problem 2 15 points solve the following two simultaneous differential

Question

Problem 3 [28 points, 4 points each] Consider the continuous-time linear time-invariant
system with transfer-function:
Answer the following questions:
a. What is the differential equation associated with the above transfer-function?
b. Calculate the poles and zeros of G(s).
c. Is G(s) asymptotically stable?
d. Use the bilinear transformation (aka Tustin transformation)
S =
2 z 1
Tsz + 1
to calculate the corresponding discretized transfer-function Ga(z).
e. Calculate the poles and zeros of Ga(z).
f. Is Ga(z) asymptotically stable? (A discrete-time system is asympotically stable if the poles
satisfy |pi|< 1.)
g. Use a computer program or calculator to sketch the magnitude and the phase of the frequency
response G(jw). Now sketch the magnitude and phase of Gd(es) as a function of w when
Ts = {0.01, 0.1, 1}s. Compare all the obtained responses. What is the role of Ts?