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### Course: AP®︎/College Physics 1>Unit 5

Lesson 1: Period of simple harmonic oscillators

# Period of a Pendulum

A pendulum behaves as a simple harmonic oscillator. Learn about the period of a pendulum, how it can be adjusted, and how it compares to a mass on a spring. Created by David SantoPietro.

## Want to join the conversation?

• At , David says that only 1 L shows up in the equation for the pendulum's period because torque is proportional to length. What does torque have to do with the period of a pendulum?
• Torque produced by gravity acts as the restoring force for the pendulum. Thus, the time period would be inversely proportional to the restoring force or the square root of gravitational acceleration or, the higher the torque on the pendulum, the lesser the time period would be and vice versa.
• So I've been studying bout large angles in a pendulum, and I know that the formula is

T = sqrt(l/g).[1+∅²/16]

Where ∅ is the angle of pendulum.

Any way to derive this one?
• what about a pendulum motion that has got a spring instead of an ordinary string
(1 vote)
• That would actually make the problem quite a bit more difficult!

You actually can solve this problem but it involves the usage of Lagrangian mechanics and multivariable calculus. If you want to learn more, try Googling it. If you need more help with understanding Lagrangian mechanics, feel free to ask here and I'll try my best to answer!
• he said "If you wanna get technical, rotational inertia is proportional to length squared, but the torque would only be proportional to length. That's why only one L shows up here." what did he meant?
• Learn calculus or you can't understand