How Do You Measure the Length of a Pendulum with Non-Spherical Bobs?

[Orb Brehs]

Hello,

I should preface that we are not physicists. We are just a few relatively ordinary guys that committed to building a large pendulum wave (6ft tall, 8ft long). The construction went very well. The frame and the individual pendulum are all strung up. We have a rather ingenious rig that allows us to very easily adjust the length of the wire connecting the pendulum.

However, we are running into some issues that hopefully some of you experts will be able to shed some light on. We are using a calculator to determine our 'length' of each pendulum. So for a time period of 60 seconds and an oscillation value of 30 we are provided with a 'length' for the initial pendulum of aprox 100cm. But when we string it up the oscillation only runs for 29.

Other considerations:
- We are using mason jars as the bobs. So not spherical, roughly cylindrical
- We have no idea what 'length' actually refers to. We assumed (wrongly I suspect) that it was the distance between the top of the jar (bob) to the support bar, and that is what we have measured.

So, I guess the overall question, after such a lengthy preamble, is where do we measure our 'length' from when using mason jar bobs on a large pendulum wave? Top, middle, or bottom of the jar?

And just as an aside, we spent a lot of time eyeballing and counting oscillations by eye, and although this was pretty good in terms of results we believe this exact measuring should be better. Maybe not?

Thank you very much!

 

[sophiecentaur]

Hi and welcome to PF.
It looks as if your period is shorter than you expected so perhaps there is another 'restoring force', apart from gravity, acting on the jars. Could it be due to the wire? How free is the wire at the top? Posh pendulums use a knife edge to eliminate torque as the bob swings.
I wonder if the jars are empty or full (of what?). If they are empty then you could fill them with sand, perhaps and then the g force would be proportionally greater compared with the torque on the wire. You could see what difference the mass of the bob makes on your agreement with theory. (Period =2Π √(l/g) . . . . . yes?) Also, the effective length of the pendulum is really to the Centre of Mass of the bob - and assumes that the length of the bob is small c/w the length of the string. If the bob is not a 'point mass, then the moment of inertia of the bob will slow it down. But I don;t think, on such a long wire, it's relevant. Look up the formula for a swinging bar, pivoting at a point along its length. (A little nerdy diversion for you)
PS aren't Jars likely to smash and ruin your fun? Bean cans would be stronger :).

 

[Orb Brehs]

Thanks for your reply! Some more info.

- We tested the 'free wire' factor and there wasn't any change when we switched methods. So we believe the torque is insignificant.
- The jars are filled with glass beads (the point of this whole thing is for it to be lit up so sand isn't an option)

So you're suggesting that the centre of mass would be the middle of the filled jar?

Formula we used for length is

l(n)=g(Γ/2π(N+n))^2

N is number of oscillations the longest pendula performs

n is number of pendula

Γ is the duration of a cycle

Is this formula not effective for such long lengths? our longest length would be aprox 1meter. Is our formula no good? Remember, we are just amateurs here!

 

[sophiecentaur]

There are several steps in this problem.
My formula is just for the period of a single pendulum of length l (when n=0, in your formula, I think). If N is not what this formula would give you then I think there must be something wrong - it's a standard experiment in School and kids tend to get it right with very simple equipment,
I guess we should make sure we're talking about the same thing here. I assume you are talking about a row of pendulums that you view end-on and get a wave like pattern when they are started off at the same time.

I am just wondering whether the n you are using, starts from the value 1. I think it should start with value 0. n would stand for the additional pendulums and not the total number, I think. Think it over and see if that helps.