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ase330m_f08_hw03

# ase330m_f08_hw03 - ASE 330M Linear Systems Fall 2008...

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ASE 330M – Linear Systems: Fall 2008 Homework #3: Due 10/7/2008 by 5PM Consider the linear systems described by the differential equations below: a)       2 56 1 DD y tDu t     6 ut  02 , 0 1 yy  b)   2 44 DDy t D u t   sin 3 t 03 ,0 4 c) 12 yt D    3 t e 01 ,01 d)    2 93 2 Dy tD u t   t 00 , 06 e) 2 41 3 4 2 y t Du t   2 t e 0 5, 0 15.98  Problem #1: For cases (a)-(e), find the characteristic equation, the characteristic roots, and the characteristic modes. Use these results to identify the general form of the zero-input solution for each case. (Hint: You DO NOT need to evaluate coefficients using initial conditions yet) Problem #2: For cases (a)-(e), find the zero-state solution associated with each of the inputs provided.
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