models:basic_models:pendulum
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models:basic_models:pendulum [2018/05/15 06:51] jakobadmin [Intuitive] |
models:basic_models:pendulum [2020/04/02 15:37] (current) 75.97.173.144 |
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| <tabbox Concrete> | <tabbox Concrete> | ||
| {{ :models:pendulum.png?nolink&300|}} | {{ :models:pendulum.png?nolink&300|}} | ||
| - | [[models:basic_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. | ||
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| The [[formalisms:lagrangian_formalism|Lagrangian]] of the pendulum is therefore | The [[formalisms:lagrangian_formalism|Lagrangian]] of the pendulum is therefore | ||
| - | $$ L = T-V= \frac{1}{2} ml^2\dot{\phi}^2 - mgl (1-cos \phi), $$ | + | $$ L = T-U= \frac{1}{2} ml^2\dot{\theta}^2 - mgl (1-cos \theta), $$ |
| - | where $\dot{\phi}\equiv d\phi /dt $ denotes the time derivative. | + | where $\dot{\theta}\equiv d\theta /dt $ denotes the time derivative. |
| Using the Euler-Lagrange equation we can derive the corresponding __equation of motion__ | Using the Euler-Lagrange equation we can derive the corresponding __equation of motion__ | ||
models/basic_models/pendulum.1526359905.txt.gz · Last modified: 2018/05/15 04:51 (external edit)
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