ambitious

Hello

I am trying to work out the acceleration due to gravity using compound pendulum method. However I am totally stumped and don't understand how you find it using this method,I am able to carry out the experiment properly. I am just confused about how you use the graph to find the value of g, can anyone explain in layman's terms what you are supposed to do? I am not looking for a full worked solution, I would just like some guidance on how to start and hopefully I'll be able to do the rest.

Thanks so much

topsquark

Could you be a bit more explicit about what your experiment is? The equation of motion for a compound pendulum generally need to be solved numerically. They are also chaotic so interpreting a graph is going to be difficult.

-Dan

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ChipB

Sometimes the term "compound pendulum" is used to mean a pendulum with two lengths joined by a pivot, which is what I suspect topsquark is thinking about. But the term may also be used to describe any pendulum that has a distributed mass. For a pendulum consisting of a bar (of non-negligible mass) the period of vibration is:

T = 2 pi sqrt (I/mgh)

where h is the distance from the pivot point of the center of mass of the bar, and I is the moment of inertia of the bar. If you have values for T from your experiment plus m, h, and I, you can calculate g.

ambitious

Okay a description of the experiment is as follows:


The compound pendulum AB is suspended by passing a knife edge through the first hole. The pendulum is pulled aside through a small angle and released, whereupon it oscillates in a vertical plane with a small amplitude. The time for 10 oscillations is measured. From this the period T of oscillation of the pendulum is determined.


A graph is drawn with the distance d of the various holes a straight line is drawn parallel to the X- axis from a given period T on the Y- axis, cutting the graph at four points A, B, C, D. The distances AC and BD, determined from the graph, are equal to the corresponding length l. The average length l = (AC+BD)/2. In a similar way , l/T2 is calculated for different periods by drawing lines parallel to the X-axis from the corresponding values of T along the Y- axis. l/T2 should be constant over all periods T, so the average over all suspension points is taken. the acceleration due to gravity is calculated from the equation g= 4π2(l/T2).


Could you please explain what the given period is? Or do you just use any random period?

For I/T2, do you just like draw vertical lines parallel to all the values of T and then average the T values?

Could you possibly provide an example on what you're supposed to do with the graph part, like a picture maybe

topsquark

Interesting. I was taught the term "physical pendulum" for the distributed mass case.

-Dan

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