models:basic_models:harmonic_oscillator
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models:basic_models:harmonic_oscillator [2018/03/28 09:10] jakobadmin [Intuitive] |
models:basic_models:harmonic_oscillator [2018/06/06 10:35] (current) jakobadmin |
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| - | ====== Harmonic Oscillator: $\quad L= \frac{m}{2} \left(\frac{dx}{dt}\right) - \frac{k}{2}x^2$ ====== | + | <WRAP lag>$ L= \frac{ \color{blue}{m}}{2} \left( \color{olive}{\frac{dx}{dt}}\right)^2 - \frac{ \color{red}{k}}{2} \color{magenta}{x}^2$</WRAP> |
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| + | ====== Harmonic Oscillator ====== | ||
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| {{ :hookeslaw.png?nolink&300|}} | {{ :hookeslaw.png?nolink&300|}} | ||
| - | A harmonic oscillator simply consists of an object attached to a spring and is one of the simplest fundamentals systems we can study. | + | A harmonic oscillator simply consists of an object attached to a spring and is one of the simplest physical systems we can study. |
| - | To describe the system we usually track the position of the object at the end of the spring. The continuous up and down movement is called an oscillaton, which is where the name "oscillator" comes from. | + | To describe the system we usually track the $\color{magenta}{\text{position}}$ of the object at the end of the spring. The continuous up and down movement is called an oscillation, which is where the name "oscillator" comes from. |
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| - | The movement depends crucial on the properties of the spring. When the spring is harder, the movements of the object will be smaller. In addition, the motion of the object depends on its mass. A heavier object will perform larger swings. | + | |
| + | The movement depends crucial on the $\color{red}{\text{properties of the spring}}$. When the spring is harder, the movements of the object will be smaller. In addition, the motion of the object depends on its $\color{blue}{\text{mass}}$. A heavier object will perform larger swings. | ||
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| <tabbox Concrete> | <tabbox Concrete> | ||
| - | * A good description can be found at http://www.hep.caltech.edu/~fcp/physics/quantumMechanics/SHO/SHO.pdf | + | * A good description of the harmonic oscillator in quantum mechanics can be found at http://www.hep.caltech.edu/~fcp/physics/quantumMechanics/SHO/SHO.pdf |
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| <tabbox Abstract> | <tabbox Abstract> | ||
| + | The [[basic_tools:phase_space|phase space]] of a harmonic oscillator | ||
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| + | {{ :basic_tools:phasespaceoscillator.png?nolink&600 |}} | ||
| <tabbox Why is it interesting?> | <tabbox Why is it interesting?> | ||
models/basic_models/harmonic_oscillator.1522221002.txt.gz · Last modified: 2018/03/28 07:10 (external edit)
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