Ordinary differential equations
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: * 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 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. (Wikipedia).
Let's Learn Physics: All About Oscillators
Harmonic oscillators are incredibly fundamental to almost all areas of physics. But how do we deal with systems that have more than one harmonic oscillators which all talk to each other? In this stream, we will discuss how to solve systems of coupled harmonic oscillators using the method o
From playlist Let's Learn (Classical) Physics: ZAP Physics Livestreams
B03 Simple harmonic oscillation
Explaining simple (idealised) harmonic oscillation, through a second-order ordinary differential equation.
From playlist Physics ONE
Harmonic Oscillator | Classical Mechanics Introduction
In this video, we will talk about the harmonic oscillator in classical mechanics. The term "harmonic oscillator" refers to any kind of motion where we have a linear force trying to pull the object back to equilibrium. Contents: 00:00 Introduction 00:34 Differential Equation 01:13 Soluti
From playlist Classical Mechanics
Why Pretty Much Everything is a Harmonic Oscillator
Here we discuss why the harmonic oscillator is such an important and ubiquitous system. We give a basic summary of classical mechanics and attempt to both sketch a rigorous idea and focus on the connections that can be found between systems using mathematics. 0:00 - Introduction 2:23 - Ma
From playlist Summer of Math Exposition 2 videos
Quantum Harmonic Oscillator Part 1
We set up the Schrodinger equation for the Quantum Harmonic Oscillator, and discuss what to expect from solutions..
From playlist Quantum Mechanics Uploads
From playlist Fall 2020 Course
B04 Example problem of simple harmonic oscillation
Solving an example problem of simple harmonic oscillation, which requires calculating the solution to a second order ordinary differential equation.
From playlist Physics ONE
The Quantum Harmonic Oscillator Part 1: The Classical Harmonic Oscillator
For our third quantum problem we will visit harmonic oscillators. In a classical setting, this is like the ball on a spring we examined when learning about Hooke's law in the classical physics series. But this has quantum application as well, in modeling the vibrations of molecules and thi
From playlist Modern Physics
Harmonic Oscillator: Introduction | Quantum Mechanics
Why is it called "harmonic oscillator"? #QuantumMechanics 🍿 Follow Us [Instagram] @prettymuchvideo If you want to help us get rid of ads on YouTube, you can support us on Patreon! https://www.patreon.com/prettymuchphysics
From playlist Quantum Mechanics, Quantum Field Theory
Why Quantum Mechanics Uses the Physics of SPRINGS - Quantum Harmonic Oscillators EXPLAINED
A spring is a great example of a Classical Harmonic Oscillator. The physics behind it is insightful and interesting... but it becomes even more amazing when applied to the world of Quantum Physics! Hey guys, I'm back with a video discussing Simple Harmonic Motion - something you may have
From playlist Quantum Physics by Parth G
How Quantum Physics Explains Creation of Energy (from Outside a System) - Parth G Quantum Mechanics
The Creation and Annihilation Operators (collectively known as the Ladder Operators) are a very useful tool in quantum mechanics. We'll be taking a look at what they represent and how we can use them. Before delving into the world of quantum mechanics, we'll first be looking at an importa
From playlist Quantum Physics by Parth G
Wolfram Physics Project: Working Session Friday, Apr. 17, 2020 [Spin & Charge | Part 1]
Stephen Wolfram & Jonathan Gorard & Max Piskunov continue answering questions about the new Wolfram Physics Project, this time specifically for the first live working session of the project. Originally livestreamed at: https://twitch.tv/stephen_wolfram Stay up-to-date on this project by
From playlist Wolfram Physics Project Livestream Archive
Thermodynamics 6d - Heat Capacity and the Third Law IV
We have seen how quantum mechanical "freezing" of degrees of freedom accounts for heat capacities below the classical prediction. Here we examine how anharmonic oscillations explain heat capacities above the classical prediction. Thermodynamics playlist: https://www.youtube.com/playlist?l
From playlist Thermodynamics
MIT Electronic Feedback Systems (1985) View the complete course: http://ocw.mit.edu/RES6-010S13 Instructor: James K. Roberge License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT Electronic Feedback Systems (1985)
Intuition about simple harmonic oscillators | Physics | Khan Academy
In this video David defines what it means for something to be a simple harmonic oscillator and gives some intuition about why oscillators do what they do as well as where the speed, acceleration, and force will be largest and smallest. Created by David SantoPietro. Watch the next lesson:
From playlist Oscillations and mechanical waves | Physics | Khan Academy
009 Dynamics of Oscillators and the Anharmonic Oscillator
In this series of physics lectures, Professor J.J. Binney explains how probabilities are obtained from quantum amplitudes, why they give rise to quantum interference, the concept of a complete set of amplitudes and how this defines a "quantum state". Notes and problem sets here http://www
From playlist James Binney - 2nd Year Quantum Mechanics
Lecture 7 | Modern Physics: Statistical Mechanics
May 11, 2009 - Leonard Susskind lectures on harmonic oscillators, quantum states, boxes of radiation and all associated computations such as wavelengths, volume, energy and temperature. Stanford University: http://www.stanford.edu/ Stanford Continuing Studies Program: http://csp.s
From playlist Lecture Collection | Modern Physics: Statistical Mechanics
MIT 8.421 Atomic and Optical Physics I, Spring 2014 View the complete course: http://ocw.mit.edu/8-421S14 Instructor: Wolfgang Ketterle In this lecture, the professor discussed harmonic oscillator and precision frequency measurement. License: Creative Commons BY-NC-SA More information at
From playlist MIT 8.421 Atomic and Optical Physics I, Spring 2014
8.01x - Module 15.04 - What is Simple Harmonic Oscillation SHO.
What is Simple Harmonic Oscillation SHO.
From playlist 8.01x - MIT Help Sessions