Given the equation
ai(t)+ 1 + —z(t) = u(t)
where a = 28 and ry = 7 are fixed, and u(t) is a generic forcing function, do the following:
(a) (10 points): Determine the value(s) of /3 that yield (1) real unique roots, (2) real repeated roots, (3) complex conjugate roots. (b) (10 points): Select a value of 11 such that there are complex conjugate roots (not purely imaginary), and the system is stable. (Stability is important!) What are the roots (where are they located)?
Sample Solution
