Analyzing Simple Harmonic Motion in a Bifilar Pendulum Experiment

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To analyze simple harmonic motion in a bifilar pendulum experiment, measure the time for multiple oscillations and the distance of the rod. Plotting the time against the inverse of the distance will help establish a relationship. The gradient of this graph can be used to derive equations linking acceleration to either velocity or displacement. Computing potential energy as a function of angular displacement may also be beneficial, particularly if it shows a quadratic relationship for small angles. This approach will help confirm that the motion is indeed simple harmonic.
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Could someone please give me an overview of how I get from measuring the time taken for x oscillations and the distance of the rod, to proving it moves with simple harmonic motion? I know i have to plot t--d^-1 on a graph, then using the gradient (td) i need to do some maths magic to get either an equation linking acceleration to velocity or displacement (to prove the motion is simple harmonic).

the setup is like this http://www.egglescliffe.org.uk/physics/gravitation/bifilar/Image7.gif but i don't understand the rest of the experiment he has done...

thanks :)
 
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I think you could try to compute the potential energy as a function of the angular displacement. You simply (...well, I didn't try it, I don't know how simple it is) have to find the height of the center of mass with a bit of trigonometry.

If the energy is quadratic in phi (or nearly quadratic for small phi), the motion is harmonic (anyone correct me if I'm wrong).
 

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