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Unformatted text preview: ME 132, Spring 2005, Quiz # 1 # 1 10 # 2 20 # 3 15 TOTAL 45 Fact: Both roots of λ 2 + a 1 λ + a 2 = 0 have negative real-parts if and only if a 1 > and a 2 > 0. Fact: All three roots of λ 3 + a 1 λ 2 + a 2 λ + a 3 = 0 have negative real-parts if and only if a 1 > , a 3 > , and a 1 a 2 > a 3 . 1. Your answers in part 1a and 1c both should have two free constants. I would like there to be no √- 1 in the answers, just exponentials, cos and sin. (a) What is the general form of real (as opposed to complex) solutions to the differential equation ¨ y ( t ) + 2 ˙ y ( t ) + 17 y ( t ) = 0 (b) The solutions in part 1a are made up of an exponentially decaying envelope, superimposed on a sinusoid. What (approximately) is the ratio Period- of- Oscillation Time- to- Decay Explain. (c) What is the general form of real solutions to the differential equation ¨ y ( t ) + 2 ˙ y ( t ) + 17 y ( t ) =- 51 1 2. A process has a very simple model, y ( t ) = Hu ( t ) + w ( t ) ....
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This note was uploaded on 08/01/2008 for the course ME 132 taught by Professor Tomizuka during the Spring '08 term at University of California, Berkeley.
- Spring '08