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Simple harmonic motion

Index Simple harmonic motion

In mechanics and physics, simple harmonic motion (sometimes abbreviated) 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. [1]

Table of Contents

  1. 61 relations: Acceleration, Amplitude, Angular acceleration, Angular frequency, Calculus, Circle group, Circular motion, Closed manifold, Complex harmonic motion, Damping, Differential equation, Displacement (geometry), Dissipation, Elasticity (physics), Energy, Exertion, Fixed point (mathematics), Force, Fourier analysis, Frequency, Friction, Harmonic oscillator, Hertz, Hooke's law, HyperPhysics, International System of Units, Isochronous timing, Kinetic energy, Mass, Mathematical model, Mechanical energy, Mechanical equilibrium, Mechanics, Molecular vibration, Moment of inertia, Momentum, Motion, Net force, Newton (unit), Newton's laws of motion, Ordinary differential equation, Origin (mathematics), Oscillation, Particle, Pendulum, Pendulum (mechanics), Periodic function, Phase (waves), Phase space, Physics, ... Expand index (11 more) »

  2. Motion (physics)
  3. Pendulums

Acceleration

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

See Simple harmonic motion and Acceleration

Amplitude

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

See Simple harmonic motion and Amplitude

Angular acceleration

In physics, angular acceleration (symbol α, alpha) is the time rate of change of angular velocity.

See Simple harmonic motion and Angular acceleration

Angular frequency

In physics, angular frequency (symbol ω), also called angular speed and angular rate, is a scalar measure of the angle rate (the angle per unit time) or the temporal rate of change of the phase argument of a sinusoidal waveform or sine function (for example, in oscillations and waves).

See Simple harmonic motion and Angular frequency

Calculus

Calculus is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations.

See Simple harmonic motion and Calculus

Circle group

In mathematics, the circle group, denoted by \mathbb T or, is the multiplicative group of all complex numbers with absolute value 1, that is, the unit circle in the complex plane or simply the unit complex numbers \mathbb T.

See Simple harmonic motion and Circle group

Circular motion

In physics, circular motion is a movement of an object along the circumference of a circle or rotation along a circular arc. Simple harmonic motion and circular motion are classical mechanics and motion (physics).

See Simple harmonic motion and Circular motion

Closed manifold

In mathematics, a closed manifold is a manifold without boundary that is compact.

See Simple harmonic motion and Closed manifold

Complex harmonic motion

In physics, complex harmonic motion is a complicated realm based on the simple harmonic motion. Simple harmonic motion and complex harmonic motion are classical mechanics and motion (physics).

See Simple harmonic motion and Complex harmonic motion

Damping

In physical systems, damping is the loss of energy of an oscillating system by dissipation. Simple harmonic motion and damping are classical mechanics.

See Simple harmonic motion and Damping

Differential equation

In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives.

See Simple harmonic motion and Differential equation

Displacement (geometry)

In geometry and mechanics, a displacement is a vector whose length is the shortest distance from the initial to the final position of a point P undergoing motion. Simple harmonic motion and displacement (geometry) are motion (physics).

See Simple harmonic motion and Displacement (geometry)

Dissipation

In thermodynamics, dissipation is the result of an irreversible process that affects a thermodynamic system.

See Simple harmonic motion and Dissipation

Elasticity (physics)

In physics and materials science, elasticity is the ability of a body to resist a distorting influence and to return to its original size and shape when that influence or force is removed.

See Simple harmonic motion and Elasticity (physics)

Energy

Energy is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat and light.

See Simple harmonic motion and Energy

Exertion

Exertion is the physical or perceived use of energy.

See Simple harmonic motion and Exertion

Fixed point (mathematics)

In mathematics, a fixed point (sometimes shortened to fixpoint), also known as an invariant point, is a value that does not change under a given transformation.

See Simple harmonic motion and Fixed point (mathematics)

Force

A force is an influence that can cause an object to change its velocity, i.e., to accelerate, meaning a change in speed or direction, unless counterbalanced by other forces. Simple harmonic motion and force are classical mechanics.

See Simple harmonic motion and Force

Fourier analysis

In mathematics, Fourier analysis is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions.

See Simple harmonic motion and Fourier analysis

Frequency

Frequency (symbol f), most often measured in hertz (symbol: Hz), is the number of occurrences of a repeating event per unit of time.

See Simple harmonic motion and Frequency

Friction

Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. Simple harmonic motion and Friction are classical mechanics.

See Simple harmonic motion and Friction

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: \vec F.

See Simple harmonic motion and Harmonic oscillator

Hertz

The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), equivalent to one event (or cycle) per second.

See Simple harmonic motion and Hertz

Hooke's law

In physics, Hooke's law is an empirical law which states that the force needed to extend or compress a spring by some distance scales linearly with respect to that distance—that is, where is a constant factor characteristic of the spring (i.e., its stiffness), and is small compared to the total possible deformation of the spring.

See Simple harmonic motion and Hooke's law

HyperPhysics

HyperPhysics is an educational website about physics topics.

See Simple harmonic motion and HyperPhysics

International System of Units

The International System of Units, internationally known by the abbreviation SI (from French Système international d'unités), is the modern form of the metric system and the world's most widely used system of measurement.

See Simple harmonic motion and International System of Units

Isochronous timing

A sequence of events is isochronous if the events occur regularly, or at equal time intervals.

See Simple harmonic motion and Isochronous timing

Kinetic energy

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

See Simple harmonic motion and Kinetic energy

Mass

Mass is an intrinsic property of a body.

See Simple harmonic motion and Mass

Mathematical model

A mathematical model is an abstract description of a concrete system using mathematical concepts and language.

See Simple harmonic motion and Mathematical model

Mechanical energy

In physical sciences, mechanical energy is the sum of potential energy and kinetic energy.

See Simple harmonic motion and Mechanical energy

Mechanical equilibrium

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

See Simple harmonic motion and Mechanical equilibrium

Mechanics

Mechanics (from Ancient Greek: μηχανική, mēkhanikḗ, "of machines") is the area of physics concerned with the relationships between force, matter, and motion among physical objects.

See Simple harmonic motion and Mechanics

Molecular vibration

A molecular vibration is a periodic motion of the atoms of a molecule relative to each other, such that the center of mass of the molecule remains unchanged.

See Simple harmonic motion and Molecular vibration

Moment of inertia

The moment of inertia, otherwise known as the mass moment of inertia, angular/rotational mass, second moment of mass, or most accurately, rotational inertia, of a rigid body is a quantity that determines the torque needed for a desired angular acceleration about a rotational axis, akin to how mass determines the force needed for a desired acceleration.

See Simple harmonic motion and Moment of inertia

Momentum

In Newtonian mechanics, momentum (momenta or momentums; more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. Simple harmonic motion and momentum are motion (physics).

See Simple harmonic motion and Momentum

Motion

In physics, motion is when an object changes its position with respect to a reference point in a given time. Simple harmonic motion and motion are motion (physics).

See Simple harmonic motion and Motion

Net force

In mechanics, the net force is the sum of all the forces acting on an object.

See Simple harmonic motion and Net force

Newton (unit)

The newton (symbol: N) is the unit of force in the International System of Units (SI).

See Simple harmonic motion and Newton (unit)

Newton's laws of motion

Newton's laws of motion are three physical laws that describe the relationship between the motion of an object and the forces acting on it. Simple harmonic motion and Newton's laws of motion are classical mechanics.

See Simple harmonic motion and Newton's laws of motion

Ordinary differential equation

In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable.

See Simple harmonic motion and Ordinary differential equation

Origin (mathematics)

In mathematics, the origin of a Euclidean space is a special point, usually denoted by the letter O, used as a fixed point of reference for the geometry of the surrounding space.

See Simple harmonic motion and Origin (mathematics)

Oscillation

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

See Simple harmonic motion and Oscillation

Particle

In the physical sciences, a particle (or corpuscule in older texts) is a small localized object which can be described by several physical or chemical properties, such as volume, density, or mass.

See Simple harmonic motion and Particle

Pendulum

A pendulum is a device made of a weight suspended from a pivot so that it can swing freely. Simple harmonic motion and pendulum are pendulums.

See Simple harmonic motion and Pendulum

Pendulum (mechanics)

A pendulum is a body suspended from a fixed support such that it freely swings back and forth under the influence of gravity. Simple harmonic motion and pendulum (mechanics) are pendulums.

See Simple harmonic motion and Pendulum (mechanics)

Periodic function

A periodic function or cyclic function, also called a periodic waveform (or simply periodic wave), is a function that repeats its values at regular intervals or periods.

See Simple harmonic motion and Periodic function

Phase (waves)

In physics and mathematics, the phase (symbol φ or ϕ) of a wave or other periodic function F of some real variable t (such as time) is an angle-like quantity representing the fraction of the cycle covered up to t. It is expressed in such a scale that it varies by one full turn as the variable t goes through each period (and F(t) goes through each complete cycle).

See Simple harmonic motion and Phase (waves)

Phase space

In dynamical systems theory and control theory, a phase space or state space is a space in which all possible "states" of a dynamical system or a control system are represented, with each possible state corresponding to one unique point in the phase space.

See Simple harmonic motion and Phase space

Physics

Physics is the natural science of matter, involving the study of matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force.

See Simple harmonic motion and Physics

Potential energy

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

See Simple harmonic motion and Potential energy

Projection (mathematics)

In mathematics, a projection is an idempotent mapping of a set (or other mathematical structure) into a subset (or sub-structure).

See Simple harmonic motion and Projection (mathematics)

Proportionality (mathematics)

In mathematics, two sequences of numbers, often experimental data, are proportional or directly proportional if their corresponding elements have a constant ratio.

See Simple harmonic motion and Proportionality (mathematics)

Rayleigh–Lorentz pendulum

Rayleigh–Lorentz pendulum (or Lorentz pendulum) is a simple pendulum, but subjected to a slowly varying frequency due to an external action (frequency is varied by varying the pendulum length), named after Lord Rayleigh and Hendrik Lorentz. Simple harmonic motion and Rayleigh–Lorentz pendulum are classical mechanics.

See Simple harmonic motion and Rayleigh–Lorentz pendulum

Resonance

In physics, resonance refers to a wide class of phenomena that arise as a result of matching temporal or spatial periods of oscillatory objects.

See Simple harmonic motion and Resonance

Restoring force

In physics, the restoring force is a force that acts to bring a body to its equilibrium position.

See Simple harmonic motion and Restoring force

Sine wave

A sine wave, sinusoidal wave, or sinusoid (symbol: ∿) is a periodic wave whose waveform (shape) is the trigonometric sine function.

See Simple harmonic motion and Sine wave

Small-angle approximation

The small-angle approximations can be used to approximate the values of the main trigonometric functions, provided that the angle in question is small and is measured in radians: \begin \sin \theta &\approx \theta \\ \cos \theta &\approx 1 - \frac \approx 1\\ \tan \theta &\approx \theta \end These approximations have a wide range of uses in branches of physics and engineering, including mechanics, electromagnetism, optics, cartography, astronomy, and computer science.

See Simple harmonic motion and Small-angle approximation

Spring (device)

A spring is a device consisting of an elastic but largely rigid material (typically metal) bent or molded into a form (especially a coil) that can return into shape after being compressed or extended.

See Simple harmonic motion and Spring (device)

String vibration

A vibration in a string is a wave.

See Simple harmonic motion and String vibration

Velocity

Velocity is the speed in combination with the direction of motion of an object. Simple harmonic motion and Velocity are motion (physics).

See Simple harmonic motion and Velocity

See also

Motion (physics)

Pendulums

References

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

Also known as Mass on a spring, Oscillating spring, Simple Harmonic Oscillator.

, Potential energy, Projection (mathematics), Proportionality (mathematics), Rayleigh–Lorentz pendulum, Resonance, Restoring force, Sine wave, Small-angle approximation, Spring (device), String vibration, Velocity.