Renegade343 Posted October 11, 2014 Share Posted October 11, 2014 So, I delayed this series for two weeks due to various computer and program problems, and I said this: I promise by the next weekend, it will be fixed, and I will do something to make up for it. The first promise is done, so I went and fulfil the second promise (warning: Since this is rather, for a lack of a better acronym, NSFW, I have hidden the images and the gif in spoilers.): Now, this gif came from a place (and also appears in various threads): While I did cringe a bit from viewing this, the mathematical part of my mind took over, and analysed it. It then noticed that this gif seems to be executing simple harmonic motion (look it up if you do not know) (at least on the horizontal plane), and thus raised this question: What is the approximate sinusoidal wave of this motion (horizontal component only)? Thus, I took the gif, went into Final Cut Pro 7, and slowly analysed the clip frame by frame, finding the maximum and minimum values of the motion (and their associated times [30FPS]), as well as the equilibrium point. Afterwards, I took still images of these points (four in total, but only took three still images, as the fourth one is also the equilibrium point [but when time = 0.45s]), then pasted them into Geogebra (first image is at first equilibrium point, second is at minimum point, and third is at maximum point): Taking the x-values of these points, then shifting it by 0.111 (so that equilibrium point can be 0), I then plotted a graph of time vs. distance from equilibrium point. I then used the equation: a * sin(bx + c) + d And started to find the function: a * sin(bx + c) + d a = (First max or min point - Second min or max point) / 2 a = (-0.01326 - 0.01365) / 2 a = -0.013455 Period = 2π/b 14/15 = 2π/b b = 5.864 d = (Max + min) / 2 d = (0.01365 - 0.01326) / 2 d = 0.000195 Let x = 0.0333, y = 0, 0.01346 * sin(0.195 + c) + 0.000195 = 0 -0.0146 = sin(0.195 + c) arcsin(-0.0146) = 0.195 + c Since arcsin(θ) ≈ θ when θ is very, very small, -0.0146 = 0.195 + c c = -0.21 And so, I plotted the graph, and the result is thus: It is relatively accurate (and thus does prove that the horizontal motion executes simple harmonic motion [to a good degree]), although it could be improved with installing better programs to track a certain point in a clip (or maybe I could play around with Final Cut Pro 7 more). But anyways, here is my artwork of combining Warframe and mathematics. Link to comment Share on other sites More sharing options...
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