models:basic_models:harmonic_oscillator
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models:basic_models:harmonic_oscillator [2018/03/28 09:06] jakobadmin [FAQ] |
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 physical systems we can study. | ||
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| + | 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 $\color{red}{\text{properties of the spring}}$. 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.1522220795.txt.gz · Last modified: 2018/03/28 07:06 (external edit)
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