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MCQOPTIONS
This section includes 51 Mcqs, each offering curated multiple-choice questions to sharpen your Mechanical Vibrations knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
A thin uniform rod of length L and mass M is free to rotate in vertical plane as shown in figure below. The time period of its oscillation in vertical plane is |
| A. | \(T = 2\;\pi \sqrt {\frac{l}{g}} \) |
| B. | \(T = 2\;\pi \sqrt {\frac{3l}{4g}} \) |
| C. | \(T = 2\;\pi \sqrt {\frac{2l}{3g}} \) |
| D. | \(T = 2\;\pi \sqrt {\frac{l}{2g}} \) |
| Answer» D. \(T = 2\;\pi \sqrt {\frac{l}{2g}} \) | |
| 2. |
Four linear elastic springs are connected to mass ‘M’ as shown in Figure. The natural frequency of the system is |
| A. | \(\frac{{\left( {\sqrt {\frac{{4{\rm{k}}}}{{3{\rm{m}}}}} } \right)}}{{\left( {2{\rm{\pi }}} \right)}}\) |
| B. | \(\frac{{\left( {\sqrt {\frac{{4{\rm{k}}}}{{\rm{m}}}} } \right)}}{{\left( {2{\rm{\pi }}} \right)}}\) |
| C. | \(\frac{{\left( {\sqrt {\frac{{\rm{k}}}{{4{\rm{m}}}}} } \right)}}{{\left( {2{\rm{\pi }}} \right)}}\) |
| D. | \(\frac{{\left( {\sqrt {\frac{{3{\rm{k}}}}{{4{\rm{m}}}}} } \right)}}{{\left( {2{\rm{\pi }}} \right)}}\) |
| Answer» E. | |
| 3. |
A simple spring mass vibrating system has a natural frequency of fn. If the spring stiffness is halved and mass is doubled, then the natural frequency will become |
| A. | \(\frac {f_n}{2}\) |
| B. | 2fn |
| C. | 4fn |
| D. | 8fn |
| Answer» B. 2fn | |
| 4. |
Critical or whirling speed is the speed at which the shaft tends to vibrate violently in ________. |
| A. | Transverse direction |
| B. | Longitudinal direction |
| C. | Linear direction |
| D. | None of these |
| Answer» B. Longitudinal direction | |
| 5. |
An elastic beam, simply supported at the ends, carries a concentrated mass at the middle of its length. If the natural frequency of the beam neglecting the weight is ωn, considering the weight of the beam the natural frequency of the system will be |
| A. | greater than ωn |
| B. | less than ωn |
| C. | zero |
| D. | equal to ωn, as the natural frequency is independent of concentrated load |
| Answer» C. zero | |
| 6. |
A body is vibrating at 10 vibrations/second in Simple Harmonic Motion of 10 cm amplitude. The maximum velocity in cm/sec can be _____. |
| A. | 100π |
| B. | 50π |
| C. | 200π |
| D. | 100 |
| Answer» D. 100 | |
| 7. |
A pendulum clock calibrated at earth’s surface will read on the surface of the moon (acceleration due to gravity on the moon is 1/6th of that on earth) |
| A. | Identically the same |
| B. | \(\sqrt {6}\) times faster |
| C. | \(\sqrt {6}\) times slower |
| D. | 6 times faster |
| Answer» D. 6 times faster | |
| 8. |
A shaft has two rotors mounted on it. The transverse natural frequency considering each rotor separately is 100 Hz and 200 Hz respectively. The lowest critical speed is |
| A. | 13000 rpm |
| B. | 5367 rpm |
| C. | 6450 rpm |
| D. | 9343 rpm |
| Answer» C. 6450 rpm | |
| 9. |
In the two-rotor system shown in the figure, (I1 < I2), a node of vibration is situated |
| A. | Between I1 and I2 but nearer to I1 |
| B. | Between I1 and I2 but nearer to I2 |
| C. | Exactly in the middle of the shaft |
| D. | Nearer to I1 but outside |
| Answer» C. Exactly in the middle of the shaft | |
| 10. |
Considering massless rigid rod and small oscillations, the natural frequency (in rad/s) of vibration of the system shown in the figure is |
| A. | \(\sqrt {\frac{{400}}{1}}\) |
| B. | \(\sqrt {\frac{{400}}{2}}\) |
| C. | \(\sqrt {\frac{{400}}{3}}\) |
| D. | \(\sqrt {\frac{{400}}{4}}\) |
| Answer» E. | |
| 11. |
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 spring constant k = 300 N/m. The natural frequency ωn in rad/s is |
| A. | 10 |
| B. | 20 |
| C. | 30 |
| D. | 40 |
| Answer» D. 40 | |
| 12. |
An automotive engine having a mass of 135 kg is supported on 4 springs with linear characteristics. Each of the 2 front springs have stiffness of 3 MN/m while the stiffness of each of 2 rear springs is 4.5 MN/m. The engine speed (RPM) at which resonance is likely to occur is |
| A. | 103/(6π) |
| B. | 1/(6π) |
| C. | 104/(π) |
| D. | 103/(3) |
| Answer» D. 103/(3) | |
| 13. |
A mass m is attached to two identical springs having spring constant k as shown in the figure. The natural frequency ω of this single degree of freedom system is |
| A. | \(\sqrt {\frac{{2k}}{m}} \) |
| B. | \(\sqrt {\frac{k}{m}} \) |
| C. | \(\sqrt {\frac{k}{{2m}}} \) |
| D. | \(\sqrt {\frac{{4k}}{m}} \) |
| Answer» B. \(\sqrt {\frac{k}{m}} \) | |
| 14. |
If a mass 'M' oscillation a spring having mass 'm' and stiffness 'S', then the natural frequency of the system is |
| A. | \(\frac S{m_s}\) |
| B. | \(\frac Sm\) |
| C. | \(\sqrt{\frac{S}{m+\frac{{{m}_{s}}}{3}}}\) |
| D. | \(\sqrt{\frac{S}{m+{{{m}_{s}}}{}}}\) |
| Answer» D. \(\sqrt{\frac{S}{m+{{{m}_{s}}}{}}}\) | |
| 15. |
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 1 sec. The value of m is |
| A. | 1 kg |
| B. | 1.6 kg |
| C. | 2 kg |
| D. | 2.4 kg |
| Answer» C. 2 kg | |
| 16. |
A rigid uniform rod AB of length L and mass m is hinged at C such that AC = L/3, CB = 2L/3. Ends A and B are supported by springs of spring constant k. The natural frequency of the system is given by |
| A. | \(\sqrt {\frac{K}{{2m}}}\) |
| B. | \(\sqrt {\frac{K}{m}}\) |
| C. | \(\sqrt {\frac{{2K}}{m}}\) |
| D. | \(\sqrt {\frac{{5K}}{m}}\) |
| Answer» E. | |
| 17. |
A simple spring – mass vibrating system has a natural frequency of ‘ωn’. If the spring stiffness is halved and the mass is doubled, then the natural frequency will become |
| A. | ωn / 2 |
| B. | 2ωn |
| C. | 4ωn |
| D. | 8ωn |
| Answer» B. 2ωn | |
| 18. |
A block whose mass m = 4 kg is fastened to a spring with a spring constant k = 64 N/m. The block is pulled from its equilibrium position on a frictionless surface and released. The period of the resulting motion in seconds is |
| A. | π/4 |
| B. | π/2 |
| C. | 2π |
| D. | π |
| Answer» C. 2π | |
| 19. |
Determine meq and keq for the system in below Fig., when X, the downward displacement of the block, measured from the system’s equilibrium position, is used as the generalized coordinate. Take I as the M.I. of the wheel. |
| A. | \({K_{eq}} = 3k,{m_{eq}} = m + \frac{I}{{{r^2}}}\) |
| B. | \({K_{eq}} = 3k,{m_{eq}} = m{r^2} + I\) |
| C. | \({K_{eq}} = 3k,{m_{eq}} = m - \frac{I}{{{r^2}}}\) |
| D. | \({K_{eq}} = \frac{k}{3},{m_{eq}} = m + \frac{I}{{{r^2}}}\) |
| Answer» B. \({K_{eq}} = 3k,{m_{eq}} = m{r^2} + I\) | |
| 20. |
Consider the system shown in the figure. A rope goes over a pulley. A mass, m is hanging from the rope. A spring of stiffness, k is attached at one end of the rope. Assume rope is inextensible, massless and there is no slip between pulley and rope.The pulley radius is r and its mass moment of inertia is J. Assume that the mass is vibrating harmonically about its static equilibrium position. The natural Frequency of the system is |
| A. | \(\sqrt{\frac{kr^2}{J + mr^2}}\) |
| B. | \(\sqrt{k/m}\) |
| C. | \(\sqrt{\frac{kr^2}{J - mr^2}}\) |
| D. | \(\sqrt{\frac{kr^2}{J }}\) |
| Answer» B. \(\sqrt{k/m}\) | |
| 21. |
Consider a single degree-of-freedom system with viscous damping excited by a harmonic force. At resonance, the phase angle (in degree) of the displacement with respect to the exciting force is |
| A. | 0 |
| B. | 45 |
| C. | 90 |
| D. | 135 |
| Answer» D. 135 | |
| 22. |
A machine component of 90 kg mass needs to be held in position using three springs as shown below. The spring constants k1, k2 and k3 are 4, 4 and 8 N/m respectively. Find the natural frequency of the system in rad/sec. |
| A. | 0.33 |
| B. | 0.42 |
| C. | 0.13 |
| D. | 3 |
| Answer» B. 0.42 | |
| 23. |
As compared to the time period of a simple pendulum on the earth, its time period on the moon will be |
| A. | 5 times higher |
| B. | 6 times lower |
| C. | √6 times higher |
| D. | √6 times lover |
| Answer» D. √6 times lover | |
| 24. |
A disc of mass m is attached to a spring of stiffness k as shown in the figure. The disc rolls without slipping on a horizontal surface. The natural frequency of vibration of the system is |
| A. | \(\frac{1}{{2\pi }}\sqrt {\frac{k}{m}}\) |
| B. | \(\frac{1}{{2\pi }}\sqrt {\frac{{2k}}{m}}\) |
| C. | \(\frac{1}{{2\pi }}\sqrt {\frac{{2k}}{{3m}}}\) |
| D. | \(\frac{1}{{2\pi }}\sqrt {\frac{{3k}}{{2m}}} \) |
| Answer» D. \(\frac{1}{{2\pi }}\sqrt {\frac{{3k}}{{2m}}} \) | |
| 25. |
Periodic time of simple pendulum is given by |
| A. | \(2\pi \sqrt {\frac{l}{g}}\) |
| B. | \(2\pi \sqrt {\frac{g}{l}} \) |
| C. | \(\frac{1}{{2\pi }}\sqrt {\frac{g}{l}} \) |
| D. | \(\frac{1}{{2\pi }}\sqrt {\frac{l}{g}}\) |
| Answer» B. \(2\pi \sqrt {\frac{g}{l}} \) | |
| 26. |
A cantilever beam of cross section area ‘A’, moment of Inertia I and length ‘L’ is having natural frequency ω1. If the beam is accidentally broken into two halves, the natural frequency of the remaining cantilever beam ω2 will be such that |
| A. | ω2 < ω1 |
| B. | ω2 > ω1 |
| C. | ω2 = ω1 |
| D. | Cannot be obtained from the given data |
| Answer» C. ω2 = ω1 | |
| 27. |
A solid steel shaft transmits 40 kW of power at a speed of \(\frac{75}{\pi}\)Hz. The internal torque needed in the shaft is |
| A. | \(\frac{812}{3}~Nm\) |
| B. | \(\frac{800}{3}~Nm\) |
| C. | \(\frac{541}{2}~Nm\) |
| D. | \(\frac{400}{3}~Nm\) |
| Answer» C. \(\frac{541}{2}~Nm\) | |
| 28. |
A slender uniform rigid bar of mass m is hinged at O and supported by two springs, with stiffnesses 3k and k, and a damper with damping coefficient c, as shown in the figure. For the system to be critically damped, the ratio \(\frac{c}{\sqrt {km} }\) should be |
| A. | 2 |
| B. | 4 |
| C. | 2√7 |
| D. | 4√7 |
| Answer» E. | |
| 29. |
If two nodes are observed at a frequency of 1800 rpm during whirling of a simply supported long slender rotating shaft, the first critical speed of the shaft in rpm is |
| A. | 200 |
| B. | 450 |
| C. | 600 |
| D. | 900 |
| Answer» B. 450 | |
| 30. |
A diver of mass 100 kg is standing at the tip of a spring board of negligible mass. The natural frequency of the spring board with the diver is 1.6 Hz. What is the static deflection at the tip of the spring board when the diver is standing at the tip? |
| A. | 0.1 mm |
| B. | 981 mm |
| C. | 98.1 mm |
| D. | 9.81 mm |
| Answer» D. 9.81 mm | |
| 31. |
A vertical shaft of 100 mm diameter and 1 m length has its upper end fixed at the top. The other end carries a disc of 5000 N and the modulus of elasticity of the shaft material is 2 × 105 N/mm2. Neglecting the weight of the shaft, the frequency of the longitudinal vibrations will be nearly |
| A. | 279.5 Hz |
| B. | 266.5 Hz |
| C. | 253.5 Hz |
| D. | 241.5 Hz |
| Answer» B. 266.5 Hz | |
| 32. |
For the shown figure, if k1 = 10 N/m, k2 = 20 N/m and θ = 30°, then equivalent stiffness of the system will be ________ N/m. |
| A. | 6.66 |
| B. | 12 |
| C. | 15 |
| D. | 30 |
| Answer» E. | |
| 33. |
Consider the arrangement shown in the figure below where J is the combined polar mass moment of inertia of the disc and the shafts. K1, K2 and K3 are the torsional stiffness of the respective shafts. The natural frequency of the torsional oscillation of the disc is given by- |
| A. | \(\sqrt{\frac{K_1\;+\;K_2\;+\;K_3}{J}}\) |
| B. | \(\sqrt{\frac{K_1K_2\;+\;K_2K_3\;+\;K_3K_1}{J(K_1\;+\;K_2)}}\) |
| C. | \(\sqrt{\frac{K_1K_2K_3}{J(K_1K_2\;+\;K_2K_3\;+\;K_3K_1)}}\) |
| D. | \(\sqrt{\frac{K_1K_2\;+\;K_2K_3\;+\;K_3K_1}{J(K_2\;+\;K_3)}}\) |
| Answer» C. \(\sqrt{\frac{K_1K_2K_3}{J(K_1K_2\;+\;K_2K_3\;+\;K_3K_1)}}\) | |
| 34. |
A flexible rotor-shaft system comprises of a 10 kg rotor disc placed in the middle of a massless shaft of diameter 30 mm and length 500 mm between bearings (shaft is being taken mass-less as the equivalent mass of the shaft is included in the rotor mass) mounted at the ends. The bearings are assumed to simulate simply supported boundary conditions. The shaft is made of steel for which the value of E is 2.1 x 1011 Pa. What is the critical speed of rotation of the shaft? |
| A. | 60 Hz |
| B. | 90 Hz |
| C. | 135 Hz |
| D. | 180 Hz |
| Answer» C. 135 Hz | |
| 35. |
A shaft of span 1 m and diameter 25 mm is simply supported at the ends. It carries a 1.5 kN concentrated load at mid-span. If E is 200 GPa, its fundamental frequency will be nearly |
| A. | 3.5 Hz |
| B. | 4.2 Hz |
| C. | 4.8 Hz |
| D. | 5.5 Hz |
| Answer» E. | |
| 36. |
A mass of 2 kg is attached to two identical springs each with stiffness k = 40 kN/m as shown in the figure. Under frictionless condition, the natural frequency of the system in Hz is close to |
| A. | 32 |
| B. | 16 |
| C. | 24 |
| D. | 200 |
| Answer» B. 16 | |
| 37. |
Critical speed is expressed as |
| A. | rotational of shaft in degrees |
| B. | rotation of shaft in radians |
| C. | rotation of shaft in minutes |
| D. | natural frequency of the shaft |
| Answer» E. | |
| 38. |
A block of mass 10 kg is placed at the free end of cantilever beam of length 1 m and second moment of area 300 mm4 Taking Young’s modulus of the beam, material as 200 GPa, the natural frequency of the system is |
| A. | 30√2 rad/s |
| B. | 2√3 rad/s |
| C. | 3√ 2 rad /s |
| D. | 20√3 rad /s |
| Answer» D. 20√3 rad /s | |
| 39. |
A solid disc with radius a is connected to a spring at a point d above the centre of the disc. The other end of the spring is fixed to the vertical wall. The disc is free to roll without slipping on the ground. The mass of the disc is M and the spring constant is K. The polar moment of inertial for the disc about its centre is J = Ma2/2The natural frequency of this system in rad/s is given by |
| A. | \(\sqrt {\frac{{2K{{\left( {a + d} \right)}^2}}}{{3M{a^2}}}} \) |
| B. | \(\sqrt {\frac{{2K}}{{3M}}}\) |
| C. | \(\sqrt {\frac{{2K{{\left( {a + d} \right)}^2}}}{{M{a^2}}}}\) |
| D. | \(\sqrt {\frac{{K{{\left( {a + d} \right)}^2}}}{{M{a^2}}}}\) |
| Answer» B. \(\sqrt {\frac{{2K}}{{3M}}}\) | |
| 40. |
For two springs having same stiffness (S) are in series, the equivalent stiffness would be |
| A. | S/4 |
| B. | S/2 |
| C. | S |
| D. | 2S |
| Answer» C. S | |
| 41. |
A thin uniform rigid bar of length L and mass M is hinged at point O, located at a distance of L/3 from one of its ends. The bar is further supported using spring, each of stiffness k, located at the two ends. A particle of mass \(m = \frac{M}{4}\) is fixed at one end of the bar, as shown in the figure. For small rotations of the bar about O, the natural frequency of the system is |
| A. | \(\sqrt {\frac{{5k}}{M}} \) |
| B. | \(\sqrt {\frac{{5k}}{{2M}}} \) |
| C. | \(\sqrt {\frac{{3k}}{{2M}}} \) |
| D. | \(\sqrt {\frac{{3k}}{M}} \) |
| Answer» C. \(\sqrt {\frac{{3k}}{{2M}}} \) | |
| 42. |
A mass of 100 kg is held between two springs as shown in figure. The natural frequency of vibration of the system in cycles/second is |
| A. | 10/π |
| B. | 5/π |
| C. | ½π |
| D. | 20/π |
| Answer» B. 5/π | |
| 43. |
A weighing machine consists of a 2 kg pan resting on a spring having linear characterises. In this condition of resting on the spring, the length of spring is 200 mm. When a 20 kg mass is placed on the pan, the length of the spring becomes 100 mm. The un-deformed length L in mm and the spring stiffness k in N/m are |
| A. | L = 220, k = 1862 |
| B. | L = 200, k = 1960 |
| C. | L = 210, k = 1960 |
| D. | L = 200, k = 2 |
| Answer» D. L = 200, k = 2 | |
| 44. |
For an underdamped harmonic oscillator, resonance |
| A. | occurs when excitation frequency is greater than undamped natural frequency |
| B. | occurs when excitation frequency is less than undamped natural frequency |
| C. | occurs when excitation frequency is equal to undamped natural frequency |
| D. | never occurs |
| Answer» D. never occurs | |
| 45. |
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 |
| A. | 6040 |
| B. | 3020 |
| C. | 1424 |
| D. | 955 |
| Answer» B. 3020 | |
| 46. |
A concentrated mass m is attached at the centre of a rod of length 2L as shown in the figure. The rod is kept in a horizontal equilibrium position by a spring of stiffness k. For very small amplitude of vibration, neglecting the weights of the rod and spring, the undamped natural frequency of the system is: |
| A. | \(\sqrt {\frac{k}{m}}\) |
| B. | \(\sqrt {\frac{{2k}}{m}}\) |
| C. | \(\sqrt {\frac{k}{{2m}}} \) |
| D. | \(\sqrt {\frac{{4k}}{m}}\) |
| Answer» E. | |
| 47. |
Critical speed of the shaft is affected by |
| A. | diameter and eccentricity of the shaft |
| B. | span and eccentricity of the shaft |
| C. | diameter and span of the shaft: |
| D. | span of the shaft |
| Answer» D. span of the shaft | |
| 48. |
A three rotor system has following number of natural frequencies. |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» C. 3 | |
| 49. |
A mass of 1 kg is attached to two identical springs each with stiffness k = 20 kN/m as shown in the figure. Under frictionless condition, the natural frequency of the system in Hz is close to |
| A. | 32 |
| B. | 23 |
| C. | 16 |
| D. | 11 |
| Answer» B. 23 | |
| 50. |
According to Dunkerley’s empirical equation, the frequency of the transverse vibration of the system of several loads attached to the same shaft is |
| A. | \(\frac{{1}}{{f_n}}=\frac{{1}}{{f_{n_1}}}~+~\frac{{1}}{{f_{n_2}}}~+~\frac{{1}}{{f_{n_3}}}~+~...+\;\frac{{1}}{{f_{n_s}}}\) |
| B. | \(\frac{{1}}{{f_n^2}}=\frac{{1}}{{f_{n_1}^2}}~+~\frac{{1}}{{f_{n_2}^2}}~+~\frac{{1}}{{f_{n_3}^2}}~+~...+\;\frac{{1}}{{f_{n_s}^2}}\) |
| C. | \(f_{n} =f_{n_1}+f_{n_2}+f_{n_3}+.....+f_{n_s}\) |
| D. | None of the above |
| Answer» C. \(f_{n} =f_{n_1}+f_{n_2}+f_{n_3}+.....+f_{n_s}\) | |