# What is Harmonic oscillator: Definition and 741 Discussions

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:

F

=

k

x

,

{\displaystyle {\vec {F}}=-k{\vec {x}},}
where k is a positive constant.
If F is the only force acting on the system, the system is called a simple harmonic oscillator, and it undergoes simple harmonic motion: sinusoidal oscillations about the equilibrium point, with a constant amplitude and a constant frequency (which does not depend on the amplitude).
If a frictional force (damping) proportional to the velocity is also present, the harmonic oscillator is described as a damped oscillator. Depending on the friction coefficient, the system can:

Oscillate with a frequency lower than in the undamped case, and an amplitude decreasing with time (underdamped oscillator).
Decay to the equilibrium position, without oscillations (overdamped oscillator).The boundary solution between an underdamped oscillator and an overdamped oscillator occurs at a particular value of the friction coefficient and is called critically damped.
If an external time-dependent force is present, the harmonic oscillator is described as a driven oscillator.
Mechanical examples include pendulums (with small angles of displacement), masses connected to springs, and acoustical systems. Other analogous systems include electrical harmonic oscillators such as RLC circuits. The harmonic oscillator model is very important in physics, because any mass subject to a force in stable equilibrium acts as a harmonic oscillator for small vibrations. Harmonic oscillators occur widely in nature and are exploited in many manmade devices, such as clocks and radio circuits. They are the source of virtually all sinusoidal vibrations and waves.

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2. ### I Translating the harmonic oscillator

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3. ### I Thoughts about coupled harmonic oscillator system

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4. ### Modification to the simple harmonic oscillator

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5. ### I Driven harmonic oscillator

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6. ### X^4 perturbative energy eigenvalues for harmonic oscillator

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7. ### I How to interpret complex solutions to simple harmonic oscillator?

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10. ### Question on Intro QM pertaining to Harmonic Oscillator

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11. ### I Particle on a cylinder with harmonic oscillator along z-axis

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12. ### Position expectation value of 2D harmonic oscillator in magnetic field

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29. ### Perturbation from a quantum harmonic oscillator potential

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31. ### A Equipartition theorem and Coupled harmonic oscillator system

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32. ### Calculating degeneracy of the energy levels of a 2D harmonic oscillator

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33. ### Griffiths Problem 3.35. Harmonic Oscillator, Bra-ket notation

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34. ### I Time averages for a 2-dimensional harmonic oscillator

I'm studying Ergodic Theory and I think I "got" the concept, but I need an example to verify it... Let's take the simplest possible 2D classical harmonic oscillator whose kinetic energy is $$T=\frac{\dot x^2}{2}+\frac{\dot y^2}{2}$$ and potential energy is $$U=\frac{ x^2}{2}+\frac{y^2}{2}$$...
35. ### Phase space of a harmonic oscillator and a pendulum

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36. ### Normalization constant A of a harmonic oscillator

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37. ### I Atoms in a harmonic oscillator and number states

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38. ### Working out harmonic oscillator operators at ##L \rightarrow \infty##

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40. ### A critically damped simple harmonic oscillator - Find Friction

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41. ### Harmonic Oscillator Ladder Operators - What is (ahat_+)^+?

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42. ### A Understanding Harmonic oscillator conventions

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43. ### I Why is this SHM the way it is?

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44. ### Simple Harmonic Oscillator Squeezing

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45. ### Time Derivatives of Expectation Value of X^2 in a Harmonic Oscillator

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