AMATH 582 Winter Quarter 2012 Homework 4: PCA DUE: Wednesday, Feb. 22, 2012 On the webpage are movie ﬁles created from three diﬀerent cameras (videos are from 2011). The experiments are an attempt to illustrate various aspects of the PCA and its practical usefulness and the eﬀects of noise on the PCA algorithms. • (test 1) Ideal case: Consider a small displacement of the mass in the z direction and the ensuing oscillations. In this case, the entire motion is in the z directions with simple harmonic motion being observed. • (test 2) noisy case: Repeat the ideal case experiment, but this time, introduce camera shake into the video recording. This should make it more diﬃcult to extract the simple harmonic motion. But if the shake isn’t too bad, the dynamics will still be extracted with the PCA algorithms. • (test 3) horizontal displacement: In this case, the mass is released oﬀ-center so as to produce motion in the x-y plane as well as the z direction. Thus there is both a pendulum motion and a simple harmonic
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