Why small swings make pendulums the perfect model for simple harmonic motion
In short: Discover how the small-angle approximation transforms the complex physics of a swinging pendulum into a predictable model of simple harmonic motion. This video explains the relationship between gravity, pendulum length, and the restoring torque that dictates its period.
When a pendulum swings with a small angular displacement, the restoring torque exerted by gravity becomes directly proportional to that displacement. This mathematical relationship allows physicists to apply the small-angle approximation, effectively modeling the motion as simple harmonic motion.
The period of such a pendulum is determined by two primary factors: the length of the pendulum arm and the strength of the local gravitational field. By understanding these variables, one can accurately predict the timing of the pendulum's oscillation.
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Sources
- Summary by Intellect · source: SHM of simple pendulums | AP Physics | Khan Academy
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