English
Hindi

Question

Download Solution PDF

The equation of motion for a single degree of freedom system is

4ẍ + 9ẋ + 16x = 0

The critical damping coefficient for the system is

This question was previously asked in
ESE Mechanical 2016 Paper 2: Official Paper
Attempt in App
View all UPSC IES Papers >
  1. 32
  2. 16
  3. 8
  4. 4

Answer (Detailed Solution Below)

Option 2 : 16
Free Tests
View all Free tests >
Free
ST 1: UPSC ESE (IES) Civil - Building Materials
20 Qs. 40 Marks 24 Mins
Start Now

Detailed Solution

Download Solution PDF

Concept:

Equation of motion for a single degree of freedom system with one damper is given by

Critical damping coefficient, cc = 2ζmωn

Calculation:

Given:

ζ = 1 (for critically damped)

The equation of motion for a single degree of freedom system is

4ẍ + 9ẋ + 16x = 0

Comparing it with the equation of motion

m = 4 kg, c = 9 N/m/s, k = 16 N/m

Download Solution PDF
Latest UPSC IES Updates

Last updated on Jul 2, 2025

-> ESE Mains 2025 exam date has been released. As per the schedule, UPSC IES Mains exam 2025 will be conducted on August 10. 

-> UPSC ESE result 2025 has been released. Candidates can download the ESE prelims result PDF from here.

->  UPSC ESE admit card 2025 for the prelims exam has been released. 

-> The UPSC IES Prelims 2025 will be held on 8th June 2025.

-> The selection process includes a Prelims and a Mains Examination, followed by a Personality Test/Interview.

-> Candidates should attempt the UPSC IES mock tests to increase their efficiency. The UPSC IES previous year papers can be downloaded here.

Exams Tests Super Practice

More Damping Coefficient and Damping Ratio Questions

Q1.Ratio of actual to critical damping coefficient in forced vibrations is known as ________.
Q2.A single degree of freedom spring-mass-damper system has mass 2 kg and stiffness 200 N/m with damping coefficient of 10 Ns/m. What will be damping ratio?
Q3.Large military field guns which come to their initial position after firing in the shortest possible time are
Q4.The transmissibility ratio will be equal to unity for all values of damping factor, if \(\dfrac{\omega }{{{\omega _n}}}\;\) is equal to:
Q5.Which of the following is the response of a spring-mass-damper with under-damping?  
Q6.A body of mass 100 kg with natural frequency 10 rad/sec has critical damping:
Q7.In the viscous damped vibration, the logarithmic decrement value over five cycles is found to be 8.11. What is viscous damping factor of vibratory system?
Q8.The equation of motion of a spring-mass-damper system is given by \(\frac{{{d^2}x}}{{d{t^2}}} + 3\frac{{dx}}{{dt}} + 9x = 10\sin \left( {5t} \right)\) The damping factor for the system is
Q9.The equation of motion for a single degree of freedom system is 4ẍ + 9ẋ + 16x = 0 The critical damping coefficient for the system is

More Forced Vibration Questions

Q1.Which of the following is TRUE for vibration of a mechanical system
Q2.For a single degree of freedom viscous damped system, if the frequency ratio is greater than √2, it implies that:
Q3.A vibrating system having a mass of 30 kg is supported by 4 springs, each having a stiffness of k. The system runs at 420 rpm. If only 10% of the shaking force is allowed to be transmitted to the supporting structure, then the value of stiffness k will be close to:
Q4.For forced damped vibration system, the vibration isolation is possible only when
Q5.Seismic vibrations are measured with
Q6.The amplitude ratio of two successive oscillations of a damped vibratory system is
Q7.When ω/ωn = 1, the transmissibility is where ω = frequency of excitation, rad/s ωn = Natural frequency, rad/s
Q8.In vibration isolation system, if ω/ωn is less than \(\sqrt{2}\), then for all values of the damping factor, the transmissibility will be where ω-circular frequency of excitation in rad/s and ωn = Natural circular frequency, rad/s
Q9.Dynamic Magnification Factor is computed as:
Q10.Ratio of actual to critical damping coefficient in forced vibrations is known as ________.
Suggested Test Series
View All >
UPSC ESE (IES) Civil Mock Test Series
116 Total Tests with 1 Free Tests
Start Free Test
UPSC ESE (IES) Prelims Paper 1 Mock Test Series
54 Total Tests with   1 Free Tests
Start Free Test

NTPC Diploma Trainee Important Links

Eligibility CriteriaSalary and Job profileAdmit CardSyllabus and Exam PatternAnswer KeyCut Off

More Mechanical Vibrations Questions

Q1.At a certain speed, revolving shafts tend to vibrate violently in transverse direction. This speed is known as
Q2.Which of the following is TRUE for vibration of a mechanical system
Q3.A cantilever beam of cross section area 'A', moment of Inertia 'T' and length 'L' is having natural frequency ω1. If the beam is accidently broken into two halves, the natural frequency of the remaining cantilever beam ω2 will be such that
Q4.A mass of 2 kg is hung from the ceiling by a helical spring. When hung, the spring suffers an extension of 100 mm. If the mass is slightly displaced downward and released, it will oscillate at a frequency of (acceleration due gravity at the location is 10 m/s2)
Q5.The whirling speed of a rotating shaft depends on its _________.
Q6.For a single degree of freedom viscous damped system, if the frequency ratio is greater than √2, it implies that:
Q7.A suspended mass of 10 kg completes 40 oscillations in 20 seconds in a single-degree damped vibrating system. The stiffness of the spring is approximately _________. 
Q8.Consider a uniform shaft of length L fixed at its upper end and carrying a disc of the moment of inertia I at its lower end. The disc is twisted about the vertical axis and released. 'fa' is the natural frequency of the system when the shaft is assumed as massless, and 'fb' is the natural frequency of the system when the shaft is considered of the same moment of inertia as that of the disc. Find the ratio fa/fb.
Q9.A vibrating system having a mass of 30 kg is supported by 4 springs, each having a stiffness of k. The system runs at 420 rpm. If only 10% of the shaking force is allowed to be transmitted to the supporting structure, then the value of stiffness k will be close to:
Q10.A spring-mass system consists of a mass of 5 kg and two springs of stiffness 8 N/mm and 12 N/mm. The system is arranged in different manners, that is: (i) the mass is suspended at the bottom of two springs in series, and (ii) the mass is fixed between two springs. The ratio of natural frequencies of the case (ii) to those of case (i) is approximately ___________. 
Testbook Edu Solutions Pvt. Ltd.
1st & 2nd Floor, Zion Building,
Plot No. 273, Sector 10, Kharghar,
Navi Mumbai - 410210
support@testbook.com
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
Copyright © 2014-2022 Testbook Edu Solutions Pvt. Ltd.: All rights reserved
User PolicyTermsPrivacy
Hot Links： teen patti master king teen patti master golden india teen patti gold download