Testbook Logo
Exams SuperCoaching Test Series Skill Academy
More
English
Hindi

Question

Download Solution PDF

For a second order system having its transfer function as:

H(s) = 25 / (s2 + 8s + 25)

Find the damping ratio.

This question was previously asked in
HPCL Engineer Electrical 11 Aug 2021 Official Paper
Download PDF Attempt Online
View all HPCL Engineer Papers >
  1. 0.6
  2. 0.5
  3. 0.4
  4. 0.8

Answer (Detailed Solution Below)

Option 4 : 0.8
Free Tests
View all Free tests >
Free
Environmental Engineering for All AE/JE Civil Exams Mock Test
10.6 K Users
20 Questions 20 Marks 20 Mins
Start Now

Detailed Solution

Download Solution PDF

Concept:

The transfer function of a 2nd order is given by:

\(H(s) = {ω^2_n \over s^2+\space2ζω_ns+\space ω^2_n }\)

where, ωn = Natural frequency

ζ = Damping ratio

Calculation:

Given, \(H(s) = {25 \over s^2\space+\space8s\space+\space 25 }\)

ωn2 = 25

ωn = 5

2ζωn = 8

\(ζ = {8 \over 2\times\omega_n}\)

\(ζ = {8 \over 2\times5}\)

ζ = 0.8

Download Solution PDF
Latest HPCL Engineer Updates

Last updated on Jun 2, 2025

-> HPCL Engineer 2025 notification has been released on June 1, 2025.

-> A total of 175 vacancies have been announced for the HPCL Engineer post in Civil, Electrical, Mechanical, Chemical engineering.

-> HPCL Engineer Online application will be activated from 1st June 2025 to 30th June 2025.

-> Candidates with a full-time engineering discipline in the relevant stream are eligible to apply.

-> The selection will be based on a Computer Based Test Group Task and/or Interview. Prepare for the exam using HPCL Engineer Previous Year Papers.

More Time Domain Specifications Questions

Q1.In the circuit shown switch is closed at t = 0. The time constant of the circuit is :
Q2.Consider a causal second-order system with the transfer function \(G(s)=\frac{1}{s^2+2 s+1}\) with a unit-step \(R(s)=\frac{1}{s}\) as an input. Let c(s) be the corresponding output. The time taken by the system output c(t) to reach 94% of its steady-state value \(\displaystyle \lim _{t \rightarrow \infty} c(t)\), rounded off to two decimal places, is
Q3.The nature of the response shown below is:
Q4.When the damping ratio ζ (zeta) lies in between 0 < ζ < 1, then the circuit classification comes under:
Q5.The time required for the response curve to reach and stay within the specified 2-5% of final value is referred to as :
Q6.Consider a standard second order system given by \(\frac{w_{n}^{2}}{s^{2}+2\zeta w_{n} s+w_{n}^{2}}\). The correlation between the maximum peak overshoot in the time domain and the resonant peak in the frequency domain exists when:
Q7.Consider the second order closed loop control system. If the characteristics polynomial is given by S2 + 3S + 2 = 0, then the control system is:
Q8.A second order system has only imaginary conjugate poles, what is the damping factor value for this system?
Q9.For a second order underdamped control system, the settling time for the 5% band is given by the equation:
Q10.Consider a standard second order system given by \(\frac{w_{n}^{2}}{s^{2}+2 \zeta w_{n} s+w_{n}^{2}}\). The speed of response is measured in time and frequency domain by:

More Time Response Analysis Questions

Q1.A unity feedback system is characterized by the open-loop transfer function \(G(s)=\frac{100}{s(5 s+10)(2 s+10)}\) The steady-state errors for unit-step and unit-ramp inputs are :
Q2.In the circuit shown switch is closed at t = 0. The time constant of the circuit is :
Q3.Consider a causal second-order system with the transfer function \(G(s)=\frac{1}{s^2+2 s+1}\) with a unit-step \(R(s)=\frac{1}{s}\) as an input. Let c(s) be the corresponding output. The time taken by the system output c(t) to reach 94% of its steady-state value \(\displaystyle \lim _{t \rightarrow \infty} c(t)\), rounded off to two decimal places, is
Q4.The output of a standard second-order system for a unit-step input is given as \(y(t)=1-\frac{2}{\sqrt{3}} e^{-t} \cos \left(\sqrt{3} t-\frac{\pi}{6}\right)\). What is the transfer function of the system?
Q5.A second-order system has a closed-loop transfer function given by \(G(s)=\frac{25}{s^2+8 s+25}\). The settling time for 5 percentage band in tolerance error is
Q6.A second-order system has a transfer function given by \(G(s)=\frac{25}{s^2+8 s+25}\). If the system, initially at rest, is subjected to a unit-step input at t = 0, the second peak in the response will occur at
Q7.Steady state error is the value of error signal when:
Q8.A closed loop system is shown in the figure where k > 0 and α > 0. The steady state error due to a ramp input (R(s) = α/s2) is given by 
Q9.The nature of the response shown below is:
Q10.When the damping ratio ζ (zeta) lies in between 0 < ζ < 1, then the circuit classification comes under:
Suggested Test Series
View All >
Vocabulary Master for All Government Exams Mock Test
309 Total Tests with 1 Free Tests
Start Free Test
AE & JE Electrical Engg. Exams Previous Year Papers Mock Test
276 Total Tests with   9 Free Tests
Start Free Test

More Control Systems Questions

Q1.A unity feedback system is characterized by the open-loop transfer function \(G(s)=\frac{100}{s(5 s+10)(2 s+10)}\) The steady-state errors for unit-step and unit-ramp inputs are :
Q2.In the circuit shown switch is closed at t = 0. The time constant of the circuit is :
Q3.The loop transfer function of a closed-loop control system is given as : \(G(s) H(s)=\frac{k(s+1)}{s(s+2)(s+3)}\) The centroid of the asymptotes in root locus is :
Q4.For a control system having fourteen poles and two zeros, the slope in its magnitude plot for high frequency asymptote will be :
Q5.The Routh Array is as below : \(\begin{array}{lllll} \mathrm{S}^{6} & 1 & 8 & 20 & 16 \\ \mathrm{S}^{5} & 2 & 12 & 16 & \\ \mathrm{S}^{4} & 2 & 12 & 16 & \\ \mathrm{S}^{3} & 0 & 0 & & \end{array}\) The row of zero of this array will be replaced by coefficients of 
Q6.The number of roots in the left half of the s-plane for a system having characteristic equations : s3 + 5s2 + 7s + 3 = 0 is : 
Q7.Explain the pattern and trend of public expenditure on social services in the post reforms period in India. To what extent this has been in consonance with achieving objective of inclusive growth? 
Q8.The Nyquist criterion for stability states that an amplifier is unstable if the Nyquist curve encloses the -1 + j0 point, and the amplifier is stable if the curve does not enclose this point. If Aβ
Q9.The phase margin of a system with the open-loop transfer function \(G(s) H(s)=\frac{1-s}{(s+1)(s+2)}\) is
Q10.The phase margin of a system having the loop transfer function \(G(s) H(s)=\frac{2 \sqrt{3}}{s(s+1)}\) is
Important Exams
Super Coaching
Exams
Test Series
Previous Year Papers
Objective Questions
Testbook Edu Solutions Pvt. Ltd.
1st & 2nd Floor, Zion Building,
Plot No. 273, Sector 10, Kharghar,
Navi Mumbai - 410210
[email protected]
Toll Free:1800 833 0800
Office Hours: 10 AM to 7 PM (all 7 days)
Company
About usCareers We are hiringTeach Online on TestbookPartnersMediaSitemap
Products
Test SeriesTestbook PassOnline CoursesOnline VideosPracticeBlogRefer & EarnBooks
Our Apps
Follow us on
Copyright © 2014-2022 Testbook Edu Solutions Pvt. Ltd.: All rights reserved
User PolicyTermsPrivacy
Get Free Access Now
Hot Links： teen patti master king teen patti gold online teen patti octro 3 patti rummy