**Mechanical vibration** is a phenomenon that can occur in any system with mass and stiffness. In most cases, it's an undesired effect that can cause damage to equipment or lead to other safety issues. It's important to be aware of the causes and effects of mechanical vibration so that you can take steps to prevent it from happening in your own systems.

There are two main types of mechanical vibration: free vibration and forced vibration. Free vibration occurs when a system is set in motion by an initial force, but there is no external force acting on the system after that. Forced vibration happens when there is an external force acting on the system while it's in motion. The most common cause of forced vibration is an unbalanced force, such as when a machine is running off-center.

There are several ways to prevent mechanical vibration from occurring in your systems. One way is to make sure that all of the moving parts in your system are properly balanced. Another way is to use damping devices, which absorb energy and reduce vibration. If you're already experiencing vibration, you can try to reduce it by changing the frequency of the vibrating component or by adding mass to the system.

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

### 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}ωnω is

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

### 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)

### 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?

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

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

### 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

### 9. The rotor of a turbine is generally rotated at

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

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

### 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

### 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

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

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

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

### 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

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

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

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

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

### 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)

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

### 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)

### 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

### 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=Fosin(ωt) is the equation of motion of a system. The steady state frequency at which the system will oscillate

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

### 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

### 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

### 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

### 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

### 32. The critical speed of a rotating shaft depends upon

### 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

### 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

### 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?

### 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.

### 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

### 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 ?

### 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

### 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

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