# Formula for pendulums

## Recommended Posts

Hello,

I'm basing my IA on bifilar pendulums and require the formula of the time period of a bifilar pendulum and simple pendulum. When I researched online, different sources claim different things. One formula I obtained was T = 2pi*(L/g)^0.5 (2 times pi times square root of L/g), where L = length of the pendulum and g = gravity. Is this formula applicable for both simple and bifilar pendulums? If not, what is the formula for each kind of pendulum?

Thanks in advance for the help!

##### Share on other sites

I'm quite certain that the formula is not applicable towards bifilar pendulums - there would be more forces acting on the mass in the bifilar pendulum compared to the single pendulum, and so the derivation of a formula would be different.  The formula that you provided is for the simple pendulum (actually in the Physics HL data booklet), so you'd need a different formula.

This source provides a derivation of the moment of intertia of the bifilar pendulum, assuming simple harmonic motion, which in turn matches the formula provided by this source (although they do use different variables).  You can rearrange the formula (which I've attached in a word file below so it's easier to see) to make it in terms of T.  I'd recommend searching around more for the sake of completeness.

Formula.docx

##### Share on other sites

Thank you! But one thing that is different in my experiment is that instead of twisting the pendulum in the horizontal axis to form a circular motion, which is how bifilar pendulums are usually oscillated, I'm simply oscillating it back and forth, meaning the two ends of the pendulum will behave like simple pendulums. Doesn't this mean that I can use the simple pendulum formula for each end?

Thanks once again for the help

##### Share on other sites

I'm assuming that you're swinging the pendulum as in the image below:

In this case, the source (a physics paper) states that this is indeed equivalent to simple harmonic motion of a single pendulum, based on the idea that the net tension on the strings are constant during oscillation, although I would definitely check with your teacher and other sources too.  It would be interesting to compare this with your experimental results.

Edited by SC2Player

##### Share on other sites

I am also doing bifilar pendulum (Going to twist it to a certain angle and release it) for my Physics IA , and I came across with this equation: T = KsmLn where T is the period , K is a constant, s is the distance between the separation of 2 strings and L is the length of the strings, m and n are unknown indices. I saw it somewhere but I don't know if this equation applies or not to bifilar pendulum since I have never seen it before and I could not find it on the internet. Can someone confirm with this equation? Thank you.

##### Share on other sites
On 5/11/2017 at 8:58 PM, Cher said:

I am also doing bifilar pendulum (Going to twist it to a certain angle and release it) for my Physics IA , and I came across with this equation: T = KsmLn where T is the period , K is a constant, s is the distance between the separation of 2 strings and L is the length of the strings, m and n are unknown indices. I saw it somewhere but I don't know if this equation applies or not to bifilar pendulum since I have never seen it before and I could not find it on the internet. Can someone confirm with this equation? Thank you.

I would suggest against using that equation if you haven't seen it anywhere. Use an equation that you've seen in at at least 2 trustworthy resources (or check that eqn with your teacher).

## Create an account

Register a new account