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Question 3 For each of the following systems: a) b) $G_1(s) = \frac{28}{s^2 + 21s + 98}$ $G_2(s) = \frac{8}{0.5s^2 + 4s + 8}$ i) Determine the values of the gain K, undamped natural frequency $\omega_n$, and damping ratio $\zeta$. (3 marks) ii) Determine the damping of the system, i.e. whether it is underdamped, critically- damped, or overdamped. (1 mark) iii) Determine the output of the system in the time-domain due to a step response with magnitude 3. (6 marks) *Note: 10 marks are allocated for each part of Questions 3(a) and 3(b), re- spectively. Therefore, the total marks allocated for Question 3(a) and 3(b): 10 marks x 2 = 20 marks.

          Question 3
For each of the following systems:
a)
b)
$G_1(s) = \frac{28}{s^2 + 21s + 98}$
$G_2(s) = \frac{8}{0.5s^2 + 4s + 8}$
i) Determine the values of the gain K, undamped natural frequency $\omega_n$, and damping
ratio $\zeta$.
(3 marks)
ii) Determine the damping of the system, i.e. whether it is underdamped, critically-
damped, or overdamped.
(1 mark)
iii) Determine the output of the system in the time-domain due to a step response with
magnitude 3.
(6 marks)
*Note: 10 marks are allocated for each part of Questions 3(a) and 3(b), re-
spectively. Therefore, the total marks allocated for Question 3(a) and 3(b): 10
marks x 2 = 20 marks.

Question 3
For each of the following systems:
a)
b)
G1(s) = (28)/(s^2 + 21s + 98)
G2(s) = (8)/(0.5s^2 + 4s + 8)
i) Determine the values of the gain K, undamped natural frequency , and damping
ratio ζ.
(3 marks)
ii) Determine the damping of the system, i.e. whether it is underdamped, critically-
damped, or overdamped.
(1 mark)
iii) Determine the output of the system in the time-domain due to a step response with
magnitude 3.
(6 marks)
*Note: 10 marks are allocated for each part of Questions 3(a) and 3(b), re-
spectively. Therefore, the total marks allocated for Question 3(a) and 3(b): 10
marks x 2 = 20 marks.

Added by Marisa H.

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