HW_4_Sol - HW 4 From Lindner's notes ECE 3704 Due 2-23-07...

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HW 4 1/3 HW 4 ECE 3704 Due 2-23-07 From Lindner’s notes 3.2.1 Consider the following polynomial. ( s + 6) 2 + 36 (a) (5) By hand find the roots of each of these polynomials in rectangular form and using ( ζ , ω n ). Express each polynomial in standard second-order form. (b) (5) Enter each polynomial into MATLAB. Use MATLAB to confirm the answers to part (a). Show the vector you entered. Show the command you used for each calculation. (The damp command will calculate ( ζ , ω n ) for complex roots.) (c) (5) Plot the roots of these equations in the s -plane. Label ( ζ , ω n ). (vi) (a) The roots of this polynomial are ( s + 6) 2 + 36, ! " = 6, # c = 6 # n = (6) 2 + 6 2 = 8.49, $ = tan % 1 6 6 ( ) * + = , 4 rad, - = cos( $ ) = 0.707 In standard second order form, this polynomial is given by s 2 + 2(0.707)(8.49) s + (8.49) 2 (b) »damp(conv([1,6],[1,6])+[0,0,36]) Eigenvalue Damping Freq. (rad/sec)
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HW_4_Sol - HW 4 From Lindner's notes ECE 3704 Due 2-23-07...

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