Unformatted text preview: (b) Chapter 5, Problem 71. ±or this problem, note that for a secondorder circuit with a constant forcing function K : d 2 y dt 2 + 2 ζω n dy dt + ω 2 n y = Kω n with ζ > 0 the following calculation applies: lim t →∞ y ( t ) = K ±urthermore, if the system is underdamped , that is, if 0 < ζ < 1, a = ζω n , ω d = ω n r 1ζ 2 , and y ( t ) = K p 1eat p cos( ω d t ) + a ω d sin( ω d t ) PP , t > and there is no energy stored initially, the peak time and value at that time can be given by: t peak = π ω n r 1ζ 2 = π ω d y ( t peak ) = K (1 + eat peak ) = K p 1 + eπζ √ 1ζ 2 P Part II: (a) Chapter 5, Problem 73. (b) Chapter 5, Problem 74. Part III: (a) Chapter 8, Problem 1. (b) Chapter 8, Problem 5. (c) Chapter 8, Problem 7. Part IV: (a) Chapter 8, Problem 10. (b) Chapter 8, Problem 13. Copyright 2009, Gustafson Hwk 9 – 1...
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 Spring '07
 MALKIN
 Q factor, Gustafson Hwk, constant forcing function, following calculation applies

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