Pendulum Period

  • #1
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Homework Statement



Prove the equation: T = 2 pi * sqrt(L/g), then determine the period of a "seconds pendulum" (period = 2 sec on Earth) on the surface of the moon.

Homework Equations



T = 2pi * r/v
T = 2pi/ω
ar = rω2

The Attempt at a Solution



Do you assume ar is ag?

T = 2pi/ω
= 2 * pi / sqrt(a/r)
= 2 * pi * sqrt(r/a)

...Apparently, L is supposed to be the length of the pendulum, so somewhere along the line, I completely screwed up.

I can solve the second part of the question just fine, but since I've never actually seen T = 2 pi * sqrt(L/g) used or proved, I'd rather not work with it until I understand where it comes from and how it works.
 

Answers and Replies

  • #2
694
114
Start with the component of gravity which causes the bob to move towards the mean position. See how this relates to the SHM equation. Remember that for small displacements from the mean position, the motion is SH. You should be able to derive it now.
Hint: Use angular displacement.
 
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  • #3
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If you get stuck, keep in mind that most introductory physics textbooks will have a derivation of this.
 

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