Mechanical vibration MCQ Mechanical Engineering

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About Mechanical vibration

Following are some of the multiple choice questions on the Mechanical vibration with answers that will help the students in developing their knowledge.

Mechanical vibration MCQ

1. The natural frequency of an undamped vibrating system is 100 rad/s A damper with a damping factor of 0.8 is introduced into the system, The frequency of vibration of the damped system, rad/s, is

  • 60
  • 75
  • 80
  • 100

2. The transmitted force through a mass-spring damper system will be greater than the transmitted through rigid supports for all values of damping factors, if the frequency ratio ωωn\frac{\omega}{\omega_n}ωn​ω​ is

  • more than  2\sqrt{2}2​  
  • less than  2\sqrt{2}2​  
  • equal to one
  • less than one

3. For a harmonically excited single degree of freedom viscous damped system, which one of the following is correct?

  • Inertia force leads damping force by 90° while damping force leads spring force by 90°
  • Spring force leads damping force by 90° while damping force leads inertia force by 180°
  • Spring force and damping force are in phase, and inertia force leads them by 90°
  • Spring force and inertia force are in phase, and damping force leads them by 90°

4. In a spring-mass system, the mass is 0.1 kg and the stiffness of the spring is 1 kN/m. By introducing a damper, the frequency of oscillation is found to be 90% of the original value. What is the damping coefficient of the damper (Ns/m)

  • 1.2
  • 3.4
  • 8.7
  • 12

5. Consider the following methods: 1. Energy method 2. Equilibrium method 3. Rayleigh's method Which of these methods can be used for determining the natural frequency of the free vibrations?

  • 1 & 2
  • 2 & 3
  • 3 & 1
  • 1, 2 & 3

6. In a forced vibration with viscous damping, maximum amplitude occurs when forced frequency is

  • Equal to natural frequency
  • Slightly less than natural frequency
  • Slightly greater than natural frequency
  • Zero

7. A uniform cantilever beam undergoes transverse vibrations. The number of natural frequencies associated with the beam is

  • 1
  • 10
  • 100
  • ∞\infty∞

8. When a shaking force is transmitted through the spring, damping becomes less than the applied force when the ratio of its frequency to the natural frequency is greater than

  • 0.25
  • 0.5
  • 1
  • 2\sqrt{2}2​

9. The rotor of a turbine is generally rotated at

  • the critical speed
  • a speed much below the critical speed
  • a speed much above the critical speed
  • a speed having no relation to critical speed

10. For steady-state forced vibrations, the phase lag at resonance is

  • 0°0\degree0°
  • 45°45\degree45°
  • 90°90\degree90°
  • 180°180\degree180°

11. Rotating shafts tend of vibrate violently at whirling speeds because

  • the shafts are rotating at very high speeds
  • Bearing centre line coincides with the shaft axis
  • The system is unbalanced
  • Resonance is caused due to the heavy weight of the rotor

12. A slender shaft supported on two bearings at its ends carries a disc with an eccentricity e from the axis of rotation. The critical speed of the shaft is N. If the disc is replaced by a second one of same weight but mounted with an eccentricity 2e, critical speed of the shaft in the second case is

  • N2\frac{N}{2}2N​
  • N2\frac{N}{\sqrt{2}}2​N​
  • NNN
  • 2N2N2N

13. A mass M attached to a light spring oscillates with a period of 2 sec. If the mass is increased by 2 kg, the period increases by 1sec. The value of M (in Kg) is

  • 1
  • 1.6
  • 2
  • 2.4

14. A viscous damping system with free vibrations will be critically damped if the damping factor is

  • Zero
  • Less than one
  • Equal to one
  • Greater than one

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

  • two
  • equal to the number of rotor plus one
  • equal to the number of rotors
  • equal to the number of rotors minus one

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

  • maximum angular velocity
  • maximum angular displacement
  • maximum angular acceleration
  • zero angular displacement

17. A shaft has two heavy rotors mounted on it. The transverse natural frequencies, considering each of the rotors separately, are 100 cycles/sec and 200 cycles/sec respectively. The lowest critical speed is

  • 5367 rpm
  • 6000 rpm
  • 9360 rpm
  • 12000rpm

18. The natural frequency of a spring-mass system on earth is N .The natural frequency of this system on the moon is

  • N
  • 0.408N
  • 0.204N
  • 0.167N

19. In a system subjected to damped forced vibrations, the ratio of maximum displacement to the static deflection is known as

  • Critical damping ratio
  • Damping factor
  • Logarithmic decrement
  • Magnification factor

20. When the mass of a critically damped single degree of freedom system is deflected from its equilibrium position and released, it will

  • return to equilibrium position without oscillation
  • Oscillate with increasing time period
  • Oscillate with decreasing amplitude
  • Oscillate with constant amplitude.

21. A motion is aperiodic at what value of the damping factor?

  • 1 or above
  • 0.5
  • 0.3
  • 0.866

22. A vibratory system consists of a mass 12.5 kg, a spring of stiffness 1000 N/m, and a dashpot with damping coefficient of 15 Ns/m.The value of critical damping of the system is (Ns/m)

  • 0.223
  • 17.88
  • 71.4
  • 223.6

23. Under logarithmic decrement, the amplitude of successive vibrations are

  • Constant
  • in arithmetic progression
  • In geometric progression
  • in logarithmic progression

24. d2xdt2+36x=0\frac{\text{d}^2x}{\text{d}t^2}+36\text{x=0}dt2d2x​+36x=0 is the equation of free vibrations of a system. Its natural frequency is (Rad/s)

  • 36
  • 6
  • 9
  • 0

25. Logarithmic decrement of a damped single degree of freedom system is δ\deltaδ .If the stiffness of the spring is doubled and the mass is made half, then the logarithmic decrement of the new system will be equal to

  •  δ4\frac{\delta}{4}4δ​  
  •  δ2\frac{\delta}{2}2δ​  
  •  δ\deltaδ  
  •  2δ2\delta2δ  

26. md2xdt2+cdxdt+kx=Fosin⁡(ωt)m\frac{\text{d}^2x}{\text{d}t^2}+c\frac{\text{d}x}{\text{d}t}+kx=F_o\sin\left(\omega t\right)mdt2d2x​+cdtdx​+kx=Fo​sin(ωt) is the equation of motion of a system. The steady state frequency at which the system will oscillate

  •  km\sqrt{\frac{k}{m}}mk​​  
  •  km+ω\sqrt{\frac{k}{m}}+\omegamk​​+ω  
  •  ω\omegaω  
  • Data insufficient

27. Transmissibility is unity at two points. Which one of the following is true for these two points? r=\frac{\omega}{\omega_n}r=ωn​ω​

  • r is zero and  3\sqrt{3}3​  for all values of damping
  • r is zero and  2\sqrt{2}2​  for all values of damping
  • r is unity and  3\sqrt{3}3​  for all values of damping
  • r is unity and  2\sqrt{2}2​  for all values of damping

28. 3d2xdy2+9dxdy+27x=03\frac{\text{d}^2x}{\text{d}y^2}+9\frac{\text{d}x}{\text{d}y}+27x=03dy2d2x​+9dydx​+27x=0 is the equation of motion for a damped viscous vibration. The damping factor is

  • 0.25
  • 0.5
  • 0.75
  • 1.0

29. A vehicle suspension system consists of a spring and a damper. The stiffness of the spring is 3.6 kN/m and constant of the damper is 400 Ns/m. If the mass is 50 kg, then the damping factor and damped natural frequency (in Hz), respectively, are

  • 0.471 and 1.19 Hz
  • 0.471 and 7.48 Hz
  • 0.666 and 1.35 Hz
  • 0.666 and 8.5 Hz

30. A uniform rigid rod of mass m = 1 kg and length L = 1 m is hinged at its centre and laterally supported at one end by a spring of constant k = 300 N/m. The natural frequency ( in rad/s) is

  • 10
  • 20
  • 30
  • 40

31. A vibrating machine is isolated from the floor using springs. If the ratio of excitation frequency of vibration of machine to the natural frequency of the isolation system is equal to 0.5, then transmissibility of ratio of isolation is

  • 1/2
  • 3/4
  • 4/3
  • 2

32. The critical speed of a rotating shaft depends upon

  • Mass
  • stiffness
  • mass and stiffness
  • mass, stiffness and eccentricity

33. A shaft of 50 mm diameter and 1 m length carries a disc which has mass eccentricity equal to 190 microns. The displacement of the shaft at a speed which is 90% of critical speed in microns is

  • 810
  • 900
  • 800
  • 820

34. An automotive engine weighing 240 kg is supported on four springs with linear characteristics. Each of the front two springs have a stiffness of 16 MN/m while the stiffness of each rear spring is 32 MN/m. The engine speed (in rpm), at which resonance is likely to occur, is

  • 6040
  • 3020
  • 1424
  • 955

35. A spring-mass suspension has a natural frequency of 40 rad/s. What is the damping ratio required if it is desired to reduce this frequency to 20 rad/s by adding a damper to it?

  • 32\frac{\sqrt{3}}{2}23​​
  • 12\frac{1}{2}21​
  • 12\frac{1}{\sqrt{2}}2​1​
  • 14\frac{1}{4}41​

36. A machine mounted on a single coil spring has a period of free vibration of T. If the spring is cut into four equal parts and placed in parallel and the machine is mounted on them, then the period of free vibration of the new system will become.

  • 16T
  • 4T
  • T4\frac{T}{4}4T​
  • T16\frac{T}{16}16T​

37. If air resistance is neglected, while it is executing small oscillations the acceleration of the bob of a simple pendulum at the mid-point of its swing will be

  • zero
  • a minimum but not equal to zero
  • a maximum
  • not determinable unless the length of the pendulum and the mass of the bob are known

38. The static deflection of a shaft under a flywheel is 4 mm. Take g = 10m/s2 . What is the critical speed in rad/s ?

  • 50
  • 20
  • 10
  • 5

39. A machine of 250 kg mass is supported on springs of total stiffness 100 kN/m. Machine has an unbalanced rotating force of 350 N at speed of 3600 rpm. Assuming a damping factor of 0.15, the value of transmissibility ratio is

  • 0.0531
  • 0.9922
  • 0.0162
  • 0.0028

40. If the length of the cantilever beam is halved, then natural frequency of the mass M at the end of this, cantilever beam of negligible mass is increased by a factor of

  • 2
  • 4
  • 8
  •  8\sqrt{8}8​  

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