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yahoo4 · Jul 24, 2009, 07:41 PM

Hello

I am interested in finding out the equation for the period of the broken pendulum. This is a simple pendulum which hits a rod that breaks its swing directly beneath the equilibrium point.

kiwiminstp · Aug 1, 2010, 07:42 PM

T = pi * sqrt(B/g) + pi * sqrt(L/g) where B is the short length, L is the full length assuming half the swing is at the full length and half at the shorter length

Corneil · Jun 29, 2011, 12:05 AM

Hey. Could you by any chance explain why that is? In physics terms?

kiwiminstp · Jun 29, 2011, 12:26 AM

Yes I can!

The "normal" period of a pendulum is
$T = 2\pi \sqrt{\frac{l}{g}}$

"Half a swing" would be
$\pi \sqrt{\frac{l}{g}}$

So the period of a broken pendulum would be
$\pi\sqrt{\frac{l_{long}}{g}} + \pi \sqrt{\frac{l_{short}}{g}}$

How hard is that?

kittykat12 · May 23, 2012, 12:46 AM

Can anyone help on the physics theory of the broken pendulum?

ebaines · May 23, 2012, 11:30 AM

Originally Posted by kittykat12

Can anyone help on the physics theory of the broken pendulum?

What do you want to know? The previous post did a good job of explaining why the period is what it is, but it assumes you know that the period for a simple pendulum is $2 \pi \sqrt{\frac L g }$ . If you would like to know why that is - it requires solving the differential equation for a pendulum's motion, which you can get by drawing the free body diagram and considering that F=ma. If you want to see more about how to do this - see:

http://www.physicsclassroom.com/class/waves/u10l0c.cfm