Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2019 Winter 6th Sem New 2160109 Theory Of Vibration Previous Question Paper
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ? VI (New) EXAMINATION ? WINTER 2019
Subject Code: 2160109 Date: 09/12/2019
Subject Name: Theory of Vibration
Time: 02:30 PM TO 05:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
MARKS
Q.1 (a) Define Vibration. Which organs of human body are having low
frequency oscillations? Which organs of human body are having high
frequency oscillations?
03
(b) Derive the equation to calculate natural frequency of Simple pendulum. 04
(c) Find the sum of two harmonic motions of equal amplitude but of slightly
different frequencies. Discuss the beats phenomenon that results from
this sum.
07
Q.2 (a) Define: Degree of freedom. What is DOF for cantilever beam? Why? 03
(b) Derive the equation of natural frequency for a disc of mass moment of
inertia I suspended on shaft of length L with diameter d, when the disc is
given an angular twist of ?.
04
(c) Show that for finding natural frequency of a spring mass system, the
mass of the spring can be taken into account by adding one-third its mass
to the main mass.
07
OR
(c) A vibrating system consists of a mass of 50 kg, a spring of stiffness of
30 kN/m and a damper. The damping provided is only 20 % of the critical
value.
Determine:
i) Damping factor
ii) Critical damping coefficient
iii) Natural frequency of damped vibration
iv) Logarithmic decay
v) Ratio of two consecutive amplitudes
07
Q.3 (a) Why are soldiers ordered to break their marching steps while crossing a
bridge?
03
(b) Explain vibration isolation. Name the various materials for the same. 04
(c) Write down the equation of motion for damped free vibration. Derive the
solution for that equation.
07
OR
Q.3 (a) Represent 3+ i6 in exponential form. 03
(b)
Define Transmissibility. Briefly explain the concept of support motion.
04
(c) Derive the solution: ?? ?? ? + c ?? ? + kx = F sin ?t. 07
Q.4 (a) Define: Overshooting. Why guns are designed based on critical
damping?
03
FirstRanker.com - FirstRanker's Choice
1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ? VI (New) EXAMINATION ? WINTER 2019
Subject Code: 2160109 Date: 09/12/2019
Subject Name: Theory of Vibration
Time: 02:30 PM TO 05:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
MARKS
Q.1 (a) Define Vibration. Which organs of human body are having low
frequency oscillations? Which organs of human body are having high
frequency oscillations?
03
(b) Derive the equation to calculate natural frequency of Simple pendulum. 04
(c) Find the sum of two harmonic motions of equal amplitude but of slightly
different frequencies. Discuss the beats phenomenon that results from
this sum.
07
Q.2 (a) Define: Degree of freedom. What is DOF for cantilever beam? Why? 03
(b) Derive the equation of natural frequency for a disc of mass moment of
inertia I suspended on shaft of length L with diameter d, when the disc is
given an angular twist of ?.
04
(c) Show that for finding natural frequency of a spring mass system, the
mass of the spring can be taken into account by adding one-third its mass
to the main mass.
07
OR
(c) A vibrating system consists of a mass of 50 kg, a spring of stiffness of
30 kN/m and a damper. The damping provided is only 20 % of the critical
value.
Determine:
i) Damping factor
ii) Critical damping coefficient
iii) Natural frequency of damped vibration
iv) Logarithmic decay
v) Ratio of two consecutive amplitudes
07
Q.3 (a) Why are soldiers ordered to break their marching steps while crossing a
bridge?
03
(b) Explain vibration isolation. Name the various materials for the same. 04
(c) Write down the equation of motion for damped free vibration. Derive the
solution for that equation.
07
OR
Q.3 (a) Represent 3+ i6 in exponential form. 03
(b)
Define Transmissibility. Briefly explain the concept of support motion.
04
(c) Derive the solution: ?? ?? ? + c ?? ? + kx = F sin ?t. 07
Q.4 (a) Define: Overshooting. Why guns are designed based on critical
damping?
03
2
(b) Write short note on Torsionally equivalent shaft. 04
(c) Write a short note on Lagrange?s equation. 07
OR
Q.4 (a) Give the difference between vibration isolation & vibration absorber. 03
(b) A vibrometer indicates 2% error n measurement and its natural frequency
is 5 Hz. If the frequency that can be measured is 40 Hz. Find the value
of damping factor.
04
(c) For Two rotor system prove that angular displacements of the rotors are
inversely proportional to their moment of inertia with neat sketch.
07
Q.5 (a) Define:
1. Fundamental mode of vibration
2. Principal mode of vibration
3. Normal mode of vibration
03
(b) Define: Whirling Speed of shaft. Explain critical speed of shaft carrying
single rotor (Without damping).
04
(c)
What is the working principle of vibration measuring instruments? Explain the
working of anyone instrument designed on low natural frequency.
07
OR
Q.5 (a) Define: Multi degree of freedom system. Name the various methods used
to analyze these systems.
03
(b) Explain the working of vibration absorber with respect to electricity
transmission lines.
04
(c)
What is the working principle of Frequency measuring instruments? With neat
sketch explain working of Frahm tachometer.
07
*************
FirstRanker.com - FirstRanker's Choice
This post was last modified on 20 February 2020