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# Class Note for MATH 3321 at UH

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COURSE
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TYPE
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PAGES
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KARMA
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This 1 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 16 views.

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Date Created: 02/06/15
7 w i zll rl11 gt gtquotJl l 71 2 rxxxyyy 72 ltt i Exercises 1 Sketch the phase plane for the following systems m 1 z m m m2 7 1 a b C 7 9 79 9 y y i y i 2 Solve the system for the damped pendulum 3 4 when 6 0 Sketch the vector eld and the solutions What happens to the amplitude of the solutions as the pendulum oscillates in this case Solution In this case the solutions have the form 105 01 cost Cg sin 257 2 02 cos 701 sin 25 They oscillate forever with constant amplitude v 1e r 1HH tyr Ill11177 lltivr iigt v Illlttvv f1414444 V 44414 4 V llltAi V 7 5 I v ysquot1lu 39 quotquotifl A I rtI V 54A l A x 39Irx 39lt H 3 Solve the equation for the damped linear pendulum 3 4 Show that when 6 gt 0 equations oscillate with diminishing amplitude 303

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