1. A mass of 1 kg is suspended by means of 3 springs as shown in figure. The spring constants K_{1}, K_{2} and K_{3} are respectively 1 kN/m, 3 kN/m and 2 kN/m. The natural frequency of the system is approximately
(a) 46.90 Hz
(b) 52.44 Hz
(c) 60.55 Hz
(d) 77.46 Hz
(2 Mark, 1996)

Ans: b
2. Consider the system of two wagons shown in the figure. The natural frequencies of this system are
(a) 0, \sqrt { \frac { 2k }{ m } }
(b) \sqrt { \frac { k }{ m } } ,\sqrt { \frac { 2k }{ m } }
(c) \sqrt { \frac { k }{ m } } ,\sqrt { \frac { k }{ 2m } }
(d) 0, \sqrt { \frac { k }{ 2m } }
(2 Mark, 1999)

Ans: a
3. As shown in the figure, a mass of 100 kg is held between two springs. The natural frequency of vibration of the system, in cycles/s, is
(a) \frac { 1 }{ 2\pi }
(b) \frac { 5 }{ \pi }
(c) \frac { 10 }{ \pi }
(d) \frac { 20 }{ \pi }
(2 Mark, 2000)

Ans: c
4. In the figure shown, the spring deflects by \delta to position A ( the equilibrium position) when a mass m is kept on it. During free vibration, the mass is at position B at some instant. The change in potential energy of the springmass system from position A to position B is
(a) \frac { 1 }{ 2 } kx^{2}
(b) \frac { 1 }{ 2 } kx^{2} – mgx
(c) \frac { 1 }{ 2 } k(x +δ)
(d) \frac { 1 }{ 2 } kx^{2} + mgx
(1 Mark, 2001)

Ans: b
5. The assembly shown in the figure is composed of two massless rods of length l with two particles, each of mass m. the natural frequency of this assembly for small oscillations is
(a) \sqrt { g/l }
(b) \sqrt { 2g/l(cos\alpha ) }
(c) \sqrt { g/l(cos\alpha ) }
(d) \sqrt { (gcos\alpha )/l }
(2 Mark, 2001)

Ans: d
6. Consider the arrangement shown in the figure below where J is the combined polar mass moment of inertia of the disc and the shafts. K_{1}, K_{2}, K_{3} are the torsional stiffness of the respective shafts. The natural frequency of torsional oscillation of the disc is given by
(a) \sqrt { \frac { { k }_{ 1 }+{ k }_{ 2 }+{ k }_{ 3 } }{ J } }
(b) \sqrt { \frac { { k }_{ 1 }{ k }_{ 2 }+{ k }_{ 2 }{ k }_{ 3 }+{ k }_{ 3 }{ k }_{ 1 } }{ J\left( { k }_{ 1 }{ +k }_{ 2 } \right) } }
(c) \sqrt { \frac { { k }_{ 1 }+{ k }_{ 2 }+{ k }_{ 3 } }{ J\left( { k }_{ 1 }{ k }_{ 2 }+{ k }_{ 2 }{ k }_{ 3 }+{ k }_{ 3 }{ k }_{ 1 } \right) } }
(d) \sqrt { \frac { { k }_{ 1 }{ k }_{ 2 }+{ k }_{ 2 }{ k }_{ 3 }+{ k }_{ 3 }{ k }_{ 1 } }{ J\left( { k }_{ 2 }{ +k }_{ 3 } \right) } }
(1 Mark, 2003)

Ans: b
7. A flexible rotorshaft 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 massless 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 ×10^{11 }Pa. What is the critical speed of rotation of the shaft?
(a) 60 Hz
(b) 90 Hz
(c) 135 Hz
(d) 180 Hz
(2 Mark, 2003)

Ans: b
Data for Q.8 – 9 are given below.
A uniform rigid slender bar of mass 10 kg, hinged at the left end is suspended with the help of spring and damper arrangement as shown in the figure where K = 2kN/m, C = 500 Ns/m and the stiffness of the torsional spring K_{θ} is 1 kN/m/rad. Ignore the hinge dimensions.
8. The undamped natural frequency of oscillations of the bar about the hinge point is
(a) 42.43 rad/s
(b) 30 rad/s
(c) 17.32 rad/s
(d) 14.14 rad/s
(2 Mark, 2003)

Ans: a
9. The damping coefficient in the vibration equation is given by
(a) 500 Nms/rad
(b) 500 N/(m/s)
(c) 80 Nms/rad
(d) 80 N/(m/s)
(2 Mark, 2003)

Ans: c
10. 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, the transmissibility of ratio of isolation is
(a) \frac { 1 }{ 2 }
(b) \frac { 3 }{ 4 }
(c) \frac { 4 }{ 3 }
(d) 2
(1 Mark, 2004)

Ans: c
11. A uniform stiff rod of length 300 mm and having a weight of 300 N is pivoted at one end and connected to a spring at the other end. For keeping the rod vertical in a stable position the minimum value of spring constant K needed is
(a) 300 N/m
(b) 400 N/m
(c) 500 N/m
(d) 1000 N/m
(2 Mark, 2004)

Ans: c
12. A mass M, of 20 kg is attached to the free end of a steel cantilever beam of length 1000 mm having a crosssection of 25 × 25 mm. Assume the mass of the cantilever to be negligible and E_{steel} = 200GPa . If the lateral vibration of this system is critically damped using a viscous damper, the damping constant of the damper is
(a) 1250 Ns/m
(b) 625 Ns/m
(c) 312.50 Ns/m
(d) 156.25 Ns/m
(2 Mark, 2004)

Ans: a
13. There are four samples P, Q, R and S, with natural frequencies 64, 96, 128 and 256 Hz respectively. There are mounted on test setups for conducting vibration experiments. If a loud pure not of frequency 144 Hz is produced by some instrument, which of the samples will show the most perceptible induced vibration?
(a) P
(b) Q
(c) R
(d) S
(1 Mark, 2005)

Ans: c
15. In a springmass 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?
(a) 1.2 N.s/m
(b) 3.4 N.s/m
(c) 8.7 N.s/m
(d) 12.0 N.s/m
(2 Mark, 2005)

Ans: c
16. The differential equation governing the vibrating system is:
(a) m\ddot { x } +c\ddot { x } +k(xy)=0
(b) m\left( \ddot { x } \ddot { y } \right) +c\left( \dot { x } \dot { y } \right) +kx=0
(c) m\ddot { x } +c\left( \dot { x } \dot { y } \right) +kx=0
(d) m\left( \ddot { x } \ddot { y } \right) +c\left( \dot { x } \dot { y } \right) +k(xy)=0
(1 Mark, 2006)

Ans: c
17. 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:
(a) 0.0531
(b) 0.9922
(c) 0.0162
(d) 0.0028
(2 Mark, 2006)

Ans: c
Statement for Linked Answer Questions 18 & 19:
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.
18. The value of critical damping of the system is:
(a) 0.223 Ns/m
(b) 17.88 Ns/m
(c) 71.4 Ns/m
(d) 223.6 Ns/m
(2 Mark, 2006)

Ans: d
19. The value of logarithmic decrement is:
(a) 1.35
(b) 1.32
(c) 0.68
(d) 0.421
(2 Mark, 2006)

Ans: d
20. For an under damped 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
(1 Mark, 2007)

Ans: c
21. The natural frequency of the system shown below is
(a) \sqrt { \frac { k }{ 2m } }
(b) \sqrt { \frac { k }{ m } }
(c) \sqrt { \frac { 2k }{ m } }
(d) \sqrt { \frac { 3k }{ m } }
(2 Mark, 2007)

Ans: a
22. The equation of motion of a harmonic oscillator is given by \frac { { d }^{ 2 }x }{ d{ t }^{ 2 } } +2\xi { \omega }_{ n }\frac { dx }{ dt } +{ \omega }_{ n }^{ 2 }x=0 and the initial conditions at t = 0 are x(0) =X, \frac { dx }{ dt } (0) = 0. The amplitude of x(t) after n complete cycles is
(a) X{ e }^{ 2n\pi \left( \frac { \xi }{ \sqrt { 1{ \xi }^{ 2 } } } \right) }
(b) X{ e }^{ 2n\pi \left( \frac { \xi }{ \sqrt { 1{ \xi }^{ 2 } } } \right) }
(c) X{ e }^{ 2n\pi \left( \frac { \sqrt { 1{ \xi }^{ 2 } } }{ \xi } \right) }
(d) X
(2 Mark, 2007)

Ans: a
23. The natural frequency of the spring mass system shown in the figure is closest to
(a) 8 Hz
(b) 10 Hz
(c) 12 Hz
(d) 14 Hz
(2 Mark, 2008)

Ans: b
24. 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 ω_{n} in rad/s is
(a) 10
(b) 20
(c) 30
(d) 40
(2 Mark, 2008)

Ans: c
25. The rotor shaft of a large electric motor supported between short bearings at both deflection of 1.8 mm in the middle of the rotor. Assuming the rotor to be perfectly balanced and supported at knife edges at both the ends, the likely critical speed (in rpm) of the shaft is
(a) 350
(b) 705
(c) 2810
(d) 4430
(1 Mark, 2009)

Ans: b
26. 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
(2 Mark, 2009)

Ans: a
27. A vehicle suspension system consists of a spring and a damper. The stiffness of the spring is 3.6 kN/m and the damping constant of the damper is 400 Ns/m. If the mass is 50 kg, then the damping factor (d) and damped natural frequency (f_{n}), respectively, are
(a) 0.471 and 1.19 Hz
(b) 0.471 and 7.48 Hz
(c) 0.666 and 1.35 Hz
(d) 0.666 and 8.50 Hz
(2 Mark, 2009)

Ans: a
28. The natural frequency of a springmass system on earth is ω_{n}. The natural frequency of this system on the moon (g_{moon} = g_{earth}/6) is
(a) ω_{n}
(b) 0.408ω_{n}
(c) 0.204ω_{n}
(d) 0.167ω_{n}
(1 Mark, 2010)

Ans: a
29. A mass m attached to a spring is subjected to a harmonic force as shown in figure. The amplitude of the forced motion is observed to be 50 mm. the value of m (in kg) is
(a) 0.1
(b) 1.0
(c) 0.3
(d) 0.5
(2 Mark, 2010)

Ans: a
30. 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
(2 Mark, 2011)

Ans: a
31. 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 }{ 2m } }
(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 } }
(2 Mark, 2011)

Ans: c
32. 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 } }
(2 Mark, 2012)

Ans: d
33. 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
(1 Mark, 2013)

Ans: b
34. Critical damping is the
(a) Critical damping is the largest amount of damping for which no oscillation occurs in free vibration
(b) Smallest amount of damping for which no oscillation occurs in free vibration
(c) Largest amount of damping for which the motion is simple harmonic in free vibration
(d) Smallest amount of damping for which the motion is simple harmonic in free vibration
(1 Mark, 2014[1])

Ans: b
34. Consider a cantilever beam, having negligible mass and uniform flexural rigidity, with length 0.01 m. The frequency of vibration of the beam, with a 0.5 kg mass attached at the free tip, is 100 Hz. The flexural rigidity (in N.m^{2}) of the beam is _____.
(2 Mark, 2014[1])

Ans: 0.065
35. 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 } }
(2 Mark, 2014[1])

Ans: d
36. In vibration isolation, which one of the following statements is NOT correct regarding Transmissibility (T)?
(a) T is nearly unity at small excitation frequencies
(b) T can be always reduced by using higher damping at any excitation frequency
(c) T is unity at the frequency ratio of \sqrt { 2 }
(d) T is infinity at resonance for undamped systems
(1 Mark, 2014[2])

Ans: b
37. What is the natural frequency of the spring mass system shown below? The contact between the block and the inclined plane is frictionless. The mass of the block is denoted by m and the spring constants are denoted by k_{1} and k_{2} as shown below.
(a) \sqrt { \frac { { k }_{ 1 }+{ k }_{ 2 } }{ 2m } }
(b) \sqrt { \frac { { k }_{ 1 }+{ k }_{ 2 } }{ 4m } }
(c) \sqrt { \frac { { k }_{ 1 }{ k }_{ 2 } }{ m } }
(d) \sqrt { \frac { { k }_{ 1 }+{ k }_{ 2 } }{ m } }
(2 Mark, 2014[2])

Ans: d
38. Consider a single degreeoffreedom 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
(1 Mark, 2014[3])

Ans: c
39. The damping ratio of a single degree of freedom springmassdamper system with mass of 1 kg, stiffness 100 N/m and viscous damping coefficient of 25 Ns/m is ____.
(2 Mark, 2014[3])

Ans: 1.25
40. A massspringdashpot system with mass m = 10 kg, spring constant k = 6250 N/m is excited by a harmonic excitation of 10 cos(25t) N. At the steady state, the vibration amplitude of the mass is 40 mm. The damping coefficient (c, in N.s/m) of the dashpot is _____.
(2 Mark, 2014[3])

Ans: 10
41. A point mass is executing simple harmonic motion with an amplitude of 10 mm and frequency of 4 Hz. The maximum acceleration (m/s^{2}) of the mass is ____.
(1 Mark, 2014[4])

Ans: 6.3
42. A single degree of freedom system has a mass of 2 kg, stiffness 8 N/m and viscous damping ratio 0.02. The dynamic magnification factor at an excitation frequency of 1.5 rad/s is ____.
(2 Mark, 2014[4])

Ans: 2.29
43. 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 } }
(2 Mark, 2015[1])

Ans: d
44. A precision instrument package (m = 1 kg) needs to be mounted on a surface vibrating at 60 Hz. It is desired that only 5% of the base surface vibration amplitude be transmitted to the instrument. Assume that the isolation is designed with its natural frequency significantly lesser than 60 Hz, so that the effect of damping may be ignored. The stiffness (in N/m) of the required mounting pad is _____.
(2 Mark, 2015[1])

Ans: 6767.6
45. In a springmass system, the mass is m and the spring constant is k. The critical damping coefficient of the system is 0.1 kg/s. In another springmass system, the mass is 2m and the spring constant is 8k. The critical damping coefficient (in kg/s) of this system is ___.
(1 Mark, 2015[2])

Ans: 0.4
46. A singledegreefreedom springmass system is subjected to a sinusoidal force of 10 N amplitude and frequency ω along the axis of the spring. The stiffness of the spring is 150 N/m, damping factor is 0.2 and the undamped natural frequency is 10ω. At steady state, the amplitude of vibration (in m) is approximately
(a) 0.05
(b) 0.07
(c) 0.70
(d) 0.90
(2 Mark, 2015[2])

Ans: b
47. Which of the following statements are TRUE for damped vibrations?
P. For a system having critical damping, the value of damping ratio is unity and system does not undergo a vibratory motion.
Q. Logarithmic decrement method is used to determine the amount of damping in a physical system.
R. In case of damping due to dry friction between moving surfaces resisting force of constant magnitude acts opposite to the relative motion.
S. For the case of viscous damping, drag force is directly proportional to the square of relative velocity.
(a) P and Q only
(b) P and S only
(c) P, Q and R only
(d) Q and S only
(1 Mark, 2015[3])

Ans: c
48. Figure shows a single degree of freedom system. The system consists of a massless rigid bar OP hinged at O and a mass m at end P. The natural frequency of vibration of the system is
(a) f_{n} = \frac { 1 }{ 2\pi } \sqrt { \frac { k }{ 4m } }
(b) f_{n} = \frac { 1 }{ 2\pi } \sqrt { \frac { k }{ 2m } }
(c) f_{n} = \frac { 1 }{ 2\pi } \sqrt { \frac { k }{ m } }
(d) f_{n} = \frac { 1 }{ 2\pi } \sqrt { \frac { 2k }{ m } }
(2 Mark, 2015[3])

Ans: a
49. A single degree of freedom spring mass system with viscous damping has a spring constant of 10 kN/m. The system is excited by a sinusoidal force of amplitude 100 N. If the damping factor (ratio) is 0.25, the amplitude of steady state oscillation at resonance is _____mm.
(1 Mark, 2016[1])

Ans: 20
50. A solid disc with radius a is connected to a spring at a point d above the center 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 inertia for the disc about its centre is J = \frac { M{ a }^{ 2 } }{ 2 } .
The 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 } } }
(2 Mark, 2016[1])

Ans: a
51. A single degree of freedom massspringviscous damper system with mass m, spring constant k and viscous damping coefficient q is critically damped. The correct relation among m, k, and q is
(a) 𝑞 = \sqrt { 2km }
(b) 𝑞 = 2\sqrt { km }
(c) 𝑞 = \sqrt { \frac { 2k }{ m } }
(d) 𝑞 = 2\sqrt { \frac { k }{ m } }
(1 Mark, 2016[2])

Ans: b
52. The system shown in the figure consists of block A of mass 5 kg connected to a spring through a massless rope passing over pulley B of radius r and mass 20 kg. The spring constant k is 1500 N/m. If there is no slipping of the rope over the pulley, the natural frequency of the system is_____ rad/s.
(2 Mark, 2016[2])

Ans: 10
53. A single degree of freedom springmass system is subjected to a harmonic force of constant amplitude. For an excitation frequency of \sqrt { \frac { 3k }{ m } } , the ratio of the amplitude of steady state response to the static deflection of the spring is ____.
(2 Mark, 2016[3])

Ans: 0.5
54. The static deflection of a spring under gravity, when a mass of 1 kg is suspended from it, is 1 mm. Assume the acceleration due to gravity g =10 m/s^{2}. The natural frequency of this springmass system (in rad/s) is________.
(1 Mark, 2016[3])

Ans: 100
55. The damping ratio for a viscosity damped spring mass system, governed by the relationship m\frac { { d }^{ 2 }x }{ d{ t }^{ 2 } } +c\frac { dx }{ dt } +kx = F(t), is given by ______.
(a) \sqrt { \frac { c }{ km } }
(b) \frac { c }{ 2\sqrt { km } }
(c) \frac { c }{ \sqrt { km } }
(d) \sqrt { \frac { c }{ \sqrt { 2km } } }
(1 Mark, 2017[1])

Ans: b
56. 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 is ends. The bar is further supported using springs, each of stiffness k, located at the two ends. A particle of mass m = 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 } }
(2 Mark, 2017[1])

Ans: b
57. A mass m is attached to two identical springs having 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 } }
(1 Mark, 2017[2])

Ans: a
58. The radius of gyration of a compound pendulum about the point of suspension is 100 mm. the distance between the point of suspension and the centre of mass is 250 mm. Considering the acceleration due to gravity is 9.81 m/s^{2}, the natural frequency (in radian/s) of the compound pendulum is ____.
(2 Mark, 2017[2])

Ans: 15.66
59. The equation of motion for a springmass system excited by a harmonic force is M\ddot { x } +Kx=Fcos(\omega t), where M is the mass, K is the spring stiffness, F is the force amplitude and ω is the angular frequency of excitation. Resonance occurs when ω is equal to
(a) \sqrt { \frac { M }{ K } }
(b) \frac { 1 }{ 2\pi } \sqrt { \frac { K }{ M } }
(c) 2\pi \sqrt { \frac { K }{ M } }
(d) \sqrt { \frac { K }{ M } }
(1 Mark, 2018[1])

Ans: d
60. A machine of mass 𝑚 = 200 kg is supported on two mounts, each of stiffness 𝑘 = 10 kN/m. The machine is subjected to an external force (in N) (𝑡) = 50 cos 5𝑡. Assuming only vertical translatory motion, the magnitude of the dynamic force (in N) transmitted from each mount to the ground is ______ (correct to two decimal places).
(2 Mark, 2018[1])

Ans: 33.33
61. In a single degree of freedom underdamped springmassdamper system as shown in the figure, an additional damper is added in parallel such that the system still remains underdamped. Which one of the following statements is ALWAYS true?
(a) Transmissibility will increase
(b) Transmissibility will decrease
(c) Time period of free oscillations will increase
(d) Time period of free oscillations will decrease
(1 Mark, 2018[2])

Ans: c
62. The natural frequencies corresponding to the springmass systems I and II are { \omega }_{ I } and { \omega }_{ II }, respectively. The ratio \frac { { \omega }_{ I } }{ { \omega }_{ II } } is
(a) \frac { 1 }{ 2 }
(b) 4
(c) 2
(d) \frac { 1 }{ 4 }
(1 Mark, 2019[1])

Ans: a
63. A uniform thin disk of mass 1 kg and radius 0.1 m is kept on a surface as shown in the figure. A spring of stiffness k_{1} = 400 N/m is connected to the disk centre A and another spring of stiffness k_{2} = 100 N/m is connected at point B just above point A on the circumference of the disk. Initially, both the springs are unstretched. Assume pure rolling of the disk. For small disturbance from the equilibrium, the natural frequency of vibration of the system is ____ rad/s (round off to one decimal place).
(2 Mark, 2019[1])

Ans: 23.094
64. 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 c/\sqrt { km } should be
(a) 2
(b) 4
(c) 2\sqrt { 7 }
(d) 4\sqrt { 7 }
(2 Mark, 2019[2])

Ans: d