A stable real linear time-invariant system with single pole at p, has a transfer function H(s)=s2+100sp with a dc gain of 5. The smallest positive frequency, in rad/s at unity gain is closest to:

This question was previously asked in
GATE EE 2020 Official Paper
View all GATE EE Papers >
  1. 8.84
  2. 11.08
  3. 78.13
  4. 122.87

Answer (Detailed Solution Below)

Option 1 : 8.84
Free
GATE EE 2023: Full Mock Test
5.5 K Users
65 Questions 100 Marks 180 Mins

Detailed Solution

Download Solution PDF

Given the transfer function, H(s)=s2+100sp

dc gain = 5

To find the DC gain, put s = 0 in the above transfer function.

100p=5p=20

Now, the transfer function becomes

H(s)=s2+100s+20

Put the value of s = jω in transfer function

H(jω)=ω2+100jω+20

|H(jω)|=ω2+100(ω2+400)

We need to find the frequency ω at |H(jω)| = 1

ω2+100(ω2+400)=1

(ω2+100)2=ω2+400

Let ω2 = t, now the above equation becomes

(100 – t)2 = t + 400

⇒ 10000 + t2 – 200t = t + 400

⇒ t2 – 201t + 9600 = 0

⇒ t = 122.86 and 78.13

⇒ ω = 11.08 and 8.84

The smallest possible frequency = 8.84 rad/sec

Latest GATE EE Updates

Last updated on Feb 19, 2024

-> GATE EE 2024 Answer Key has been released.

-> The exam was held on 3rd, 4th, 10th and 11th February 2024. 

-> Candidates preparing for the exam can refer to the GATE EE Important Questions to improve their preparation for the exam and increase their chances of selection.

-> Candidates must take the GATE EE mock tests to improve their performance.

-> Practice GATE EE Previous Year Papers to kickstart preparation for the upcoming cycle. 

More Steady State Output Questions

More Frequency Response Analysis Questions

Get Free Access Now
Hot Links: teen patti master gold download teen patti master new version teen patti apk download