Simple harmonic motion

simple harmonic oscillatorharmonic motionharmonic
:where : Since ω = 2πf,: and, since where T is the time period, : These equations demonstrate that the simple harmonic motion is isochronous (the period and frequency are independent of the amplitude and the initial phase of the motion). Substituting ω 2 with k⁄m, the kinetic energy K of the system at time t is :and the potential energy is :In the absence of friction and other energy loss, the total mechanical energy has a constant value : The following physical systems are some examples of simple harmonic oscillator. A mass m attached to a spring of spring constant k exhibits simple harmonic motion in closed space.


Wetwet clutchdry clutch
Creed developed a single-turn spring clutch (see above) that was particularly well suited to the repetitive start-stop action required in teleprinters. In 1942, two employees of Pitney Bowes Postage Meter Company developed an improved single turn spring clutch. In these clutches, a coil spring is wrapped around the driven shaft and held in an expanded configuration by the trip lever. When tripped, the spring rapidly contracts around the power shaft engaging the clutch. At the end of one revolution, if the trip lever has been reset, it catches the end of the spring (or a pawl attached to it) and the angular momentum of the driven member releases the tension on the spring.

Torsion bar suspension

torsion bartorsion-bartorsion bars
A disadvantage of the torsion bar suspension used in Tiger and Panther tanks (and many other WWII-era tanks and other AFV s) was the inability to incorporate an escape hatch through the bottom of the hull, a common feature of WWII-era tanks, as the torsion bar arrangement would have blocked crew access to such a hatch; however, the absence of leaf, coil or volute springs often left a large expanse of the side of the hull clear to include a side-escape hatch, and it was rare for a tank to be flipped over in such a way that all top-side hatches were unable to open, which is the purpose of ventral hatches.


pendulumssimple pendulumpendula
"Lissajous pendulum") • Kapitza's pendulum • Kater's pendulum • Metronome • N-pendulum • Pendulum (mathematics) • Pendulum clock • Pendulum rocket fallacy • Quantum pendulum • Seconds pendulum • Simple harmonic motion • Spherical pendulum • Spring pendulum • Torsional pendulum The value of g reflected by the period of a pendulum varies from place to place. The gravitational force varies with distance from the center of the Earth, i.e. with altitude - or because the Earth's shape is oblate, g varies with latitude.

History of watches

lever escapement
However, the mainspring introduced a source of error not present in weight-powered clocks. The force provided by a spring is not constant, but decreases as the spring unwinds. The rate of all timekeeping mechanisms is affected by changes in their drive force, but the primitive verge and foliot mechanism was especially sensitive to these changes, so early watches slowed down during their running period as the mainspring ran down. This problem, called lack of isochronism, plagued mechanical watches throughout their history. Efforts to improve the accuracy of watches prior to 1657 focused on evening out the steep torque curve of the mainspring.

History of timekeeping devices

timekeepinghistory of timekeepingtiming
The invention of the mainspring in the early 15th century allowed portable clocks to be built, evolving into the first pocketwatches by the 17th century, but these were not very accurate until the balance spring was added to the balance wheel in the mid 17th century. Some dispute remains as to whether British scientist Robert Hooke (his was a straight spring) or Dutch scientist Christiaan Huygens was the actual inventor of the balance spring. Huygens was clearly the first to use a spiral balance spring, the form used in virtually all watches to the present day.

Skeleton clock

Skeleton Timepiece
It is considered to be a showcase design and intentionally exposes to plain view the various gears, wheels and springs within the movement itself. There is no official definition of a skeleton clock per se, but a major portion of the main parts of the timepiece should be openly visible from the front of the clock and most often from the back as well in order for it to be considered and accepted as a skeleton clock. The parts most commonly showcased by a skeleton design are those exhibiting either the most movement or the most attractive design. These may include, but are not limited to the escapement, balance wheel and balance spring, mainspring, and tourbillon.

Balanced-arm lamp

Balanced arm lamps
Some lamps have two coil springs working in parallel on both sides of the pivoting arm. (A set of springs functions in the same way as a single spring.) Others are balanced with counterweights (a method frequently used in drawing-boards). Friction between parts of the lamp arm can also be used to maintain balance. There are a number of mechanical solutions (coupling, hydraulics and pneumatic arms) which have occasionally been used for balanced-arm lamps. There are many variations of construction with springs. Springs can be located on the mechanical equivalent of the forearm or the upper arm, or both, as well as nearer the base.

List of English inventions and discoveries

English inventions and discoveries
Most commercial rubber plants are descended from the seeds he took to Kew Gardens. 1884:Thomas Parker claimed to have invented the first electric car. 1885: First commercially successful safety bicycle, "the Rover", developed by John Kemp Starley (1855–1901). 1901: Tarmac patented by Edgar Purnell Hooley (1860–1942). c. 1902: The invention of the Bowden cable popularly attributed to Sir Frank Bowden (1848–1921), founder and owner of the Raleigh Bicycle Company. 1910: Opening of the oldest existing driving school and first formal driving tuition provider, the British School of Motoring, in Peckham, London. 1922: Horstmann suspension, a coil spring suspension system commonly used on western tanks

Index of mechanical engineering articles

List of mechanical engineering topics
spring – Toughness – Tramway track – Transmission – Truck – Truck (railway) – Turbine – Tribology – touch screen – tear – Tire manufacturing-- Understeer – Unibody – Unsprung weight – Verification and Validation – Valve – Vector – Vertical strength – Viscosity – Volt – Vibration – Velocity diagrams – Weapon - Wear – Wedge – Weight transfer – Wheel – Wheel and axle – Wheelset – x bar charts Yield strength – Young's modulus – Zeroth Law of Thermodynamics

Pendulum clock

regulator clockClock pendulumregulator
Anniversary clock (uses a torsion pendulum). Banjo clock. Bracket clock. Cartel clock. Comtoise or Morbier clock. Crystal regulator. Cuckoo clock. Grandfather clock. Lantern clock. Mantel clock. Master clock. Ogee clock. Pillar clock. Schoolhouse regulator. Turret clock. Vienna regulator. Zaandam clock. Pendulum (mathematics). Pendulum. Cycloidal pendulum. Longcase clock (grandfather clock). Steam clock. Balance spring (hairspring). The Invention of Clocks. The (Not So) Simple Pendulum. The earliest Dutch and French Pendulum clocks, 1657-1662.

Sprung floor

sprung dance floorsprungdance floor
Early sprung floors often used leaf or coil springs, whence the name; these floors tended to bounce, but modern floors have suppressed this 'trampoline' effect and so are often called semi-sprung. Other materials have also been used, a notable example is the sprung floor in Danceland, Manitou Beach which was constructed in 1928 using coiled horsehair springs under a maple floor. The earliest references on the web seem to be: Many sprung floors were installed for dance soon after 1900 in places like embassies, hotels, and private clubs. Use of sprung floors exploded with the opening of large public dance halls between 1920 and 1945.

Mechanical watch

mechanicalmechanical watchesmanual winding
When the stem is pushed in, the outer teeth turn the ratchet wheel on top of the mainspring barrel, which turns the shaft that the inner end of the mainspring is attached to, winding the mainspring tighter around the shaft. A spring-loaded pawl or click presses against the ratchet teeth, preventing the mainspring from unwinding. When the stem is pulled out, the inner teeth of the castle wheel engage with a gear which turns the minute wheel. When the crown is turned, the friction coupling of the cannon pinion allows the hands to be rotated.

Verge escapement

verge and foliotfoliotcrown wheel and verge escapement
Verge watches and clocks are sensitive to changes in the drive force; they slow down as the mainspring unwinds. This is called lack of isochronism. It was much worse in verge and foliot clocks due to the lack of a balance spring, but is a problem in all verge movements. In fact, the standard method of adjusting the rate of early verge watches was to alter the force of the mainspring. The cause of this problem is that the crown wheel teeth are always pushing on the pallets, driving the pendulum or balance wheel throughout its cycle; the timekeeping element is never allowed to swing freely.


mattressesinnerspring mattressbed mattress
While the thickness of the mattress may vary greatly depending on method of construction, the American standard sizes for mattresses intended for sleeping come in the following dimensions for the upper surface: Innerspring mattresses commonly consist of just the spring core, and the top and bottom upholstery layers. The core of the mattress supports the sleeper’s body. Modern spring mattress cores, often called "innersprings" are made up of steel coil springs, or "coils". The gauge of the coils is another factor which determines firmness and support. Coils are measured in quarter increments. The lower the number, the thicker the spring.


timerstiming devicesoftware timer
Manual timers are typically set by turning a dial to the time interval desired; turning the dial stores energy in a mainspring to run the mechanism. They function similarly to a mechanical alarm clock; the energy in the mainspring causes a balance wheel to rotate back and forth. Each swing of the wheel releases the gear train to move forward by a small fixed amount, causing the dial to move steadily backward until it reaches zero when a lever arm strikes a bell. The mechanical kitchen timer was invented in 1926 by Thomas Norman Hicks.

Alarm clock

clock radioalarmalarm clocks
Alarm clocks, like almost all other consumer goods in the United States, ceased production in the spring of 1942, as the factories which made them were converted over to war work during World War II, but they were one of the first consumer items to resume manufacture for civilian use, in November 1944. By that time, a critical shortage of alarm clocks had developed due to older clocks wearing out or breaking down. Workers were late for, or missed completely, their scheduled shifts in jobs critical to the war effort.

Marine chronometer

The balance wheel, harnessed to a spring, solved most of the problems associated with the ship's motion. Unfortunately, the elasticity of most balance spring materials changes relative to temperature. To compensate for ever-changing spring strength, the majority of chronometer balances used bi-metallic strips to move small weights toward and away from the centre of oscillation, thus altering the period of the balance to match the changing force of the spring. The balance spring problem was solved with a nickel-steel alloy named Elinvar for its invariable elasticity at normal temperatures.


trampolinesblanket tosstrampoline park
A trampoline is a device consisting of a piece of taut, strong fabric stretched between a steel frame using many coiled springs. People bounce on trampolines for recreational and competitive purposes. The fabric that users bounce on (commonly known as the "bounce mat" or "trampoline bed") is not elastic itself; the elasticity is provided by the springs that connect it to the frame, which store potential energy. A game similar to trampolining was developed by the Inuit, who would toss blanket dancers into the air on a walrus skin one at a time (see Nalukataq) during a spring celebration of whale harvest.


upholstererupholsteredupholstered furniture
Traditional upholstery uses materials like coil springs (post-1850), animal hair (horse, hog and cow), coir, straw and hay, hessians, linen scrims, wadding, etc., and is done by hand, building each layer up. In contrast, today's upholsterers employ synthetic materials like dacron and vinyl, serpentine springs, and so on. Upholder is an archaic term used for "upholsterer", but it appears to have a connotation of repairing furniture rather than creating new upholstered pieces from scratch (cobbler vs. cordwainer). In 18th-century London, upholders frequently served as interior decorators responsible for all aspects of a room's decor.

Buckling spring

A buckling spring is a type of keyswitch mechanism, popularized by IBM's keyboards for the PC, PC/AT, 5250/3270 terminals, PS/2, and other systems. It was used by IBM's Model F keyboards (for instance the AT keyboard), and the more common Model M. It is described in (Model F) and (Model M), both now expired. The name refers to the fact that the coil spring tensed between the keycap and a pivoting hammer buckles, i.e. kinks or collapses, at a certain point in its downward traverse, providing auditory and tactile feedback to the keyboard operator. Upon buckling, the hammer is pivoted forward by the spring and strikes an electrical contact which registers the key press.

Upholstery coil springs

coil springsspringspring cushions
These were helical extension springs also known as "worm" springs due to the spiral nature. in 1762, Richard Tredwell, Great Britain Patent of Rotherham in the County of York, received a patent for a leaf spring for carriages, and, again, in 1763, Richard Tredwell received Great Britain Patent 792 for "Springs For Carriages". There are four pages in this patent and the fourth page clearly shows nine iterations of helical suspension or worm springs and the patent clearly states it is "my new method of making and constructing springs for hanging of coaches". Coil compression springs would not be used for hanging a carriage.


forgedforged steeldrop forging
Press forging works by slowly applying a continuous pressure or force, which differs from the near-instantaneous impact of drop-hammer forging. The amount of time the dies are in contact with the workpiece is measured in seconds (as compared to the milliseconds of drop-hammer forges). The press forging operation can be done either cold or hot. The main advantage of press forging, as compared to drop-hammer forging, is its ability to deform the complete workpiece. Drop-hammer forging usually only deforms the surfaces of the work piece in contact with the hammer and anvil; the interior of the workpiece will stay relatively undeformed.

Mechanically powered flashlight

Faraday flashlightclockwork torchEverLife Flashlight
In an alternative "Clockwork Torch" design, produced by Freeplay Energy, the energy is mechanically stored in a flat spiral wound mainspring, rather than a battery. The owner winds the spring up by turning the crank. Then when the light is turned on, the spring unwinds, turning a generator to provide power to run the light. The purpose of this design, originally invented for use in the developing world, was to improve its reliability and useful lifetime, by avoiding or reducing reliance on a battery., the original design is no longer made, but updated smaller hand-cranked models using LEDs are available.

Beam axle

live axlesolid axlelive rear axle
A beam axle's fore & aft location is constrained by either: trailing arms, semi-trailing arms, radius rods, or leaf springs. The lateral location can be constrained by a Panhard rod, a Scott Russell linkage or a Watt's linkage, or some other arrangement, most commonly by the leaf springs. Shock absorbers and either leaf springs, coil springs, or air bags are used to control vertical movement. The Twist-beam rear suspension is a similar suspension design, however its beam axle is able to twist thereby functioning as an anti-roll bar to control the roll motion of the body and is considered to be a semi-independent suspension design.