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Harmonic oscillator

Index Harmonic oscillator

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. [1]

81 relations: Acceleration, Acoustics, Ajoy Ghatak, Alternating current, Amplitude, Angular frequency, Angular velocity, Anharmonicity, Capacitance, Capacitor, Charge (physics), Classical mechanics, Clock, Coefficient, Complex analysis, Conservative force, Constant term, Critical speed, Damping ratio, Differential equation, Drag (physics), Effective mass (spring–mass system), Elastance, Electric current, Electrical resistance and conductance, Exponential decay, Flux linkage, Force, Frequency, Frequency response, Gravity, Hooke's law, Inductance, Inductor, Instability, Kinetic energy, Laser, Linear response function, Magnetic reluctance, Mass, Mechanical equilibrium, Mechanical impedance, Moment of inertia, Newton's laws of motion, Nondimensionalization, Normal mode, Optical parametric oscillator, Ordinary differential equation, Oscillation, Parametric oscillator, ..., Pendulum, Periodic function, Phase (waves), Phasor, Potential energy, Proportionality (mathematics), Q factor, Quantum harmonic oscillator, Quantum mechanics, Relaxation (physics), Resonance, Restoring force, RLC circuit, Simple harmonic motion, Sine, Sine wave, Spring (device), Spring pendulum, Steady state, Stiff equation, Superposition principle, Swing (seat), Taylor series, The Feynman Lectures on Physics, Torque, Transient (oscillation), Varicap, Velocity, Voltage, Waveguide (electromagnetism), Yttrium aluminium garnet. Expand index (31 more) »


In physics, acceleration is the rate of change of velocity of an object with respect to time.

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Acoustics is the branch of physics that deals with the study of all mechanical waves in gases, liquids, and solids including topics such as vibration, sound, ultrasound and infrasound.

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Ajoy Ghatak

Ajoy Ghatak is an Indian physicist and author of physics textbooks.

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Alternating current

Alternating current (AC) is an electric current which periodically reverses direction, in contrast to direct current (DC) which flows only in one direction.

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The amplitude of a periodic variable is a measure of its change over a single period (such as time or spatial period).

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Angular frequency

In physics, angular frequency ω (also referred to by the terms angular speed, radial frequency, circular frequency, orbital frequency, radian frequency, and pulsatance) is a scalar measure of rotation rate.

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Angular velocity

In physics, the angular velocity of a particle is the rate at which it rotates around a chosen center point: that is, the time rate of change of its angular displacement relative to the origin.

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In classical mechanics, anharmonicity is the deviation of a system from being a harmonic oscillator.

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Capacitance is the ratio of the change in an electric charge in a system to the corresponding change in its electric potential.

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A capacitor is a passive two-terminal electrical component that stores potential energy in an electric field.

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Charge (physics)

In physics, a charge may refer to one of many different quantities, such as the electric charge in electromagnetism or the color charge in quantum chromodynamics.

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Classical mechanics

Classical mechanics describes the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars and galaxies.

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A clock is an instrument to measure, keep, and indicate time.

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In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series or any expression; it is usually a number, but may be any expression.

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Complex analysis

Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers.

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Conservative force

A conservative force is a force with the property that the total work done in moving a particle between two points is independent of the taken path.

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Constant term

In mathematics, a constant term is a term in an algebraic expression that has a value that is constant or cannot change, because it does not contain any modifiable variables.

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Critical speed

In solid mechanics, in the field of rotordynamics, the critical speed is the theoretical angular velocity that excites the natural frequency of a rotating object, such as a shaft, propeller, leadscrew, or gear.

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Damping ratio

Damping is an influence within or upon an oscillatory system that has the effect of reducing, restricting or preventing its oscillations.

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Differential equation

A differential equation is a mathematical equation that relates some function with its derivatives.

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Drag (physics)

In fluid dynamics, drag (sometimes called air resistance, a type of friction, or fluid resistance, another type of friction or fluid friction) is a force acting opposite to the relative motion of any object moving with respect to a surrounding fluid.

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Effective mass (spring–mass system)

In a real spring–mass system, the spring has a non-negligible mass m. Since not all of the spring's length moves at the same velocity v as the suspended mass M, its kinetic energy is not equal to \frac m v^2.

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Electrical elastance is the inverse of capacitance.

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Electric current

An electric current is a flow of electric charge.

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Electrical resistance and conductance

The electrical resistance of an electrical conductor is a measure of the difficulty to pass an electric current through that conductor.

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Exponential decay

A quantity is subject to exponential decay if it decreases at a rate proportional to its current value.

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Flux linkage

In circuit theory, flux linkage is a property of a two-terminal element.

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In physics, a force is any interaction that, when unopposed, will change the motion of an object.

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Frequency is the number of occurrences of a repeating event per unit of time.

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Frequency response

Frequency response is the quantitative measure of the output spectrum of a system or device in response to a stimulus, and is used to characterize the dynamics of the system.

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Gravity, or gravitation, is a natural phenomenon by which all things with mass or energy—including planets, stars, galaxies, and even light—are brought toward (or gravitate toward) one another.

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Hooke's law

Hooke's law is a principle of physics that states that the force needed to extend or compress a spring by some distance scales linearly with respect to that distance.

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In electromagnetism and electronics, inductance is the property of an electrical conductor by which a change in electric current through it induces an electromotive force (voltage) in the conductor.

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An inductor, also called a coil, choke or reactor, is a passive two-terminal electrical component that stores energy in a magnetic field when electric current flows through it.

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In numerous fields of study, the component of instability within a system is generally characterized by some of the outputs or internal states growing without bounds.

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Kinetic energy

In physics, the kinetic energy of an object is the energy that it possesses due to its motion.

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A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation.

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Linear response function

A linear response function describes the input-output relationship of a signal transducer such as a radio turning electromagnetic waves into music or a neuron turning synaptic input into a response.

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Magnetic reluctance

Magnetic reluctance, or magnetic resistance, is a concept used in the analysis of magnetic circuits.

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Mass is both a property of a physical body and a measure of its resistance to acceleration (a change in its state of motion) when a net force is applied.

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Mechanical equilibrium

In classical mechanics, a particle is in mechanical equilibrium if the net force on that particle is zero.

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Mechanical impedance

Mechanical impedance is a measure of how much a structure resists motion when subjected to a harmonic force.

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Moment of inertia

The moment of inertia, otherwise known as the angular mass or rotational inertia, of a rigid body is a tensor that determines the torque needed for a desired angular acceleration about a rotational axis; similar to how mass determines the force needed for a desired acceleration.

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Newton's laws of motion

Newton's laws of motion are three physical laws that, together, laid the foundation for classical mechanics.

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Nondimensionalization is the partial or full removal of units from an equation involving physical quantities by a suitable substitution of variables.

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Normal mode

A normal mode of an oscillating system is a pattern of motion in which all parts of the system move sinusoidally with the same frequency and with a fixed phase relation.

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Optical parametric oscillator

An optical parametric oscillator (OPO) is a parametric oscillator that oscillates at optical frequencies.

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Ordinary differential equation

In mathematics, an ordinary differential equation (ODE) is a differential equation containing one or more functions of one independent variable and its derivatives.

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Oscillation is the repetitive variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states.

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Parametric oscillator

A parametric oscillator is a driven harmonic oscillator in which the oscillations are driven by varying some parameter of the system at some frequency, typically different from the natural frequency of the oscillator.

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A pendulum is a weight suspended from a pivot so that it can swing freely.

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Periodic function

In mathematics, a periodic function is a function that repeats its values in regular intervals or periods.

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Phase (waves)

Phase is the position of a point in time (an instant) on a waveform cycle.

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In physics and engineering, a phasor (a portmanteau of phase vector), is a complex number representing a sinusoidal function whose amplitude (A), angular frequency (ω), and initial phase (θ) are time-invariant.

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Potential energy

In physics, potential energy is the energy possessed by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors.

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Proportionality (mathematics)

In mathematics, two variables are proportional if there is always a constant ratio between them.

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Q factor

In physics and engineering the quality factor or Q factor is a dimensionless parameter that describes how underdamped an oscillator or resonator is, and characterizes a resonator's bandwidth relative to its centre frequency.

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Quantum harmonic oscillator

The quantum harmonic oscillator is the quantum-mechanical analog of the classical harmonic oscillator.

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Quantum mechanics

Quantum mechanics (QM; also known as quantum physics, quantum theory, the wave mechanical model, or matrix mechanics), including quantum field theory, is a fundamental theory in physics which describes nature at the smallest scales of energy levels of atoms and subatomic particles.

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Relaxation (physics)

In the physical sciences, relaxation usually means the return of a perturbed system into equilibrium.

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In physics, resonance is a phenomenon in which a vibrating system or external force drives another system to oscillate with greater amplitude at specific frequencies.

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Restoring force

Restoring force, in a physics context, is a force that gives rise to an equilibrium in a physical system.

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RLC circuit

An RLC circuit is an electrical circuit consisting of a resistor (R), an inductor (L), and a capacitor (C), connected in series or in parallel.

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Simple harmonic motion

In mechanics and physics, simple harmonic motion is a special type of periodic motion or oscillation motion where the restoring force is directly proportional to the displacement and acts in the direction opposite to that of displacement.

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In mathematics, the sine is a trigonometric function of an angle.

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Sine wave

A sine wave or sinusoid is a mathematical curve that describes a smooth periodic oscillation.

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Spring (device)

A spring is an elastic object that stores mechanical energy.

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Spring pendulum

A spring pendulum (also called elastic pendulum or swinging spring) is a physical system where a piece of mass is connected to a spring so that the resulting motion contains elements of a simple pendulum as well as a spring.

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Steady state

In systems theory, a system or a process is in a steady state if the variables (called state variables) which define the behavior of the system or the process are unchanging in time.

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Stiff equation

In mathematics, a stiff equation is a differential equation for which certain numerical methods for solving the equation are numerically unstable, unless the step size is taken to be extremely small.

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Superposition principle

In physics and systems theory, the superposition principle, also known as superposition property, states that, for all linear systems, the net response caused by two or more stimuli is the sum of the responses that would have been caused by each stimulus individually.

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Swing (seat)

A swing is a hanging seat, often found at playgrounds for children, at a circus for acrobats, or on a porch for relaxing, although they may also be items of indoor furniture, such as Latin American hammock or the Indian oonjal.

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Taylor series

In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point.

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The Feynman Lectures on Physics

The Feynman Lectures on Physics is a physics textbook based on some lectures by Richard P. Feynman, a Nobel laureate who has sometimes been called "The Great Explainer".

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Torque, moment, or moment of force is rotational force.

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Transient (oscillation)

A transient event is a short-lived burst of energy in a system caused by a sudden change of state.

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In electronics, a varicap diode, varactor diode, variable capacitance diode, variable reactance diode or tuning diode is a type of diode designed to exploit the voltage-dependent capacitance of a reversed-biased p–n junction.

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The velocity of an object is the rate of change of its position with respect to a frame of reference, and is a function of time.

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Voltage, electric potential difference, electric pressure or electric tension (formally denoted or, but more often simply as V or U, for instance in the context of Ohm's or Kirchhoff's circuit laws) is the difference in electric potential between two points.

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Waveguide (electromagnetism)

In electromagnetics and communications engineering, the term waveguide may refer to any linear structure that conveys electromagnetic waves between its endpoints.

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Yttrium aluminium garnet

Yttrium aluminium garnet (YAG, Y3Al5O12) is a synthetic crystalline material of the garnet group.

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[1] https://en.wikipedia.org/wiki/Harmonic_oscillator

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