**A physical system in which a value oscillates above and below a mean value at one or more characteristic frequencies**. Such systems often arise when an opposing force resulting from a displacement from a force-neutral position becomes stronger in proportion to the amount of displacement.

Contents

- Why is it called harmonic oscillation?
- What is harmonic oscillation Class 11?
- What is harmonic oscillation and non harmonic oscillation?
- What is harmonic oscillator in chemistry?
- What is simple harmonic oscillation give an example?
- What is harmonic motion class 12?
- What is harmonic function in physics class 11?
- What is called simple harmonic motion?
- Why harmonic oscillator is important?
- How do you find the period of a harmonic oscillator?
- What is the difference between harmonic motion and simple harmonic motion?
- What is harmonic oscillator in quantum physics?
- What is harmonic oscillator in classical mechanics?
- Why is harmonic oscillator important in quantum mechanics?

It’s called “harmonic” **because the solution to Newton’s second law (a second-order differential equation that governs the motion of the object) is sine and cosine of time at a specific frequency** – just like the result produced by a pure musical tone heard at a specific point in space.

Simple Harmonic Motion (SHM) is **a periodic rotation around the mean position of the body, moving back and forth**. The restoring force on the oscillating body is directly proportional to its deflection and is therefore based on its mean direction.

**Harmonic oscillation is that oscillation which can be expressed in terms of a single harmonic function, ie sine or cosine function**. Example: y = a sin ωt or y = a cos ωt. An inharmonic oscillation is an oscillation that cannot be expressed in terms of a single harmonic function. Example: y = a sin ωt + b sin 2 ωt.

The harmonic oscillator is extremely useful in chemistry as a **model for the vibrational motion in a diatomic molecule**. Polyatomic molecules can be modeled by coupled harmonic oscillators. The atoms are considered as point masses connected by bonds that act (roughly) like springs that obey Hooke’s law.

Simple Harmonic Motion (S.H.M.)

For example, have you seen a pendulum? When we swing it, it moves back and forth along the same line. These movements are vibrations. **Swinging of a pendulum** is an example of a simple harmonic movement. Now imagine there is a spring attached to one end.

**A type of motion in which an object repeats its path at a regular time interval** is called harmonic motion.

**Any real function with continuous second partial derivatives that satisfies Lallace’s equation**. is called a harmonic function.

Simple harmonic motion, in physics, repeated motion back and forth through an equilibrium or central position such that the maximum displacement on one side of that position is equal to the maximum displacement on the other side. The time interval of each complete oscillation is the same.

The harmonic oscillator is important because **it is an approximate solution for almost any system with a minimum of potential energy**. this is the harmonic oscillator potential for small oscillations around x0.

Step 1: Identify the argument of the cosine function in the simple harmonic equation. Step 2: Find the number multiplied by t . This is the angular frequency of simple harmonic motion. Step 3: Find the period by substituting the angular frequency found in step 2 into the equation **T=2πω T = 2 π ω** .

**Harmonic motion would be simply any motion that is periodic**. For example, a motion that follows some sort of square wave would be harmonic. Simple harmonic motion is motion that is specifically sinusoidal; that is, it can be described by a sine wave.

The harmonic oscillator is one of the most important model systems in quantum mechanics. A. harmonic oscillator is **a particle that is subject to a restoring force that is proportional to the displacement**. **the particle**.

In physics, a harmonic oscillator often appears as **a simple model for many different types of phenomena**. The simplest physical realization of a harmonic oscillator consists of a mass m acting on a force that linearly shifts out of equilibrium.

The harmonic quantum oscillator is the quantum mechanical analogue of the classical harmonic oscillator. **Because any smooth potential can usually be approximated as a harmonic potential near a stable equilibrium point**, it is one of the most important model systems in quantum mechanics.

- https://www.compadre.org/nexusph/course/Overview_Motivating_the_harmonic_oscillator
- https://byjus.com/jee-questions/what-is-shm-in-physics-class-11/
- https://www.doubtnut.com/pcmb-questions/difference-between-harmonic-and-non-harmonic-oscillation-182666
- http://vergil.chemistry.gatech.edu/notes/ho/ho.pdf
- https://www.toppr.com/guides/physics/oscillations/simple-harmonic-motion/
- https://physicswithaj.com/shm-notes-class-12/
- https://www.topperlearning.com/answer/what-is-a-harmonic-function/r8697oll
- https://www.britannica.com/science/simple-harmonic-motion
- https://physics.stackexchange.com/questions/159021/why-is-the-harmonic-oscillator-so-important
- https://study.com/skill/learn/how-to-calculate-the-period-of-simple-harmonic-motion-explanation.html
- https://physics.stackexchange.com/questions/325349/difference-between-harmonic-motion-and-simple-harmonic-motion
- https://www.bu.edu/quantum/notes/QuantumMechanics/HarmonicOscillator.pdf
- https://www.tau.ac.il/~tsirel/dump/Static/knowino.org/wiki/Harmonic_oscillator_(classical).html
- https://en.wikipedia.org/wiki/Quantum_harmonic_oscillator

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