• 1. 
    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
  • 2. 
    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​
  • 3. 
    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
  • 4. 
    Under logarithmic decrement, the amplitude of successive vibrations are

  • Constant
  • in arithmetic progression
  • In geometric progression
  • in logarithmic progression
  • 5. 
    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.
  • 6. 
    A motion is aperiodic at what value of the damping factor?

  • 1 or above
  • 0.5
  • 0.3
  • 0.866
  • 7. 
    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
  • 8. 
    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
  • 9. 
    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
  • 10. 
    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
  • 11. 
    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​
  • 12. 
    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
  • 13. 
    A rolling disc of radius ‘r’ and mass ‘m’ is connected to one end of a linear spring of stiffness ‘k’, as shown in the above figure. The natural frequency of oscillation is given by which one of the following?

  • 2K3m\sqrt{\frac{2K}{3m}}3m2K​​
  • Km\sqrt{\frac{K}{m}}mK​​
  • K2m\sqrt{\frac{K}{2m}}2mK​​
  • 2Km\sqrt{\frac{2K}{m}}m2K​​
  • 14. 
    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
  • 15. 
    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
  • 16. 
    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
  • 17. 
    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
  • 18. 
    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
  • 19. 
    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​
  • 20. 
    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°
  • 21. 
    The above figure shows two rotors connected by an elastic shaft undergoing torsional vibration. The rotor (1) has a mass of 2 kg and a diameter of 60 cm, while the rotor (2) has a mass of 1 kg and a diameter of 20 cm. what is the distance L from rotor (2) at which the node of torsional vibration occurs?

  • 36 cm
  • 30 cm
  • 22 cm
  • 18 cm
  • 22. 
    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
  • 23. 
    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
  • 24. 
    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
  • 25. 
    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
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