MathLivePendulum equation of motion
This nonlinear differential equation describes the angular motion of an ideal simple pendulum swinging under gravity without friction. It is used to model the swing angle over time, and for small angles it reduces to the linear harmonic oscillator form.
\frac{d^2\theta}{dt^2} + \frac{g}{l}\sin\theta = 0What the symbols mean
| angular displacement of the pendulum from the vertical (radians) | |
| time (s) | |
| acceleration due to gravity (m/s^2) | |
| length of the pendulum (m) |
About this formula
- FieldPhysics
- TopicClassical mechanics
- LevelUniversity
- Also calledsimple pendulum equation, nonlinear pendulum equation, pendulum differential equation, angular acceleration of pendulum, pendulum motion equation, theta double dot pendulum
- SourceWikidata Q20702
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