In classical mechanics, a harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force F proportional to the displacement x: where k is a positive constant.
A pendulum clock is a clock that uses a pendulum, a swinging weight, as its timekeeping element. The advantage of a pendulum for timekeeping is that it is an approximate harmonic oscillator: It swings back and forth in a precise time interval dependent on its length, and resists swinging at other rates. From its invention in 1656 by Christiaan Huygens, inspired by Galileo Galilei, until the 1930s, the pendulum clock was the world's most precise timekeeper, accounting for its widespread use. Throughout the 18th and 19th centuries, pendulum clocks in homes, factories, offices, and railroad stations served as primary time standards for scheduling daily life, work shifts, and public transportation. Their greater accuracy allowed for the faster pace of life which was necessary for the Industrial Revolution. The home pendulum clock was replaced by less-expensive synchronous electric clocks in the 1930s and 1940s. Pendulum clocks are now kept mostly for their decorative and antique value.
In mechanics and physics, simple harmonic motion is a special type of periodic motion an object experiences by means of a restoring force whose magnitude is directly proportional to the distance of the object from an equilibrium position and acts towards the equilibrium position. It results in an oscillation that is described by a sinusoid which continues indefinitely.
A pendulum is a device made of a weight suspended from a pivot so that it can swing freely. When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the equilibrium position. When released, the restoring force acting on the pendulum's mass causes it to oscillate about the equilibrium position, swinging back and forth. The time for one complete cycle, a left swing and a right swing, is called the period. The period depends on the length of the pendulum and also to a slight degree on the amplitude, the width of the pendulum's swing.
The Foucault pendulum or Foucault's pendulum is a simple device named after French physicist Léon Foucault, conceived as an experiment to demonstrate the Earth's rotation. If a long and heavy pendulum suspended from the high roof above a circular area is monitored over an extended period of time, its plane of oscillation appears to change spontaneously as the Earth makes its 24-hourly rotation.
A Kater's pendulum is a reversible free swinging pendulum invented by British physicist and army captain Henry Kater in 1817, for use as a gravimeter instrument to measure the local acceleration of gravity. Its advantage is that, unlike previous pendulum gravimeters, the pendulum's centre of gravity and center of oscillation do not have to be determined, allowing a greater accuracy. For about a century, until the 1930s, Kater's pendulum and its various refinements remained the standard method for measuring the strength of the Earth's gravity during geodetic surveys. It is now used only for demonstrating pendulum principles.
An escapement is a mechanical linkage in mechanical watches and clocks that gives impulses to the timekeeping element and periodically releases the gear train to move forward, advancing the clock's hands. The impulse action transfers energy to the clock's timekeeping element to replace the energy lost to friction during its cycle and keep the timekeeper oscillating. The escapement is driven by force from a coiled spring or a suspended weight, transmitted through the timepiece's gear train. Each swing of the pendulum or balance wheel releases a tooth of the escapement's escape wheel, allowing the clock's gear train to advance or "escape" by a fixed amount. This regular periodic advancement moves the clock's hands forward at a steady rate. At the same time, the tooth gives the timekeeping element a push, before another tooth catches on the escapement's pallet, returning the escapement to its "locked" state. The sudden stopping of the escapement's tooth is what generates the characteristic "ticking" sound heard in operating mechanical clocks and watches.
A swing is a seat or platform, suspended from chains, ropes, or bars, on which one or more people can swing back and forth for enjoyment or relaxation. Swings are a common piece of equipment at children's playgrounds and may also be found in yards or gardens, on porches, inside homes, or as freestanding public play equipment like the Estonian village swing. Swings have a long history in many different parts of the world and come in various types.
In physics, complex harmonic motion is a complicated realm based on the simple harmonic motion. The word "complex" refers to different situations. Unlike simple harmonic motion, which is regardless of air resistance, friction, etc., complex harmonic motion often has additional forces to dissipate the initial energy and lessen the speed and amplitude of an oscillation until the energy of the system is totally drained and the system comes to rest at its equilibrium point.
In horology, the anchor escapement is a type of escapement used in pendulum clocks. The escapement is a mechanism in a mechanical clock that maintains the swing of the pendulum by giving it a small push each swing, and allows the clock's wheels to advance a fixed amount with each swing, moving the clock's hands forward. The anchor escapement was so named because one of its principal parts is shaped vaguely like a ship's anchor.
In automotive engineering, an exhaust manifold collects the exhaust gases from multiple cylinders into one pipe. The word manifold comes from the Old English word manigfeald and refers to the folding together of multiple inputs and outputs.
Newton's cradle is a device, usually made of metal, that demonstrates the principles of conservation of momentum and conservation of energy in physics with swinging spheres. When one sphere at the end is lifted and released, it strikes the stationary spheres, compressing them and thereby transmitting a pressure wave through the stationary spheres, which creates a force that pushes the last sphere upward. The last sphere swings back and strikes the stationary spheres, repeating the effect in the opposite direction. The device is named after 17th-century English scientist Sir Isaac Newton and was designed by French scientist Edme Mariotte. It is also known as Newton's pendulum, Newton's balls, Newton's rocker or executive ball clicker.
In mathematics, a linear approximation is an approximation of a general function using a linear function. They are widely used in the method of finite differences to produce first order methods for solving or approximating solutions to equations.
Diamond-like carbon (DLC) is a class of amorphous carbon material that displays some of the typical properties of diamond. DLC is usually applied as coatings to other materials that could benefit from such properties.
Mechanical resonance is the tendency of a mechanical system to respond at greater amplitude when the frequency of its oscillations matches the system's natural frequency of vibration closer than it does other frequencies. It may cause violent swaying motions and potentially catastrophic failure in improperly constructed structures including bridges, buildings and airplanes. This is a phenomenon known as resonance disaster.
In materials science, hardness is a measure of the resistance to localized plastic deformation, such as an indentation or a scratch (linear), induced mechanically either by pressing or abrasion. In general, different materials differ in their hardness; for example hard metals such as titanium and beryllium are harder than soft metals such as sodium and metallic tin, or wood and common plastics. Macroscopic hardness is generally characterized by strong intermolecular bonds, but the behavior of solid materials under force is complex; therefore, hardness can be measured in different ways, such as scratch hardness, indentation hardness, and rebound hardness. Hardness is dependent on ductility, elastic stiffness, plasticity, strain, strength, toughness, viscoelasticity, and viscosity. Common examples of hard matter are ceramics, concrete, certain metals, and superhard materials, which can be contrasted with soft matter.
A ballistic pendulum is a device for measuring a bullet's momentum, from which it is possible to calculate the velocity and kinetic energy. Ballistic pendulums have been largely rendered obsolete by modern chronographs, which allow direct measurement of the projectile velocity.
A parametric oscillator is a driven harmonic oscillator in which the oscillations are driven by varying some parameters of the system at some frequencies, typically different from the natural frequency of the oscillator. A simple example of a parametric oscillator is a child pumping a playground swing by periodically standing and squatting to increase the size of the swing's oscillations. The child's motions vary the moment of inertia of the swing as a pendulum. The "pump" motions of the child must be at twice the frequency of the swing's oscillations. Examples of parameters that may be varied are the oscillator's resonance frequency and damping .
Ultrasonic machining is a subtractive manufacturing process that removes material from the surface of a part through high frequency, low amplitude vibrations of a tool against the material surface in the presence of fine abrasive particles. The tool travels vertically or orthogonal to the surface of the part at amplitudes of 0.05 to 0.125 mm. The fine abrasive grains are mixed with water to form a slurry that is distributed across the part and the tip of the tool. Typical grain sizes of the abrasive material range from 100 to 1000, where smaller grains produce smoother surface finishes.
Brinelling is the permanent indentation of a hard surface. It is named after the Brinell scale of hardness, in which a small ball is pushed against a hard surface at a preset level of force, and the depth and diameter of the mark indicates the Brinell hardness of the surface. Brinelling is permanent plastic deformation of a surface, and usually occurs while two surfaces in contact are stationary and the material yield strength has been exceeded.
