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Unformatted text preview: note that INCREASING ω increases, D , (say ω = 21 gives D = 0 . 0322). So ω ≤ 20. Also note that. 03 = 18 1000ω 2 (12) gives two solutions: ω = 40 and ω =40. Keeping the second one and noting that DECREASING ω decreases (makes more negative) D , requires ω ≥ 40. So the range of allowed frequencies are ω ≤ 20 and ω ≥ 40 . (13) 3. The following Lissajous curves were plotted on Maple with the included commands: (a) plot([cos(t(1/5)*Pi), cos(2*t), t = 2*Pi . . 2*Pi]) (b) plot([cos(5*tPi), cos(4*t(1/2)*Pi), t = 2*Pi . . 2*Pi]) (c) plot([cos(10*t(1/2)*Pi), cos(11*tPi), t = 2*Pi . . 2*Pi]) (d) plot([cos(Pi*t), cos(t), t = 20000*Pi . . 20000*Pi]) Note in this last case, ω x /ω y is not a rational fraction, eﬀectively ﬁlling the square. 2 3...
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 Spring '10
 RogerMelko
 D= F0 /m

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