Chapter: Single Degree of Freedom System- Free Vibration
1.

Which type of vibrations are also known as transient vibrations?

A. Undamped vibrations
B. Damped vibrations
C. Torsional vibrations
D. Transverse vibrations
Answer» B. Damped vibrations
2.

During transverse vibrations, shaft is subjected to which type of stresses?

A. Tensile stresses
B. Torsional shear stress
C. Bending stresses
D. All of the above
Answer» C. Bending stresses
3.

What are deterministic vibrations?

A. Vibrations caused due to known exciting force
B. Vibrations caused due to unknown exciting force
C. Vibrations which are aperiodic in nature
D. None of the above
Answer» A. Vibrations caused due to known exciting force
4.

Which of the following vibrations are classified according to magnitude of actuating force?

A. Torsional vibrations
B. Deterministic vibrations
C. Transverse vibrations
D. All of the above
Answer» B. Deterministic vibrations
5.

In which type of vibrations, amplitude of vibration goes on decreasing every cycle?

A. Damped vibrations
B. Undamped vibrations
C. Both a. and b.
D. None of the above
Answer» A. Damped vibrations
6.

The resonant frequency of a mass-spring system depends upon ________

A. stiffness
B. surface density
C. depth of air space
D. all of the above
Answer» D. all of the above
7.

Calculate equivalent stiffness of the spring for the system shown below, which has spring stiffness of 3000 N/m

A. 1000 N/m
B. 2250 N/m
C. 2000 N/m
D. None of the above
Answer» B. 2250 N/m
8.

Which of the following is incorrect regarding inertia force?

A. Imaginary force
B. Acts upon a rigid body
C. Brings the body to equilibrium
D. Same direction as of accelerating force
Answer» D. Same direction as of accelerating force
9.

D-Alembert’s principle is used for which of the following?

A. Change static problem into a dynamic problem
B. Change dynamic problem to static problem
C. To calculate moment of inertia of rigid bodies
D. To calculate angular momentum of a system of masses
Answer» B. Change dynamic problem to static problem
10.

Determine logarithmic decrement, if the amplitude of a vibrating body reduces to 1/6th in two cycles.

A. 0.223
B. 0.8958
C. 0.389
D. None of the above
Answer» B. 0.8958
11.

Calculate logarithmic decrement if damping factor is 0.33.

A. 1.36
B. 3.23
C. 5.16
D. 2.19
Answer» D. 2.19
12.

In damped free vibrations, which parameters indicate vibrations?

A. Natural frequency
B. Rate of decay of amplitude
C. Both a. and b.
D. None of the above
Answer» B. Rate of decay of amplitude
13.

What is meant by critical damping coefficient?

A. Frequency of damped free vibrations is less than zero
B. The motion is aperiodic in nature
C. Both a. and b.
D. None of the above
Answer» B. The motion is aperiodic in nature
14.

Which of the following relations is true for viscous damping?

A. Force α relative displacement
B. Force α relative velocity
C. Force α (1 / relative velocity)
D. None of the above
Answer» B. Force α relative velocity
15.

Which among the following is the value of static deflection (δ) for a fixed beam with central point load?

A. (Wl3) /(192 EI)
B. (Wl2) /(192 EI)
C. (Wl3) /(384 EI)
D. None of the above
Answer» A. (Wl3) /(192 EI)
16.

According to which method, maximum kinetic energy at mean position is equal to maximum potential energy at extreme position?

A. Energy method
B. Rayleigh's method
C. Equilibrium method
D. All of the above
Answer» B. Rayleigh's method
17.

The motion of a system executing harmonic motion with one natural frequency is known as _______

A. principal mode of vibration
B. natural mode of vibration
C. both a. and b.
D. none of the above
Answer» C. both a. and b.
18.

Fluid resistance causes damping which is known as ______

A. Resistance damping
B. Fluid damping
C. Viscous damping
D. Liquid damping
Answer» C. Viscous damping
19.

In which direction does the accelerating force acts?

A. Opposite to the motion
B. Along the motion
C. Perpendicular to motion
D. Variable
Answer» B. Along the motion
20.

The time interval after which the motion is repeated itself is known as ___________ .

A. Time period
B. Cycle
C. Frequency
D. Isolation
Answer» A. Time period
21.

Frequency of vibrations is usually expressed in

A. Number of cycles per hour
B. Number of cycles per minute
C. Number of cycles per second
D. None of these
Answer» C. Number of cycles per second
22.

The motion completed during one time period is known as _______.

A. Period of vibration
B. Cycle
C. Frequency
D. All of the above
Answer» B. Cycle
23.

Which of the following is a type of free vibration?

A. Longitudinal vibrations
B. Transverse vibrations
C. Torsional vibrations
D. A, B and C
Answer» D. A, B and C
24.

In a spring-mass system, which of the following force is not considered?

A. Spring force
B. Damping force
C. Accelerating force
D. A and B
Answer» B. Damping force
25.

The periodic time is given by _______.

A. ω / 2 π
B. 2 π / ω
C. 2 π × ω
D. π/ω
Answer» B. 2 π / ω
26.

The velocity of a particle moving with simple harmonic motion is _______ at the mean position.

A. Zero
B. Minimum
C. Maximum
D. None of the mentioned
Answer» C. Maximum
27.

The maximum acceleration of a particle moving with simple harmonic motion is ____.

A. ω
B. ω.r
C. ω / 2 π
D. 2 π / ω
Answer» B. ω.r
28.

At the mean position, the potential energy of the system is _______.

A. Zero
B. Minimum
C. Maximum
D. None of the mentioned
Answer» A. Zero
29.

In a spring-mass-damper system, which of the following force is considered?

A. Spring force
B. Damping force
C. Accelerating force
D. All of the above
Answer» D. All of the above
30.

Frequency is equal to ______.

A. Time period
B. 1/time period
C. ω * time period
D. ω /time period
Answer» B. 1/time period
31.

When the body vibrates under the influence of external force, then the body is said to be under ___________ .

A. Free vibrations
B. Natural vibrations
C. Forced vibrations
D. Damped vibrations
Answer» C. Forced vibrations
32.

A vertical spring-mass system has a mass of 0.5 kg and an initial deflection of 0.2 cm. Find the spring stiffness.

A. 345 N/m
B. 245 N/m
C. 3452 N/m
D. 2452 N/m
Answer» D. 2452 N/m
33.

A system has a mass of 0.5 kg and spring stiffness of 2452 N/m. Find the natural frequency of the system.

A. 5.14 Hz
B. 9.14 Hz
C. 11.14 Hz
D. 28.14 Hz
Answer» C. 11.14 Hz
Chapter: Free Vibration
34.

What is meant by node point?

A. The point at which amplitude of vibration is maximum
B. The point at which amplitude of vibration is minimum
C. The point at which amplitude of vibration is zero
D. None of the above
Answer» C. The point at which amplitude of vibration is zero
35.

The motion of a system executing harmonic motion with one natural frequency is known as _______

A. principal mode of vibration
B. natural mode of vibration
C. both a. and b.
D. none of the above
Answer» C. both a. and b.
36.

Which of the following statements is/are true?

A. Torsional vibrations do not occur in a three rotor system, if rotors rotate in same direction
B. Shaft vibrates with maximum frequency when rotors rotate in same direction
C. Zero node behavior is observed in rotors rotating in opposite direction
D. All of the above
Answer» A. Torsional vibrations do not occur in a three rotor system, if rotors rotate in same direction
37.

In the diagram shown below, if rotor X and rotor Z rotate in same direction and rotor Y rotates in opposite direction, then specify the type of node vibration.

A. Three node vibration
B. Two node vibration
C. Single node vibration
D. None of the above
Answer» B. Two node vibration
38.

What is the total number of nodes formed in a three rotor system if the rotors at one of the ends and the one in the middle rotate in the

A. 0
B. 1
C. 2
D. 3
Answer» B. 1
39.

In a multi-rotor system of torsional vibration maximum number of nodes that can occur is:

A. Two
B. Equal to the number of rotor plus one
C. Equal to the number of rotors
D. Equal to the number of rotors minus one
Answer» D. Equal to the number of rotors minus one
40.

During torsional vibration of a shaft, the node is characterized by

A. Maximum angular velocity
B. Maximum angular displacement
C. Maximum angular acceleration
D. Zero angular displacement
Answer» D. Zero angular displacement
41.

The mass moment of inertia of the two motors in a two rotor system are 100 kgm2 and 10 kgm2 the length of the shaft of uniform

A. 80 cm
B. 90 cm
C. 100 cm
D. 110 cm
Answer» C. 100 cm
42.

What is the number of nodes in a shaft carrying three rotors?

A. zero
B. 2
C. 3
D. 4
Answer» B. 2
43.

Consider the following statements: Two rotors mounted on a single shaft can be considered to be equivalent to a geared-shaft system having two rotors provided 1. The kinetic energy of the equivalent system is equal to that of the original system. 2. The strain energy of the equivalent system is equal to that of the original system. 3. The shaft diameters of the two systems are equal. Which of these statements are correct?

A. 1, 2 and 3
B. 1 and 2
C. 2 and 3
D. 1 and 3
Answer» A. 1, 2 and 3
44.

Two rotors A and B are connected to the two ends of a shaft of uniform diameter. The mass moment of inertia of rotor A about the

A. 1/5 m
B. 4/5 m
C. 1/25 m
D. 16/25 m
Answer» A. 1/5 m
45.

Which one of the following is correct for a shaft carrying two rotors at its ends?

A. It has no node
B. It has one node
C. It has two nodes
D. It has three nodes
Answer» B. It has one node
46.

A system, which is free from both the ends

A. Definite system
B. Semidefinite system
C. Both a and b
D. None of the above
Answer» B. Semidefinite system
47.

A system, which is fixed from one end or both the ends is referred as

A. Definite system
B. Semidefinite system
C. Both a and b
D. None of the above
Answer» A. Definite system
48.

In a system with different shaft parameters, the longest shaft is taken for calculations.

A. TRUE
B. FALSE
Answer» B. FALSE
49.

In a system with different shaft parameters ------------- is taken which depends on the length and diameters of each shaft.

A. Equivalent shaft length
B. length of first shaft
C. lrngth of intermediate shaft
D. None of these
Answer» A. Equivalent shaft length
50.

From the following data, calculate the location of node from the left end of shaft (l1).l1=0.6m, l2=0.5m, l3=0.4m d1=0.095m, d2=0.06m, d3=0.05m Ma = 900 Kg, Mb = 700 Kg ka = 0.85m, kb = 0.55m

A. 0.855m
B. 0.795m
C. 0.695m
D. 0.595m
Answer» A. 0.855m
51.

For a vibration system having different shaft parameters, calculate which of the following cannot be the diameter of the equivalent shaft if the diameters of shafts in m are: 0.05, 0.06, 0.07.

A. 0.05
B. 0.06
C. 0.07
D. 0.08
Answer» D. 0.08
52.

A single cylinder oil engine works with a three rotor system, the shaft length is 2.5m and 70mm in diameter, the middle rotor is at a distance 1.5m from one end. Calculate the free torsional vibration frequency for a single node system in Hz if the mass moment of inertia of rotors in Kg-m2 are: 0.15, 0.3 and 0.09. C=84 kN/mm2

A. 171
B. 181
C. 191
D. 201
Answer» A. 171
53.

At a nodal point in the shaft, the frequency of vibration is _________

A. Zero
B. Double than at the ends
C. Minimum
D. Maximum
Answer» A. Zero
54.

For a gearing system, the equivalent system is made consisting of two rotors. How many nodes will this new equivalent system will have?

A. 0
B. 1
C. 2
D. 3
Answer» B. 1
55.

In a gearing system, pump speed is one third of the motor. Shaft from motor is 6 cm in diameter and 30cm long, the impellar shaft is 10cm diameter and 60cm long. Mass moment of inertia is 1500 Kgm2, C = 80Gn/m2. Neglecting the inertia of shaft and gears calculate the frequency of free torsional vibrations in Hz.

A. 4.7
B. 5.7
C. 4.5
D. 5.5
Answer» A. 4.7
56.

When inertia of gearing is taken into consideration, then which of the following should be taken into account.

A. Addition of rotor
B. Addition of gear
C. Addition of shaft
D. Addition of pump
Answer» A. Addition of rotor
57.

Consider P and Q as the shaft having two rotors at the end of it, what is the point N known as in the given figure?

A. Node
B. Elastic point
C. Inelastic point
D. Breaking point
Answer» A. Node
58.

For occurrence of free torsional vibration which of the condition is necessary?

A. Rotors moving in same direction
B. Rotors having same frequency
C. Rotors having different frequency
D. Rotors rotate in the same sense
Answer» B. Rotors having same frequency
59.

n the given figure if N is the node then NQ acts as which of the following system?

A. Single rotor system
B. Two rotor system
C. Three rotor system
D. Four rotor system
Answer» A. Single rotor system
60.

Keeping the mass moment of inertia of both the shafts in a two rotor system same, if the length of one shaft is doubled what should be the effect on the length of other shaft?

A. Doubled
B. Halved
C. Constant
D. increased to 4 times
Answer» A. Doubled
61.

In the figure given below, the points N1 and N2 are known as_______

A. Nodes
B. Elastic points
C. Inelastic points
D. Breaking points
Answer» A. Nodes
62.

In which of the following condition torsional vibration will not take place, considering 3 rotors A, B and C. A is rotating in clockwise direction.

A. B in clockwise C in anticlockwise
B. C in clockwise B in anticlockwise
C. B and C in clockwise
D. B and C in anticlockwise
Answer» C. B and C in clockwise
63.

For occurrence of free torsional vibration in a three rotor system which of the condition is necessary?

A. Rotors moving in same direction
B. Rotors having same frequency
C. Rotors having different frequency
D. Rotors rotate in the same sense
Answer» B. Rotors having same frequency
64.

A vertical circular disc is supported by a horizontal stepped shaft as shown below. Determine equivalent length of shaft when equivalent diameter is 20 mm.

A. 1.559 m
B. 0.559 m
C. 0.633 m
D. None of the above
Answer» B. 0.559 m
65.

In a three rotor system, for the middle rotor, if the stiffness of both the length either side of the rotor is increased to two times what will

A. Remains constant
B. Decreases by two times
C. Increases by two times
D. Increases by 4 times
Answer» C. Increases by two times
66.

A single cylinder oil engine works with a three rotor system, the shaft length is 2.5m and 70mm in diameter, the middle rotor is at a distance 1.5m from one end. Calculate the free torsional vibration frequency for a two node system in Hz if the mass moment of inertia of rotors in Kg-m2 are: 0.15, 0.3 and 0.09. C=84 kN/mm2

A. 257
B. 281
C. 197
D. 277
Answer» D. 277
67.

Increasing which of the following factor would result in increase of free torsional vibration?

A. Radius of gyration
B. Mass moment of inertia
C. Polar moment of inertia
D. Length
Answer» C. Polar moment of inertia
68.

The frequency of the free torsional vibration depends on…....

A. number of rotors
B. the number of nodes
C. Both a and b
D. Only b
Answer» C. Both a and b
69.

For a two rotor system, the mass moment of inertia of one shaft(A) is twice the other(B), then what is the relation between the length of the shafts.

A. 2L(A) = L(B)
B. L(A) = 2L(B)
C. L(A) = L(B)
D. 2L(A) = 3L(B)
Answer» A. 2L(A) = L(B)
Chapter: Balancing
70.

Which of the following is true for centrifugal force causing unbalance?

A. Direction changes with rotation
B. Magnitude changes with rotation
C. Direction and magnitude both change with rotation
D. Direction and magnitude both remain unchanged with rotation
Answer» A. Direction changes with rotation
71.

If the unbalanced system is not set right then.

A. Static forces develop
B. Dynamic forces develop
C. Tangential forces develop
D. Radial forces develop
Answer» A. Static forces develop
72.

What is the effect of a rotating mass of a shaft on a system?

A. Bend the shaft
B. Twist the shaft
C. Extend the shaft
D. Compress the shaft
Answer» A. Bend the shaft
73.

In a revolving rotor, the centrifugal force remains balanced as long as the centre of the mass of the rotor lies ___________

A. Below the axis of shaft
B. On the axis of the shaft
C. Above the axis of shaft
D. Away from the axis of shaft
Answer» B. On the axis of the shaft
74.

Often an unbalance of forces is produced in rotary or reciprocating machinery due to the ______

A. Centripetal forces
B. Centrifugal forces
C. Friction forces
D. Inertia forces
Answer» D. Inertia forces
75.

The mass used to balance the mass defect is known as ______

A. Balancing mass
B. Defect mass
C. Replacement mass
D. Fixing mass
Answer» A. Balancing mass
76.

In balancing of single-cylinder engine, the rotating unbalance is ____________

A. completely made zero and so also the reciprocating unbalance
B. completely made zero and the reciprocating unbalance is partially reduced
C. partially reduced and the reciprocating unbalance is completely made zero
D. partially reduced and so also the reciprocating unbalance
Answer» B. completely made zero and the reciprocating unbalance is partially reduced
77.

Let the disturbing mass be 100 kg and the radius of rotation be 10 cm and the rotation speed be 50 rad/s, then calculate the centrifugal force in kN.

A. 50
B. 25
C. 50000
D. 25000
Answer» B. 25
78.

Which of the following statement is correct?

A. In any engine, 100% of the reciprocating masses can be balanced dynamically
B. In the case of balancing of multicylinder engine, the value of secondary force is higher than the value of the primary force
C. In the case of balancing of multimass rotating systems, dynamic balancing can be directly started without static balancing done to the system
D. none of the mentioned
Answer» C. In the case of balancing of multimass rotating systems, dynamic balancing can be directly started without static balancing done to the system
79.

If all the masses are in one plane, then what is the maximum no. of masses which can be placed in the same plane?

A. 3
B. 4
C. 6
D. No limitation
Answer» D. No limitation
80.

Which of the following statements is correct about the balancing of a mechanical system?

A. If it is under static balance, then there will be dynamic balance also
B. If it is under dynamic balance, then there will be static balance also
C. Both static as well as dynamic balance have to be achieved separately
D. None of the mentioned
Answer» C. Both static as well as dynamic balance have to be achieved separately
81.

In a locomotive, the ratio of the connecting rod length to the crank radius is kept very large in order to

A. minimize the effect of primary forces
B. minimize the effect of secondary forces
C. have perfect balancing
D. start the locomotive conveniently
Answer» B. minimize the effect of secondary forces
82.

Secondary forces in reciprocating mass on engine frame are

A. of same frequency as of primary forces
B. twice the frequency as of primary forces
C. four times the frequency as of primary forces
D. none of the mentioned
Answer» B. twice the frequency as of primary forces
83.

For a V-twin engine, which of the following means can be used to balance the primary forces?

A. Revolving balance mass
B. Rotating balance mass
C. Reciprocating balance mass
D. By the means of secondary forces
Answer» A. Revolving balance mass
84.

The primary unbalanced force is maximum when the angle of inclination of the crank with the line of stroke is

A.
B. 90°
C. 180°
D. 360°
Answer» C. 180°
85.

From the following data of a 60 degree V-twin engine, determine the minimum value for primary forces in newtons:Reciprocating mass per cylinder = 1.5 Kg Stroke length = 10 cm Length of connecting rod = 25 cm Engine speed = 2500 rpm

A. 7711
B. 4546
C. 2570
D. 8764
Answer» C. 2570
86.

From the following data of a 60 degree V-twin engine, determine the maximum value for primary forces in newtons:Reciprocating mass per cylinder = 1.5 Kg Stroke length = 10 cm Length of connecting rod = 25 cm Engine speed = 2500 rpm

A. 7711
B. 4546
C. 2570
D. 8764
Answer» A. 7711
87.

In the given figure, m1=10 Kg, m2=30Kg and m=50 Kg, if r=0.3m, l=1m, find l2 = 0.5m, find r1 in m.

A. 1.5
B. 0.75
C. 3
D. 6
Answer» B. 0.75
88.

From the given data, find the balancing mass’s inclination in degrees if r=0.2m required in the same plane.Masses = 200kg, 300kg, 240 kg, 260Kg,

A. 201.48
B. 200.32
C. 210.34
D. 202.88
Answer» A. 201.48
89.

Which of the following statements are associated with complete dynamic balancing of rotating systems? 1. Resultant couple due to all inertia forces is zero. 2. Support reactions due to forces are zero but not due to couples . 3. The system is automatically statically balanced. 4. Centre of masses of the system lies on the axis of rotation.

A. 1, 2, 3 and 4
B. 1, 2, and 3 only
C. 2, 3 and 4 only
D. 1, 3 and 4 only
Answer» D. 1, 3 and 4 only
90.

A V-twin engine has the cylinder axes at 90 degrees and the connecting rods operate a common crank. The reciprocating mass per cylinder is 11.5 kg and the crank radius is 7.5 cm. The length of the connecting rod is 0.3 m. If the engine is rotating at the speed is 500 r.p.m. What is the value of maximum resultant secondary force in Newtons?

A. 736
B. 836
C. 936
D. 636
Answer» B. 836
91.

Let the centrifugal force in kN be 25 and the radius of rotation be 20 cm and the rotation speed be 50 rad/s, then calculate the mass defect in Kg.

A. 50
B. 25
C. 50000
D. 25000
Answer» A. 50
92.

In a multicylinder inline engine, each imaginary secondary crank with a mass attached to the crankpin is inclined to the line of stroke at which angle?

A. Twice the angle of crank
B. Half the angle of crank
C. Thrice the angle of crank
D. Four times the angle of crank
Answer» A. Twice the angle of crank
93.

In order to achieve stability, the sum of secondary forces and secondary couples must be ------- and their respective polygons must be …......

A. Zero, Closed
B. one, Open
C. Zero, open
D. one, closed
Answer» A. Zero, Closed
94.

For the secondary balancing of the engine, which of the condition is necessary?

A. Secondary force polygon must be close
B. Secondary force polygon must be open
C. Primary force polygon must be close
D. Primary force polygon must be open
Answer» A. Secondary force polygon must be close
95.

The numerical values of the secondary forces and secondary couples couples may be obtained by considering the ___________

A. Revolving mass
B. Reciprocating mass
C. Translating mass
D. Rotating mass
Answer» A. Revolving mass
96.

Which of the following is the correct expression for secondary force?

A. m𝜔^2r.cos2θ/n
B. m 𝜔^2r.sin2θ/n
C. m𝜔^2r.tan2θ/n
D. m𝜔^2r.cosθ/n
Answer» A. m𝜔^2r.cos2θ/n
97.

A V-twin engine has the cylinder axes at 90 degrees and the connecting rods operate a common crank. The reciprocating mass per cylinder is 23 kg and the crank radius is 7.5 cm. The length of the connecting rod is 0.3 m. If the engine is rotating at the speed is 500 r.p.m. What is the value of maximum resultant secondary force in Newtons?

A. 7172
B. 1672
C. 1122
D. 1272
Answer» B. 1672
98.

A V-twin engine has the cylinder axes at 90 degrees and the connecting rods operate a common crank. The reciprocating mass per cylinder is 34.5 kg and the crank radius is 7.5 cm. The length of the connecting rod is 0.3 m. If the engine is rotating at the speed is 500 r.p.m. What is the value of maximum resultant secondary force in kN?

A. 2.238
B. 2.508
C. 2.754
D. 2.908
Answer» B. 2.508
99.

From the given data, find the balancing mass in Kg if r=0.2m required in the same plane.Masses = 200kg, 300kg, 240 kg, 260Kg, corresponding radii = 0.2m, 0.15m, 0.25m and 0.3m.Angles between consecutive masses = 45, 75 and 135 degrees.

A. 116
B. 58
C. 232
D. 140
Answer» A. 116
100.

Let the disturbing mass be 200 kg and the radius of rotation be 20 cm and the rotation speed be 50 rad/s, then calculate the centripetal force in kN.

A. -50
B. -25
C. -100
D. -2500
Answer» C. -100
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