- published: 01 Oct 2013
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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.
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:
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."
Part 7 of a series: explains how the ideas of Simple Harmonic Motion can be carried into Quantum Mechanics
MIT 8.04 Quantum Physics I, Spring 2013 View the complete course: http://ocw.mit.edu/8-04S13 Instructor: Barton Zweibach In this lecture, Prof. Zweibach covers the quantum mechanics of harmonic oscillators. He begins with qualitative discussion on bound state solutions and then moves on to the quantitative treatment of harmonic oscillators. License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
Physical chemistry microlecture on the use of the quadratic harmonic oscillator potential as a model for a vibrating diatomic molecule.
We'll discover that energy is conserved in a very surprising way.
Concepts covered in this lecture begin with the restoring force of a spring (Hooke's Law) which leads to an equation of motion that is characteristic of a simple harmonic oscillator (SHO). Using the small angle approximation, a similar expression is reached for a pendulum. Demonstration was given that the period of the swing of a simple pendulum does not depend on its mass. This lecture is part of 8.01 Physics I: Classical Mechanics, as taught in Fall 1999 by Dr. Walter Lewin at MIT. This video was formerly hosted on the YouTube channel MIT OpenCourseWare. This version was downloaded from the Internet Archive, at https://archive.org/details/MIT8.01F99/. Attribution: MIT OpenCourseWare License: Creative Commons BY-NC-SA 3.0 US To view a copy of this license, visit http://creativecommons....
MIT 8.04 Quantum Physics I, Spring 2013 View the complete course: http://ocw.mit.edu/8-04S13 Instructor: Allan Adams In this lecture, Prof. Adams discusses an alternative method to solving the harmonic oscillator problem using operators. License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
A solution to the quantum harmonic oscillator time independent Schrodinger equation by cleverness, factoring the Hamiltonian, introduction of ladder operators, expression of the commutator, basic operator algebra, demonstration of the effect of the ladder operators on a hypothetical stationary state, and the resulting algebraic structure of the solutions. (This lecture is part of a series for a course based on Griffiths' Introduction to Quantum Mechanics. The Full playlist is at http://www.youtube.com/playlist?list=PL65jGfVh1ilueHVVsuCxNXoxrLI3OZAPI.)
View the complete OCW resource: http://ocw.mit.edu/resources/res-8-005-vibrations-and-waves-problem-solving-fall-2012/ Instructor: Wit Busza First, advice on how, in general, one approaches the solving of "physics problems." Then three very different oscillating systems, and how in each the equations of motion can be derived and solved to obtain the motion of the oscillator. *NOTE: These videos were originally produced as part of a physics course that is no longer available on OCW.* License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
In our last lab on the harmonic oscillator, we will add a driving force to the experiment. This will allow us to study the response of the oscillator to the driving frequency and the degree of damping in the oscillator.