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your work! All MATLAB code must be included in this .pdf file. Problem One Analyzing Roots in the Complex Plane 1. Match the
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Answer #1

1.

C and D are Real. No oscillation. So, the two bottom curves are C and D.

The value of pole C is higher because it is on the left side of D. This means, its steady-state value is lower(higher value in the denominator) than D. In the figure, Yellow is below the purple curve at the end.

So, Yellow - C. Purple - D.

The two upper graphs that have an oscillatory response, in the beginning, belong to A and B since the roots A and B have imaginary parts.

The Blue graph damps out quickly. So, it has a higher damping ratio.

You can see below that Line Joining B to origin makes a higher angle with horizontal. This means it has lower damping than A.

So, Blue - A. Orange - B.

25 Imag 20 15 B 10 5 Real D -5 Х -20 -25 -16 -12 -10 02

2.

From the figure, we can see that the poles of A are:

= CPM Fum- - 15.8 + 27j

-Swn = –15.8; wd = wn = wnV1 - 52 = 27 V1 - 52 = 27/15.8 = 1.71 5 5 = 0.5048

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