Homework 1: Practicing MATLAB. Due date: 2/01/2011. The purpose of this fairly straightforward assignment is to get you started on MATLAB programming. For problems 1(a) and 3(a),(c) please submit a separate file containing your answers/analytics. The best formats: .doc or .pdf. If you decide to submit a .doc file, please do not use MathType for equations. Instead, use the standard Microsoft Equation program. Otherwise your formulas may not show up on my computer. Problem 1: The Cycloid. (30 points) Imagine that a speck of dust attached itself to the outside of a rolling tire. The tire is rolling straight (without wobbling) with velocity vx = 1m/s on a flat surface without slipping. The tire diameter is D = 1m. (a) Work out the analytic solution to this problem (in a parametric form). (15pt) (b) Draw the x-y trajectory of the dust speck over two periods of the tire rotation. Here y is the vertical direction. Write an appropriate MATLAB script, generate the plot, save it as an encapsulated postscript file. The plot should have a title,
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