In mechanics and physics, simple harmonic motion is a special type of periodic motion or oscillation where the restoring force is directly proportional to the displacement and acts in the direction opposite to that of displacement. Simple harmonic motion can serve as a mathematical model for a variety of motions, such as the oscillation of a spring. In addition, other phenomena can be approximated by simple harmonic motion, including the motion of a simple pendulum as well as molecular vibration. Simple harmonic motion is typified by the motion of a mass on a spring when it is subject to the linear elastic restoring force given by Hooke's law; the motion demonstrates a single resonant frequency. For simple harmonic motion to be an accurate model for a pendulum, the net force on the object at the end of the pendulum must be proportional to the displacement; this is a good approximation. Simple harmonic motion provides a basis for the characterization of more complicated motions through the techniques of Fourier analysis.

The motion of a particle moving along a straight line with an acceleration whose direction is always towards a fixed point on the line and whose magnitude is proportional to the distance from the fixed point is called simple harmonic motion. In the diagram, a simple harmonic oscillator, consisting of a weight attached to one end of a spring, is shown; the other end of the spring is connected to a rigid support such as a wall. If the system is left at rest at the equilibrium position there is no net force acting on the mass. However, if the mass is displaced from the equilibrium position, the spring exerts a restoring elastic force that obeys Hooke's law. Mathematically, the restoring force F is given by F = − k x, where F is the restoring elastic force exerted by the spring, k is the spring constant, x is the displacement from the equilibrium position. For any simple mechanical harmonic oscillator: When the system is displaced from its equilibrium position, a restoring force that obeys Hooke's law tends to restore the system to equilibrium.

Once the mass is displaced from its equilibrium position, it experiences a net restoring force. As a result, it starts going back to the equilibrium position; when the mass moves closer to the equilibrium position, the restoring force decreases. At the equilibrium position, the net restoring force vanishes. However, at x = 0, the mass has momentum because of the acceleration that the restoring force has imparted. Therefore, the mass continues past the equilibrium position. A net restoring force slows it down until its velocity reaches zero, whereupon it is accelerated back to the equilibrium position again; as long as the system has no energy loss, the mass continues to oscillate. Thus simple harmonic motion is a type of periodic motion. Note if the real space and phase space diagram are not co-linear, the phase space motion becomes elliptical; the area enclosed depends on the maximum momentum. In Newtonian mechanics, for one-dimensional simple harmonic motion, the equation of motion, a second-order linear ordinary differential equation with constant coefficients, can be obtained by means of Newton's 2nd law and Hooke's law for a mass on a spring.

F n e t = m d 2 x d t 2 = − k x, where m is the inertial mass of the oscillating body, x is its displacement from the equilibrium position, k is a constant. Therefore, d 2 x d t 2 = − k m x, Solving the differential equation above produces a solution, a sinusoidal function. X = c 1 cos ⁡ + c 2 sin ⁡ This equation can be written in the form: x = A cos ⁡, where ω = k m, A = c 1 2 + c 2 2, tan ⁡ φ = c 2 c 1, In the solution, c1 and c2 are two constants determined by the initial conditions, the origin is set to be the equilibrium position; each of these constants carries a physical meaning of the motion: A is the amplitude, ω = 2πf is the angular frequency, φ is the initial phase. Using the techniqu

In periodontics, there are four reasons to seek medication. Those four reasons include infection, swelling and sedation. Although some patients may experience pain and infection as a result of an acute periodontal problem such as advanced periodontal disease, periodontic patients do not need medication until they are faced with surgery. For successful surgery, medication is introduced prior to the operation the morning before the procedure and is continued for up to two weeks after. During the surgery, dentists use medication to not only ease the pain of the procedure, but to reduce patient anxiety. With conscious sedation, you remain pain-free; the term "medication dentistry" is referred to as anxiety-free dentistry, relaxation dentistry or comfortable dentistry. This is because most of the patients have feelings of anxiety during a routine trip to the dentist's office. There are a number of sedation drugs, they have been developed for the purpose of conscious sedation in dentistry. Sleep dentistry is a common term once used to describe a visit to the dentist.

The interesting thing is that though it was referred to as sleep dentistry, the patient never went to sleep during the visit. Sleep dentistry should be applied to dentistry which uses the aid of general anesthesia; the dentist will determine. This is the most well recognized drug used today. Diazepam has been used since the 1960s, it is a well-known sedative. It is useful during appointments where the most extensive dentistry is being performed. Triazolam is the most well-known treatment for insomnia, it is a effective drug, which can be used in conjunction with an antihistamine. It is a popular choice for many different dentists. Triazolam is used for shorter appointments. Zaleplon is used in the treatment of insomnia; the patient is not in an extended sleep during throughout oral sedation, but is rather relaxed and comfortable throughout the procedure. Lorazepam is a commonly prescribed drug for anxiety, it is useful in appointments that are longer than two hours. Hydroxyzine is classified as an antihistamine.

It has anti-anxiety works in conjunction with many benzodiazepines. It has no amnesic properties. Midazolam the shortest half-life of any available drugs, it is ideal for simple procedures. It has many anti-anxiety properties as well as amnesic properties. Medications are used to control pain and anxiety in dentistry; the patient is rarely out during a dental procedure if he or she cannot remember the procedure upon waking up. Anti-inflammatory medications are used to relieve redness of the mouth and gums, they are available by prescription only and are available as pastes under some brand names such as Kenalog and Orabase. There are non-prescription anti-inflammatory medications, such as Motrin, which may be used to relieve pain and are available over-the-counter. Local anesthesia, general anesthesia, nitrous oxide and intravenous sedation are all used during common procedures to help dull and control pain and anxiety. Topical anesthetic agents are intraorally to control pain or irritation caused by toothache, teething, or sores in or around the mouth.

Topical anesthetics are available by over-the-counter. They are available in sprays, dental paste, dental gels, lozenges and solutions. Anbesol, Chloraseptic and Xylocaine are examples of available anesthetics over-the-counter; some medications are given in order to control plaque and gingivitis. This type of medication is available in a mouthwash. Antiseptics may be recommended by the dentist to help reduce plaque and gingivitis buildup, as well as kill germs, which may be the cause of bad breath. Knowing the role of supragingival plaque in the initiation of periodontal disease and insufficient control of the plate, the use of antiseptics is warranted; these anti-plaque have different mechanisms of action. There are many medications, which are used to treat tooth decay. Fluoride is used to prevent tooth decay in individuals. Fluoride is available in non-prescription form and is available in many different types of toothpaste. Muscle relaxants and antifungal medication is sometimes prescribed within dentistry.

Muscle relaxants may be prescribed in order to reduce the patient's stress levels and/or to help the patient discontinue grinding their teeth. It can be used to treat TMJ disorders. Antifungal medication may be used to treat oral thrush, common in infants; the goal of treatment is stop the spreading of the Candida fungal infection. Medications Used in Dentistry. 2009-06-18. Närhi TO, Meurman JH, Ainamo A, et al.. "Association between salivary flow rate and the use of systemic medication among 76-, 81-, 86-year-old inhabitants in Helsinki, Finland". J. Dent. Res. 71: 1875–80. Doi:10.1177/00220345920710120401. PMID 1452886. 2009-06-18. Khlil N. Ausalah N. Kissa J. Les antiseptiques en parodontie Le courrier du dentiste Akincibay H, Orsal SO, Sengün D, Tözüm TF. "Systemic administration of doxycycline versus metronidazole plus amoxicillin in the treatment of localized aggressive periodontitis: a clinical and microbiologic study". Quintessence Int. 39: e33–9. PMID 18567166. Easing Dental Phobia in Adult.2009-06-18.

"For the dental patient. Burning mouth syndrome". J Am Dent Assoc. 136: 1191. August 2005. Doi:10.14219/jada.archive.2005.0324. PMID 16161375

Religious symbolism in the United States military includes the use of religious symbols for military chaplain insignia, emblems and chapels. Symbolism sometimes includes specific images included or excluded because of religious reasons, choices involving colors with religious significance, "religious accommodation" policies regarding the wear of "religious apparel" and "grooming" with military uniforms. Additionally, military chaplains themselves are sometimes regarded as "symbols of faith" for military personnel who face challenges to their faith and values. On July 29, 1775, the Continental Congress established the military chaplaincy, but chaplains did not wear insignia until 1880. However, in 1835 Army Regulations prescribed black as the branch color for chaplains, directing that a chaplain wear a black coat. By 1861, US Army Regulations included the details that the chaplains should wear a single breast officer's frock coat made of black wool, with black cloth covering the buttons, no shoulderboards.

In 1864, the Army Uniform Board "enhanced" the frock coat by adding black "herringbone braid" in across the chest at the buttons and buttonholes, with buttons still covered in black. This coat was used by army chaplains until 1880, when shoulder boards were authorized for chaplains for the first time, the first official insignia was introduced. Although the Latin cross has long been the symbol for the majority of United States military chaplains, this first official chaplain insignia was the "shepherd's crook". Authorized in General Order Number 10, remaining in force for the period February 13, 1880 – May 5, 1888, it was described as "embroidered frosted silver bullion in center of black velvet shoulder straps, was considered appropriate for both the frock coat or undress uniform." The plain "Latin cross" became the authorized chaplain insignia in 1898, replacing the shepherd's crook. Today, despite the fact that the shepherd's crook is no longer used as an insignia for individual chaplains, it is included in the design of the Chaplain Corps regimental insignia in honor of its place in Army Chaplain Corps history.

Jewish chaplains were first authorized to serve during the Civil War, but it was during World War I that the issue of insignia reached the army, when Congressman Isaac Siegel from New York petitioned the army that rabbis serving in uniform be permitted to wear "some other insignia in place of the cross."Within two weeks of receiving this request, the army issued a directive stating that "Objections having been made to Jewish Chaplains wearing the prescribed insignia, you are authorized by the Secretary of War to omit the prescribed insignia". However, after battlefront reports indicated that difficulties arose from the fact that Jewish chaplains wore no insignia, the army began to look into various proposals, including a continuation of the practice of having Jewish chaplains wear no insignia, to the creation of a separate insignia for them, to a return to the shepherd's crook as a shared symbol for all chaplains. General Henry Jerver, acting assistant chief of staff for the army favored the third alternative, within weeks of his decision this became the official policy for the Army.

However, many Christian chaplains opposed this change of policy, in August 1918 General Pershing cabled the War Department to inform it of this opposition. Not all Christian chaplains opposed the idea of a universal symbol, some went on record agreeing with the statement of one chaplain that "I am a chaplain of the Christian faith, but I welcome the change; the shepherd's crook is symbolic of the chaplain's work."Returning to a consideration of the three options of no insignia for Jewish chaplains, a shared insignia, or a separate insignia, the army opted for a separate Jewish chaplain insignia that included an image of the two tablets of the Ten Commandments, using Roman numerals to indicate the commandments, with a small six-pointed Jewish star on top of the tablets. Other symbols considered included a six-pointed star, rejected by the army because it could too be confused with the 5-pointed star worn by generals; this symbol would remain the insignia for Jewish chaplains until 1981, when the navy changed its insignia to include the first ten letters of the Hebrew alphabet—to replace the Roman numerals—and both the army and the air force followed suit.

While the official change to Hebrew letters became official November 9, 1981 Jewish chaplains were not required to make the uniform change until January 1, 1983. Insignia decisions for chaplains representing faith groups other than Christianity and Judaism have not been made unilaterally by the army, but instead have been joint decisions for all military chaplains. See also: USN officer rank insignia and USN staff corpsThe Continental Navy, predecessor of the United States Navy, was approved by the United States Congress on October 13, 1775, with navy regulations that included as its second article: "The Commanders of the ships of the thirteen United Colonies are to take care that divine service be performed twice a day on board, a sermon preached on Sundays, unless bad weather or other extraordinary accidents prevent." But, while the need for navy chaplains was recognized from the beginning and policies toward navy uniforms or insignia for its chaplains went through many changes before final decisions

The Division of Riverina is an Australian electoral division in the state of New South Wales. The division was proclaimed in 1900, was one of the original 65 divisions to be contested at the first federal election, although it was abolished between 1984 and 1993, so has not been contested at every federal election; the division was named after the Riverina region in which it is located, though its modern borders do not correspond with the Riverina region. The division covers a agricultural, rural area with many small towns. In the 1984 redistribution, the division was abolished and replaced by Riverina-Darling, but in the 1993 redistribution it was re-created. Since its re-creation in 1993, it has been a safe Nationals seat, its first incarnation tilted toward the Nationals' predecessor, the Country Party, for much of its history, but was taken by Labor during high-tide elections. It was marginal for most of the 1970s and early 1980s, when it included the pro-Labor mining towns of Broken Hill and Cobar which have now been transferred to Farrer and Parkes.

The division is located in South-West rural New South Wales following the Murrumbidgee River valley. It includes the city of Wagga Wagga as well as the towns of Cowra, Junee, Temora, West Wyalong, Young and Gundagai; the Sturt Highway runs along the length of the division, it contains a large section of the Newell Highway. The Division of Riverina contains the major town of Parkes which has the same name as the bordering Division of Parkes; the seat has been held by Al Grassby, Minister for Immigration in the Whitlam Government. The current Member for Riverina, since the 2010 federal election, is Michael McCormack, Deputy Prime Minister and leader of the National Party of Australia. Division of Riverina – Australian Electoral Commission

James Poke is a musician known as artistic director and co-founder of the ensemble Icebreaker. Poke studied music at the University of York and composition with Erich Urbanner at the Hochschule für Musik und Darstellende Kunst in Vienna. With John Godfrey he founded Icebreaker in 1989; as well as running the group, he plays flutes, pan-pipes, keyboards and WX11 wind synthesiser in the ensemble. He has arranged many pieces for Icebreaker and produced or co-produced several of Icebreaker's albums, he works as a music copyist. He has a strong interest in politics and is treasurer of the Nicaragua Solidarity Campaign, chair of the West Surrey branch of the Palestinian Solidarity Campaign. Playing flutes, pan-pipes, wind synthesiser and keyboards: Icebreaker, Official Bootleg Graham Fitkin, Mesh, Cud Short Cuts – Breaking the sound Barrier – An Argo Sampler Icebreaker, Terminal Velocity Icebreaker, Trance Century XXI UK A–M Bang on a Can, Industry Icebreaker, Rogue's Gallery Icebreaker, Diderik Wagenaar Icebreaker, Extraction Bang on a Can, Louis Andriessen: Gigantic Dancing Human Machine Icebreaker, Trance Icebreaker, Cranial Pavement Icebreaker, Terminal Velocity Icebreaker, Music with Changing Parts Icebreaker website Icebreaker Apollo website Icebreaker MySpace site West Surrey Palestine Solidarity Campaign Nicaragua Solidarity Campaign

An inquisitor was an official in an Inquisition. An inquisitor is one who "searches out" or "inquires"; some of the more well-known inquisitors throughout history include: Peter of Verona, whose canonization was the fastest in history Pedro de Arbués Nicolau Aymerich author of Directorium Inquisitorum Stephen of Bourbon Arnaut Catalan Fabio Chigi Diego Deza Bernard Gui Hentenius Heinrich Institoris, author of Malleus Maleficarum Francisco Jimenez de Cisneros Konrad von Marburg Sebastien Michaelis Giovanni Pietro Carafa Jacob Sprenger, purported co-author of Malleus Maleficarum Tomás de Torquemada Martín García Ceniceros Grand Inquisitor Medieval Inquisition Spanish Inquisition Portuguese Inquisition Roman Inquisition Mexican Inquisition Inquisitorial system, a type of legal system