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AMATH 482-582 Homework 3 PCA solved

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On the webpage are movie files (turned into matlab 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 (camN 1.mat where N=1,2,3).
• (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. (camN 2.mat where
N=1,2,3)

• (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
oscillations. See what the PCA tells us about the system. (camN 3.mat where N=1,2,3)

• (test 4) horizontal displacement and rotation: In this case, the mass is released off-center and
rotates so as to produce motion in the x−y plane, rotation as well as the z direction. Thus there is both
a pendulum motion and a simple harmonic oscillations. See what the PCA tells us about the system.
(camN 4.mat where N=1,2,3)
Explore the PCA method on this problem and see what you find.