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:
Oscillation is the repetitive or periodic variation, typically in time, of some measure about a central value or between two or more different states. Familiar examples of oscillation include a swinging pendulum and alternating current. Oscillations can be used in physics to approximate complex interactions, such as those between atoms.
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 '40s. 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 due to 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. A long and heavy pendulum suspended from the high roof above a circular area was monitored over an extended time period, showing that its plane of oscillation rotated.
Asteroseismology is the study of oscillations in stars. Stars have many resonant modes and frequencies, and the path of sound waves passing through a star depends on the speed of sound, which in turn depends on local temperature and chemical composition. Because the resulting oscillation modes are sensitive to different parts of the star, they inform astronomers about the internal structure of the star, which is otherwise not directly possible from overall properties like brightness and surface temperature.
A torsion spring is a spring that works by twisting its end along its axis; that is, a flexible elastic object that stores mechanical energy when it is twisted. When it is twisted, it exerts a torque in the opposite direction, proportional to the amount (angle) it is twisted. There are various types:
Torsional vibration is the angular vibration of an object - commonly a shaft - along its axis of rotation. Torsional vibration is often a concern in power transmission systems using rotating shafts or couplings, where it can cause failures if not controlled. A second effect of torsional vibrations applies to passenger cars. Torsional vibrations can lead to seat vibrations or noise at certain speeds. Both reduce the comfort.
A balance wheel, or balance, is the timekeeping device used in mechanical watches and small clocks, analogous to the pendulum in a pendulum clock. It is a weighted wheel that rotates back and forth, being returned toward its center position by a spiral torsion spring, known as the balance spring or hairspring. It is driven by the escapement, which transforms the rotating motion of the watch gear train into impulses delivered to the balance wheel. Each swing of the wheel allows the gear train to advance a set amount, moving the hands forward. The balance wheel and hairspring together form a harmonic oscillator, which due to resonance oscillates preferentially at a certain rate, its resonant frequency or "beat", and resists oscillating at other rates. The combination of the mass of the balance wheel and the elasticity of the spring keep the time between each oscillation or "tick" very constant, accounting for its nearly universal use as the timekeeper in mechanical watches to the present. From its invention in the 14th century until tuning fork and quartz movements became available in the 1960s, virtually every portable timekeeping device used some form of balance wheel.
The center of percussion is the point on an extended massive object attached to a pivot where a perpendicular impact will produce no reactive shock at the pivot. Translational and rotational motions cancel at the pivot when an impulsive blow is struck at the center of percussion. The center of percussion is often discussed in the context of a bat, racquet, door, sword or other extended object held at one end.
In classical mechanics, anharmonicity is the deviation of a system from being a harmonic oscillator. An oscillator that is not oscillating in harmonic motion is known as an anharmonic oscillator where the system can be approximated to a harmonic oscillator and the anharmonicity can be calculated using perturbation theory. If the anharmonicity is large, then other numerical techniques have to be used. In reality all oscillating systems are anharmonic, but most approximate the harmonic oscillator the smaller the amplitude of the oscillation is.
Rotation around a fixed axis or axial rotation is a special case of rotational motion around an axis of rotation fixed, stationary, or static in three-dimensional space. This type of motion excludes the possibility of the instantaneous axis of rotation changing its orientation and cannot describe such phenomena as wobbling or precession. According to Euler's rotation theorem, simultaneous rotation along a number of stationary axes at the same time is impossible; if two rotations are forced at the same time, a new axis of rotation will result.
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 physics, rotational–vibrational coupling occurs when the rotation frequency of a system is close to or identical to a natural internal vibration frequency. The animation on the right shows ideal motion, with the force exerted by the spring and the distance from the center of rotation increasing together linearly with no friction.
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 torsion pendulum clock, more commonly known as an anniversary clock or 400-day clock, is a mechanical clock which keeps time with a mechanism called a torsion pendulum. This is a weighted disk or wheel, often a decorative wheel with three or four chrome balls on ornate spokes, suspended by a thin wire or ribbon called a torsion spring. The torsion pendulum rotates about the vertical axis of the wire, twisting it, instead of swinging like an ordinary pendulum. The force of the twisting torsion spring reverses the direction of rotation, so the torsion pendulum oscillates slowly, clockwise and counterclockwise. The clock's gears apply a pulse of torque to the top of the torsion spring with each rotation to keep the wheel going. The Atmos Clock made by the Swiss company Jaeger-LeCoultre is another style of this clock. The wheel and torsion spring function similarly to a watch's balance wheel and hairspring, as a harmonic oscillator to control the rate of the clock's hands.
An electric clock is a clock that is powered by electricity, as opposed to a mechanical clock which is powered by a hanging weight or a mainspring. The term is often applied to the electrically powered mechanical clocks that were used before quartz clocks were introduced in the 1980s. The first experimental electric clocks were constructed around the 1840s, but they were not widely manufactured until mains electric power became available in the 1890s. In the 1930s, the synchronous electric clock replaced mechanical clocks as the most widely used type of clock.
Vibration is a mechanical phenomenon whereby oscillations occur about an equilibrium point. Vibration may be deterministic if the oscillations can be characterised precisely, or random if the oscillations can only be analysed statistically.
Doubochinski's pendulum is a classical oscillator interacting with a high-frequency field in such a way that the oscillator takes on a discrete set of stable regimes of oscillation, each at a frequency near to the proper frequency of the oscillator, but each with a distinct, "quantized" amplitude. The phenomenon of amplitude quantization in this sort of coupled system was first discovered by the brothers Danil and Yakov Doubochinski in 1968–69.
