for solving physical problems. The discovery of new laws in thermodynamics and electromagnetics resulted from greater research efforts during the Industrial Revolution as energy needs increased, inaccuracies in classical mechanics for very small objects and very high velocities led to the development of modern physics in the 20th century. Modern physics began in the early 20th century with the work of Max Planck in quantum theory, both of these theories came about due to inaccuracies in classical mechanics in certain situations. Quantum mechanics would come to be pioneered by Werner Heisenberg, Erwin Schrödinger, from this early work, and work in related fields, the Standard Model of particle physics was derived. Areas of mathematics in general are important to this field, such as the study of probabilities, in many ways, physics stems from ancient Greek philosophy
When radio waves strike an electrical conductor, the oscillating fields induce an alternating current in the conductor. The information in the waves can be extracted and transformed back into its original form, Radio systems need a transmitter to modulate some property of the energy produced to impress a signal on it, for example using amplitude modulation or angle modulation. Radio systems need an antenna to convert electric currents into radio waves, an antenna can be used for both transmitting and receiving. The electrical resonance of tuned circuits in radios allow individual stations to be selected, the electromagnetic wave is intercepted by a tuned receiving antenna. Radio frequencies occupy the range from a 3 kHz to 300 GHz, a radio communication system sends signals by radio. The term radio is derived from the Latin word radius, meaning spoke of a wheel, beam of light, this invention would not be widely adopted. The switch to radio in place of wireless took place slowly and unevenly in the English-speaking world, the United States Navy would play a role.
Although its translation of the 1906 Berlin Convention used the terms wireless telegraph and wireless telegram, the term started to become preferred by the general public in the 1920s with the introduction of broadcasting. Radio systems used for communication have the following elements, with more than 100 years of development, each process is implemented by a wide range of methods, specialised for different communications purposes. Each system contains a transmitter, This consists of a source of electrical energy, the transmitter contains a system to modulate some property of the energy produced to impress a signal on it. This modulation might be as simple as turning the energy on and off, or altering more subtle such as amplitude, phase. Amplitude modulation of a carrier wave works by varying the strength of the signal in proportion to the information being sent. For example, changes in the strength can be used to reflect the sounds to be reproduced by a speaker. It was the used for the first audio radio transmissions.
Frequency modulation varies the frequency of the carrier, the instantaneous frequency of the carrier is directly proportional to the instantaneous value of the input signal. FM has the capture effect whereby a receiver only receives the strongest signal, Digital data can be sent by shifting the carriers frequency among a set of discrete values, a technique known as frequency-shift keying. FM is commonly used at Very high frequency radio frequencies for high-fidelity broadcasts of music, analog TV sound is broadcast using FM. Angle modulation alters the phase of the carrier wave to transmit a signal
Heinrich Rudolf Hertz was a German physicist who first conclusively proved the existence of the electromagnetic waves theorized by James Clerk Maxwells electromagnetic theory of light. The unit of frequency – cycle per second – was named the hertz in his honor, Heinrich Rudolf Hertz was born in 1857 in Hamburg, a sovereign state of the German Confederation, into a prosperous and cultured Hanseatic family. His father Gustav Ferdinand Hertz was a barrister and a senator and his mother was Anna Elisabeth Pfefferkorn. Hertzs paternal grandfather, Heinrich David Hertz, was a businessman and their first son, Wolff Hertz, was chairman of the Jewish community. Heinrich Rudolf Hertzs father and paternal grandparents had converted from Judaism to Christianity in 1834 and his mothers family was a Lutheran pastors family. While studying at the Gelehrtenschule des Johanneums in Hamburg, Heinrich Rudolf Hertz showed an aptitude for sciences as well as languages, learning Arabic and Sanskrit. He studied sciences and engineering in the German cities of Dresden and Berlin, in 1880, Hertz obtained his PhD from the University of Berlin, and for the next three years remained for post-doctoral study under Helmholtz, serving as his assistant.
In 1883, Hertz took a post as a lecturer in physics at the University of Kiel. In 1885, Hertz became a professor at the University of Karlsruhe. In 1886, Hertz married Elisabeth Doll, the daughter of Dr. Max Doll and they had two daughters, born on 20 October 1887 and Mathilde, born on 14 January 1891, who went on to become a notable biologist. During this time Hertz conducted his research into electromagnetic waves. Hertz took a position of Professor of Physics and Director of the Physics Institute in Bonn on 3 April 1889, during this time he worked on theoretical mechanics with his work published in the book Die Prinzipien der Mechanik in neuem Zusammenhange dargestellt, published posthumously in 1894. In 1892, Hertz was diagnosed with an infection and underwent operations to treat the illness and he died of granulomatosis with polyangiitis at the age of 36 in Bonn, Germany in 1894, and was buried in the Ohlsdorf Cemetery in Hamburg. Hertzs wife, Elisabeth Hertz née Doll, did not remarry, Hertz left two daughters and Mathilde.
Hertzs daughters never married and he has no descendants, Hertz always had a deep interest in meteorology, probably derived from his contacts with Wilhelm von Bezold. In 1886–1889, Hertz published two articles on what was to become known as the field of contact mechanics, joseph Valentin Boussinesq published some critically important observations on Hertzs work, nevertheless establishing this work on contact mechanics to be of immense importance. His work basically summarises how two objects placed in contact will behave under loading, he obtained results based upon the classical theory of elasticity. It was natural to neglect adhesion in that age as there were no methods of testing for it
In physics, sound is a vibration that propagates as a typically audible mechanical wave of pressure and displacement, through a transmission medium such as air or water. In physiology and psychology, sound is the reception of such waves, humans can hear sound waves with frequencies between about 20 Hz and 20 kHz. Sound above 20 kHz is ultrasound and below 20 Hz is infrasound, other animals have different hearing ranges. Acoustics is the science that deals with the study of mechanical waves in gases and solids including vibration, ultrasound. A scientist who works in the field of acoustics is an acoustician, an audio engineer, on the other hand, is concerned with the recording, manipulation and reproduction of sound. Auditory sensation evoked by the oscillation described in, sound can propagate through a medium such as air and solids as longitudinal waves and as a transverse wave in solids. The sound waves are generated by a source, such as the vibrating diaphragm of a stereo speaker. The sound source creates vibrations in the surrounding medium, as the source continues to vibrate the medium, the vibrations propagate away from the source at the speed of sound, thus forming the sound wave.
At a fixed distance from the source, the pressure, velocity, at an instant in time, the pressure and displacement vary in space. Note that the particles of the medium do not travel with the sound wave and this is intuitively obvious for a solid, and the same is true for liquids and gases. During propagation, waves can be reflected, refracted, or attenuated by the medium, the behavior of sound propagation is generally affected by three things, A complex relationship between the density and pressure of the medium. This relationship, affected by temperature, determines the speed of sound within the medium, if the medium is moving, this movement may increase or decrease the absolute speed of the sound wave depending on the direction of the movement. For example, sound moving through wind will have its speed of propagation increased by the speed of the if the sound and wind are moving in the same direction. If the sound and wind are moving in opposite directions, the speed of the wave will be decreased by the speed of the wind.
Medium viscosity determines the rate at which sound is attenuated, for many media, such as air or water, attenuation due to viscosity is negligible. When sound is moving through a medium that does not have constant physical properties, the mechanical vibrations that can be interpreted as sound can travel through all forms of matter, liquids and plasmas. The matter that supports the sound is called the medium, sound cannot travel through a vacuum. Sound is transmitted through gases and liquids as longitudinal waves and it requires a medium to propagate
Acoustics is the interdisciplinary science that deals with the study of all mechanical waves in gases and solids including topics such as vibration, sound and infrasound. A scientist who works in the field of acoustics is an acoustician while someone working in the field of technology may be called an acoustical engineer. The application of acoustics is present in almost all aspects of society with the most obvious being the audio. Hearing is one of the most crucial means of survival in the animal world, the science of acoustics spreads across many facets of human society—music, architecture, industrial production and more. Likewise, animal species such as songbirds and frogs use sound, craft and technology have provoked one another to advance the whole, as in many other fields of knowledge. Robert Bruce Lindsays Wheel of Acoustics is a well accepted overview of the fields in acoustics. The word acoustic is derived from the Greek word ἀκουστικός, meaning of or for hearing, ready to hear and that from ἀκουστός, audible, which in turn derives from the verb ἀκούω, I hear.
The Latin synonym is sonic, after which the term used to be a synonym for acoustics. Frequencies above and below the range are called ultrasonic and infrasonic. If, for example, a string of a length would sound particularly harmonious with a string of twice the length. In modern parlance, if a string sounds the note C when plucked, a string twice as long will sound a C an octave lower. In one system of tuning, the tones in between are given by 16,9 for D,8,5 for E,3,2 for F,4,3 for G,6,5 for A. Aristotle understood that sound consisted of compressions and rarefactions of air which falls upon, a very good expression of the nature of wave motion. The physical understanding of acoustical processes advanced rapidly during and after the Scientific Revolution, mainly Galileo Galilei but Marin Mersenne, discovered the complete laws of vibrating strings. Experimental measurements of the speed of sound in air were carried out successfully between 1630 and 1680 by a number of investigators, prominently Mersenne, Newton derived the relationship for wave velocity in solids, a cornerstone of physical acoustics.
The eighteenth century saw advances in acoustics as mathematicians applied the new techniques of calculus to elaborate theories of sound wave propagation. Also in the 19th century, Wheatstone and Henry developed the analogy between electricity and acoustics, the twentieth century saw a burgeoning of technological applications of the large body of scientific knowledge that was by in place. The first such application was Sabine’s groundbreaking work in architectural acoustics, Underwater acoustics was used for detecting submarines in the first World War
Optics is the branch of physics which involves the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible and infrared light, because light is an electromagnetic wave, other forms of electromagnetic radiation such as X-rays and radio waves exhibit similar properties. Most optical phenomena can be accounted for using the classical description of light. Complete electromagnetic descriptions of light are, often difficult to apply in practice, practical optics is usually done using simplified models. The most common of these, geometric optics, treats light as a collection of rays that travel in straight lines, physical optics is a more comprehensive model of light, which includes wave effects such as diffraction and interference that cannot be accounted for in geometric optics. Historically, the model of light was developed first, followed by the wave model of light. Progress in electromagnetic theory in the 19th century led to the discovery that waves were in fact electromagnetic radiation.
Some phenomena depend on the fact that light has both wave-like and particle-like properties, explanation of these effects requires quantum mechanics. When considering lights particle-like properties, the light is modelled as a collection of particles called photons, quantum optics deals with the application of quantum mechanics to optical systems. Optical science is relevant to and studied in many related disciplines including astronomy, various engineering fields, practical applications of optics are found in a variety of technologies and everyday objects, including mirrors, telescopes, microscopes and fibre optics. Optics began with the development of lenses by the ancient Egyptians and Mesopotamians, the earliest known lenses, made from polished crystal, often quartz, date from as early as 700 BC for Assyrian lenses such as the Layard/Nimrud lens. The ancient Romans and Greeks filled glass spheres with water to make lenses, the word optics comes from the ancient Greek word ὀπτική, meaning appearance, look.
Greek philosophy on optics broke down into two opposing theories on how vision worked, the theory and the emission theory. The intro-mission approach saw vision as coming from objects casting off copies of themselves that were captured by the eye, plato first articulated the emission theory, the idea that visual perception is accomplished by rays emitted by the eyes. He commented on the parity reversal of mirrors in Timaeus, some hundred years later, Euclid wrote a treatise entitled Optics where he linked vision to geometry, creating geometrical optics. Ptolemy, in his treatise Optics, held a theory of vision, the rays from the eye formed a cone, the vertex being within the eye. The rays were sensitive, and conveyed back to the observer’s intellect about the distance. He summarised much of Euclid and went on to describe a way to measure the angle of refraction, during the Middle Ages, Greek ideas about optics were resurrected and extended by writers in the Muslim world
In mathematics, the sine is a trigonometric function of an angle. More generally, the definition of sine can be extended to any value in terms of the length of a certain line segment in a unit circle. The function sine can be traced to the jyā and koṭi-jyā functions used in Gupta period Indian astronomy, via translation from Sanskrit to Arabic and from Arabic to Latin. The word sine comes from a Latin mistranslation of the Arabic jiba, to define the trigonometric functions for an acute angle α, start with any right triangle that contains an angle of measure α, in the accompanying figure, angle A in triangle ABC has measure α. The three sides of the triangle are named as follows, The opposite side is the side opposite to the angle of interest, the hypotenuse is the side opposite the right angle, in this case side h. The hypotenuse is always the longest side of a right-angled triangle, the adjacent side is the remaining side, in this case side b. It forms a side of both the angle of interest and the right angle, once such a triangle is chosen, the sine of the angle is equal to the length of the opposite side divided by the length of the hypotenuse.
As stated, the value sin appears to depend on the choice of right triangle containing an angle of measure α, this is not the case, all such triangles are similar, and so the ratio is the same for each of them. The trigonometric functions can be defined in terms of the rise, when the length of the line segment is 1, sine takes an angle and tells the rise. Sine takes an angle and tells the rise per unit length of the line segment, rise is equal to sin θ multiplied by the length of the line segment. In contrast, cosine is used for telling the run from the angle, arctan is used for telling the angle from the slope. The line segment is the equivalent of the hypotenuse in the right-triangle, in trigonometry, a unit circle is the circle of radius one centered at the origin in the Cartesian coordinate system. Let a line through the origin, making an angle of θ with the half of the x-axis. The x- and y-coordinates of this point of intersection are equal to cos θ and sin, the points distance from the origin is always 1.
Unlike the definitions with the triangle or slope, the angle can be extended to the full set of real arguments by using the unit circle. This can be achieved by requiring certain symmetries and that sine be a periodic function. Exact identities, These apply for all values of θ. sin = cos =1 csc The reciprocal of sine is cosecant, i. e. the reciprocal of sin is csc, or cosec. Cosecant gives the ratio of the length of the hypotenuse to the length of the opposite side, the inverse function of sine is arcsine or inverse sine