Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2019 Summer 6th Sem New 2160109 Theory Of Vibration Previous Question Paper
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?VI(NEW) ? EXAMINATION ? SUMMER 2019
Subject Code:2160109 Date:16/05/2019
Subject Name:Theory of Vibration
Time:10:30 AM TO 01:00 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) Explain Simple Harmonic Motion with an example. 03
(b) Explain the Energy method for vibration analysis. 04
(c) Define the following terms:
Degrees of Freedom, Natural Frequency, Node, Damping Ratio,
Resonance, Time Period, Damped natural frequency
07
Q.2 (a) Define Damping. Explain Damped and Undamped Vibration. 03
(b) Explain series and parallel spring connections. 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) Determine the natural frequency of torsional pendulum having
following characteristics:
Length of the rod: 1 m
Diameter of the rod (d): 5 mm
Diameter of the rotor (D): 0.2 m
Mass of the rotor: 2 kg
Modulus of rigidity (G): 0.83 x 10
11
N/m
2
07
Q.3 (a) How many ways you can control the vibration? 03
(b) Show that in case of a Coloumb damping the reduction in amplitude
takes place by an amount of 4F/k in one complete cycle.
04
(c)
Conclude the response of Overdamped, Underdamped and Critically
damped system by solving differential equation of undamped free
vibration with neat sketches.
07
OR
Q.3 (a) State the applications of critical damping in real life examples. 03
(b) Explain Logarithmic decrement. 04
(c) An electric motor is supported on a spring and a dashpot. The spring
has stiffness of 6400 N/m and a dashpot offers resistance of 500 N
at a velocity of 4 cm/sec. The unbalanced mass of 0.5 kg rotates at 5
cm radius and the total mass of vibratory system is 20 kg. The motor
runs at 400 rpm. Determine: Damping factor, amplitude of vibration
and phase angle, resonant speed and resonant amplitude, forces
exerted by the spring and dashpot on the motor.
07
Q.4 (a) State the role of spring mass and damper in any vibratory system. 03
(b) Discuss working of a Vibrometer. 04
(c) Derive the solution of equation of motion for forced vibration for
spring mass damper system under the influence of harmonic force.
07
OR
Q.4 (a) Show the response of transient and steady state vibration. 03
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1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?VI(NEW) ? EXAMINATION ? SUMMER 2019
Subject Code:2160109 Date:16/05/2019
Subject Name:Theory of Vibration
Time:10:30 AM TO 01:00 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) Explain Simple Harmonic Motion with an example. 03
(b) Explain the Energy method for vibration analysis. 04
(c) Define the following terms:
Degrees of Freedom, Natural Frequency, Node, Damping Ratio,
Resonance, Time Period, Damped natural frequency
07
Q.2 (a) Define Damping. Explain Damped and Undamped Vibration. 03
(b) Explain series and parallel spring connections. 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) Determine the natural frequency of torsional pendulum having
following characteristics:
Length of the rod: 1 m
Diameter of the rod (d): 5 mm
Diameter of the rotor (D): 0.2 m
Mass of the rotor: 2 kg
Modulus of rigidity (G): 0.83 x 10
11
N/m
2
07
Q.3 (a) How many ways you can control the vibration? 03
(b) Show that in case of a Coloumb damping the reduction in amplitude
takes place by an amount of 4F/k in one complete cycle.
04
(c)
Conclude the response of Overdamped, Underdamped and Critically
damped system by solving differential equation of undamped free
vibration with neat sketches.
07
OR
Q.3 (a) State the applications of critical damping in real life examples. 03
(b) Explain Logarithmic decrement. 04
(c) An electric motor is supported on a spring and a dashpot. The spring
has stiffness of 6400 N/m and a dashpot offers resistance of 500 N
at a velocity of 4 cm/sec. The unbalanced mass of 0.5 kg rotates at 5
cm radius and the total mass of vibratory system is 20 kg. The motor
runs at 400 rpm. Determine: Damping factor, amplitude of vibration
and phase angle, resonant speed and resonant amplitude, forces
exerted by the spring and dashpot on the motor.
07
Q.4 (a) State the role of spring mass and damper in any vibratory system. 03
(b) Discuss working of a Vibrometer. 04
(c) Derive the solution of equation of motion for forced vibration for
spring mass damper system under the influence of harmonic force.
07
OR
Q.4 (a) Show the response of transient and steady state vibration. 03
2
(b) Show the working of Frahm?s Tachometer to determine the
frequency of vibration body.
04
(c) Explain the torsional vibration of two rotor system. Determine the
natural frequencies and mode shapes.
07
Q.5 (a) State the importance of Vibration isolation. Explain different
materials used for vibration isolation.
03
(b) Explain the working of Vibration absorber with neat sketch. 04
(c) Using Lagrange?s equation, determine the natural frequency of the
system shown in fig. 1.
07
OR
Q.5 (a) Compare the vibration absorber with vibration isolator. 03
(b) Explain Rayleigh?s method for finding natural frequency of
transverse vibration of beams.
04
(c) Determine the two natural frequencies of vibration and the ratio of
amplitudes of motion m1 & m2 for the two mode of vibration for the
system shown in fig.2 Take m1= 1.5 kg , m2= 0.80 kg, k1=k2= 40
N/m.
07
fig.1
fig.2
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This post was last modified on 20 February 2020