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 dont understand the rest of the experiment he has done... thanks :)
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).