Match the transfer functions of the second-order systems with the nature of the system given below. Transfer functions Nature of system P. \frac{15}{s^{2}+5 s+15} I. Overdamped Q. \frac{25}{s^{2}+10 s+25} II. Critically damped R. \frac{35}{s^{2}+18 s+35} III. Underdamped

Correct Answer is : P-III, Q-II, R-I

GATE Electrical Engineering (EE) 2018 Solved Paper

Question : 22 of 65

Marks: +1, -0

Match the transfer functions of the second-order systems with the nature of the system given below.

Solution:

P=\;{15}/{s^{2}+5 s+15}

ω_{n}=√{15}=3.872 {rad} {/} {s}

2 ζ ω_{n}=5

ζ=0.645

So, P is underdamped.

Q=\;{25}/{s^{2}+10 s+25}

ω_{n}=√{25}=5 {rad} {/} {s}

2 ζ ω_{n}=10

ζ=1

So,

Q

is critically damped.

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