models:basic_models:pendulum
Differences
This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision Next revision | Previous revision Last revision Both sides next revision | ||
|
models:basic_models:pendulum [2018/04/09 08:48] lushikatome [Concrete] |
models:basic_models:pendulum [2018/06/28 10:41] jakobadmin [Concrete] |
||
|---|---|---|---|
| Line 1: | Line 1: | ||
| - | <WRAP lag>$ \quad L = \frac{1}{2} \color{blue}{m} \color{olive}{l}^2\dot{\color{red}{\phi}}^2 - \color{blue}{m}\color{magenta}{g}\color{olive}{l} (1-cos \color{red}{\phi})$</WRAP> | + | <WRAP lag>$ \quad L = \frac{1}{2} \color{blue}{m} \color{olive}{l}^2\dot{\color{firebrick}{\phi}}^2 - \color{blue}{m}\color{magenta}{g}\color{olive}{l} (1-cos \color{firebrick}{\phi})$</WRAP> |
| ====== Pendulum ====== | ====== Pendulum ====== | ||
| Line 8: | Line 8: | ||
| {{ :models:pendulumsimple.png?nolink&200|}} | {{ :models:pendulumsimple.png?nolink&200|}} | ||
| - | A pendulum is right after a harmonic oscillator the simplest physical system we can study. In fact, if the pendulum only swings a little it is a [[models:harmonic_oscillator|harmonic oscillator]]. The difference between the harmonic oscillator and the pendulum only become important for large swings. | + | |
| A pendulum consists of a freely hanging massive bob at the end of a rod. When we move the bob a little to one side it starts swinging. | A pendulum consists of a freely hanging massive bob at the end of a rod. When we move the bob a little to one side it starts swinging. | ||
| - | We usually describe it by measuring $\color{red}{\text{how far the bob has moved from its original position}}$ where it just hangs freely. How the pendulum swings depends crucially on the $\color{olive}{\text{length of the rod}}$ and the $\color{magenta}{\text{strength of the gravitational field}}$. A pendulum on the moon swings differently than a pendulum on earth. | + | We usually describe it by measuring <color firebrick>how far the bob has moved from its original position</color> where it just hangs freely. How the pendulum swings depends crucially on the <color olive>length of the rod</color> and the <color magenta>strength of the gravitational field</color>. A pendulum on the moon swings differently than a pendulum on earth. |
| - | An important observation is that the swinging of the pendulum does not depend on the $\color{blue}{\text{mass of the bob }}$. | + | An important observation is that the swinging of the pendulum does not depend on the <color blue>mass of the bob</color>. |
| + | |||
| + | A pendulum is right after a [[models:basic_models:harmonic_oscillator|harmonic oscillator]] the simplest physical system we can study. In fact, if the pendulum only swings a little it is a harmonic oscillator. The difference between the harmonic oscillator and the pendulum only become important for large swings. | ||
| + | |||
| + | ---- | ||
| + | |||
| + | * see also the nice interactive demonstration [[https://www.myphysicslab.com/pendulum/pendulum-en.html|here]]. | ||
| | | ||
| <tabbox Concrete> | <tabbox Concrete> | ||
| {{ :models:pendulum.png?nolink&300|}} | {{ :models:pendulum.png?nolink&300|}} | ||
| - | [[models:harmonic_oscillator|]] | + | |
| A normal pendulum hangs freely in a uniform gravitational field of strength $g$ on a rod with length $l$. The excitation above the ground state is measured by the angle $\phi$. At the end of the pendulum, we have a bob of mass $m$. This is shown in the picture on the right-hand side. | A normal pendulum hangs freely in a uniform gravitational field of strength $g$ on a rod with length $l$. The excitation above the ground state is measured by the angle $\phi$. At the end of the pendulum, we have a bob of mass $m$. This is shown in the picture on the right-hand side. | ||
| Line 71: | Line 77: | ||
| * For a nice complete discussion, see The Pendulum: A Case Study in Physics by Gregory L. Baker and James A. Blackburn | * For a nice complete discussion, see The Pendulum: A Case Study in Physics by Gregory L. Baker and James A. Blackburn | ||
| <tabbox Abstract> | <tabbox Abstract> | ||
| + | The [[basic_tools:phase_space|phase space]] of a pendulum | ||
| + | |||
| + | {{ :basic_tools:phasespacependulum2.png?nolink&600 |}} | ||
| + | |||
| + | |||
| + | ---- | ||
| + | |||
| + | |||
| * A thorough discussion can be found in [[https://aapt.scitation.org/doi/abs/10.1119/1.12332|Quantum pendulum]] by R. Aldrovandi and P. Leal Ferreira | * A thorough discussion can be found in [[https://aapt.scitation.org/doi/abs/10.1119/1.12332|Quantum pendulum]] by R. Aldrovandi and P. Leal Ferreira | ||
models/basic_models/pendulum.txt · Last modified: 2020/04/02 15:37 by 75.97.173.144
Page Tools
Except where otherwise noted, content on this wiki is licensed under the following license: CC Attribution-Share Alike 4.0 International
