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hw1-fa10

# hw1-fa10 - CALIFORNIA INSTITUTE OF TECHNOLOGY Control and...

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Unformatted text preview: CALIFORNIA INSTITUTE OF TECHNOLOGY Control and Dynamical Systems CDS 101 D. MacMynowski Fall 2010 Problem Set #1 Issued: 27 Sep 10 Due: 4 Oct 10 Note: In the upper left hand corner of the second page of your homework set, please put the number of hours that you spent on this homework set (including reading). 1. ˚ Astr¨ om and Murray, Exercise 1.2 2. ˚ Astr¨ om and Murray, Exercise 2.6, parts (a) and (b) CALIFORNIA INSTITUTE OF TECHNOLOGY Control and Dynamical Systems CDS 110a D. MacMynowski Fall 2010 Problem Set #1 Issued: 27 Sep 10 Due: 4 Oct 10 Note: In the upper left hand corner of the second page of your homework set, please put the number of hours that you spent on this homework set (including reading). 1. ˚ Astr¨ om and Murray, Exercise 1.2 2. ˚ Astr¨ om and Murray, Exercise 2.1 3. Consider a damped spring–mass system with dynamics m ¨ q + c ˙ q + kq = F. Let ω = radicalbig k/m be the natural frequency and ζ = c/ (2 √ km ) be the damping ratio. (a) Show that by rescaling the equations, we can write the dynamics in the form ¨ q + 2 ζω ˙ q + ω 2 q = ω 2 u, (S1.1) where u = F/k...
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hw1-fa10 - CALIFORNIA INSTITUTE OF TECHNOLOGY Control and...

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