Free and Forced Vibration with Damping - Vibrations - Engineering Sciences Previous Year Questions

1

2007 · Engineering Sciences · Vibrations · Free and Forced Vibration with Damping

Engineering Sciences (XE) 2007

A transistor oscillator uses a 3-section R-C phase shift circuit. Each section uses same R and C values. The gain of the circuit is adjusted for oscillation. The required oscillation frequency is 10 k rad/s. The suitable R-C combination is

A

R = 3 kΩ, C = 0.33 μF

B

R = \(\frac{1}{3}\) kΩ, C = 0.33 μF

C

R = \(\sqrt{3}\) kΩ, C = 0.1 μF

D

R = \(\frac{1}{\sqrt{3}}\) kΩ, C = 0.1 μF

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2

2007 · Engineering Sciences · Vibrations · Free and Forced Vibration with Damping

Engineering Sciences (XE) 2007

A single degree freedom system consisting of 2 springs and a mass is shown in the figure.

The natural frequency of the system in radians/sec is given by

A

√(k₁/m)

B

√(k₂/m)

C

√(k₁k₂/(k₁+k₂)m)

D

√((k₁+k₂)/m)

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3

2008 · Engineering Sciences · Vibrations · Free and Forced Vibration with Damping

Engineering Sciences (XE) 2008

If a mass attached to the free end of a linear spring is so constrained that it executes vertical undamped oscillations, its acceleration at the instant when it occupies the static equilibrium position is

A

vertically upward

B

vertically downward

C

the maximum

D

zero

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4

2008 · Engineering Sciences · Vibrations · Free and Forced Vibration with Damping

Engineering Sciences (XE) 2008

The natural frequency of vibration is

A

1 rad/s

B

1.59 rad/s

C

5 rad/s

D

10 rad/s

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5

2008 · Engineering Sciences · Vibrations · Free and Forced Vibration with Damping

Engineering Sciences (XE) 2008

The magnitude of velocity when the body has moved half way towards the static equilibrium position from its initial position is

A

0.212 m/s

B

0.346 m/s

C

0.4 m/s

D

1.0 m/s

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6

2008 · Engineering Sciences · Vibrations · Free and Forced Vibration with Damping

Engineering Sciences (XE) 2008

When a ball of weight \( W \) rests on a spring of constant \( k \), it produces a static deflection of 3 cm. If the ball is now dropped from a height of \( h = 30 \) cm as shown in the figure, the spring will get compressed by

A

2.45 cm

B

14.07 cm

C

16.75 cm

D

33 cm

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7

2009 · Engineering Sciences · Vibrations · Free and Forced Vibration with Damping

Engineering Sciences (XE) 2009

In the ensuing Simple Harmonic Motion of the body, the magnitude of maximum acceleration is

A

100 m/s²

B

200 m/s²

C

500 m/s²

D

1000 m/s²

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8

2010 · Engineering Sciences · Vibrations · Free and Forced Vibration with Damping

Engineering Sciences (XE) 2010

A spring-mass system shown in the figure is vibrating with very small amplitude. The natural frequency of the system is

A

\(\sqrt{\frac{k}{m}}\)

B

\(\sqrt{\frac{2k}{m}}\)

C

\(\sqrt{\frac{2k\cos\theta}{m}}\)

D

\(\sqrt{\frac{2k\cos^2\theta}{m}}\)

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9

2011 · Engineering Sciences · Vibrations · Free and Forced Vibration with Damping

Engineering Sciences (XE) 2011

A simple mass-spring system shown has a natural frequency of 5 Hz. The static deflection of the spring due to the mass is (acceleration due to gravity is 9.81 m/s² and mass of the spring is negligible)

A

0.390 m

B

0.039 m

C

0.019 m

D

0.010 m

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10

2012 · Engineering Sciences · Vibrations · Free and Forced Vibration with Damping

Engineering Sciences (XE) 2012

A rocket in the atmosphere is accelerating upwards with acceleration \(a\) m/s². The natural frequency of a spring-mass system (with mass \(m\) kg and spring constant \(k\) N/m), suspended vertically inside the rocket, is (take \(g\) m/s² to be the acceleration due to gravity)

A

\(\sqrt{\frac{k}{m}} ; (\overline{k} < k)\)

B

\(\sqrt{\frac{k}{m}}\)

C

\(\sqrt{\frac{kg}{ma}}\)

D

\(\sqrt{\frac{k}{m(1-\frac{a}{g})}}\)

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11

2012 · Engineering Sciences · Vibrations · Free and Forced Vibration with Damping

Engineering Sciences (XE) 2012

For small oscillations, the natural frequency of the system in terms of \(K\), \(a\), \(b\) and \(M\) is (assuming ideal joints and mass-less rigid rod ABC)

A

\(\sqrt{\frac{K}{M}}\)

B

\(\sqrt{\frac{Ka}{Mb}}\)

C

\(\sqrt{\frac{Kb^2}{Ma^2}}\)

D

\(\sqrt{\frac{Ka^2}{Mb^2}}\)

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12

2013 · Engineering Sciences · Vibrations · Free and Forced Vibration with Damping

Engineering Sciences (XE) 2013

A rigid massless rod ABC is hinged at A and carries a point mass M (in kg) at C. Point B is connected to a linear spring with spring constant \(k\) (in N/m) as shown in the figure. The length AB and AC area and \(L\), respectively. Neglecting the effect of gravity, the natural frequency of this spring-mass system in rad/s is

A

\(\sqrt{\frac{kL^2}{Ma^2}}\)

B

\(\sqrt{\frac{ka^2}{ML^2}}\)

C

\(\sqrt{\frac{kL}{Ma}}\)

D

\(\sqrt{\frac{ka}{ML}}\)

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13

2016 · Engineering Sciences · Vibrations · Free and Forced Vibration with Damping

Engineering Sciences (XE) 2016

A single degree of freedom vibrating system has mass of 5 kg, stiffness of 500 N/m and damping coefficient of 100 N-s/m. To make the system critically damped

A

only the mass is to be increased by 1.2 times.

B

only the stiffness is to be reduced to half.

C

only the damping coefficient is to be doubled.

D

no change in any of the system parameters is required.

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14

2016 · Engineering Sciences · Vibrations · Free and Forced Vibration with Damping

Engineering Sciences (XE) 2016

The vibrating system shown in the figure carries a mass of 10 kg at the free end, where the static deflection is 1 mm. This system is to be replaced by an equivalent vibrating spring mass system having equivalent mass of 2 kg (assume \(g=10~m/s^2\)). The natural frequency (in rad/s) and the stiffness (in kN/m) of the equivalent system respectively are

A

10 and 20

B

20 and 100

C

100 and 20

D

1000 and 20

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15

2017 · Engineering Sciences · Vibrations · Free and Forced Vibration with Damping

Engineering Sciences (XE) 2017

Two pendulums are shown below. \(Pendulum-A\) carries a bob of mass \(m\), hung using a hinged massless rigid rod of length \(L\) whereas \(Pendulum-B\) carries a bob of mass \(4m\) and length \(L/4\). The ratio of the natural frequencies of \(Pendulum-A\) and \(Pendulum-B\) is given by

A

1 : 2

B

1 : 1

C

\(\sqrt{2} : 1\)

D

2 : 1

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16

2017 · Engineering Sciences · Vibrations · Free and Forced Vibration with Damping

Engineering Sciences (XE) 2017

Consider the system shown below. Mass \(M\) is fixed to the rod \(AC\) at a distance \(x\) from the hinge point at \(B\). Two springs of stiffness \(3K\) and \(K\) are attached to the rod at points \(A\) and \(C\), respectively. The natural frequency of angular oscillation of the system about \(B\) is 20 rad/s. Assume the rod to be rigid and massless. Magnitude of \(x\) (in metres) is __________. (\(M = 30\text{kg}\), and \(K = 1\text{kN/m}\)).

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17

2018 · Engineering Sciences · Vibrations · Free and Forced Vibration with Damping

Engineering Sciences (XE) 2018

A cantilever beam with length, L = 1 m, modulus of elasticity, E = 210 GPa, and area moment of inertia, I = 1.2 × 10⁻⁷ m⁴ carries a concentrated mass m = 100 kg at its free-end. By idealizing it as a single degree-of-freedom system and neglecting the mass of the cantilever beam, the natural frequency (in rad/s) of small transverse oscillations of the mass m is ……. [up to two decimal places]

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18

2018 · Engineering Sciences · Vibrations · Free and Forced Vibration with Damping

Engineering Sciences (XE) 2018

A rigid uniform rod with mass \( m \), length \( L \) and center of gravity \( G \) is freely suspended from a hinge as shown in the figure. The rod is given a small angular displacement \( \theta \) in the counter-clockwise direction from the position in which it hangs vertically (\( \theta = 0 \)). If \( g \) is the acceleration due to gravity, the natural frequency of oscillations (in rad/s) is

A

\(\sqrt{\frac{6g}{L}} \)

B

\(\sqrt{\frac{2g}{L}} \)

C

\(\sqrt{\frac{3g}{2L}} \)

D

\(\sqrt{\frac{g}{L}} \)

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19

2019 · Engineering Sciences · Vibrations · Free and Forced Vibration with Damping

Engineering Sciences (XE) 2019

The uniform pendulum rod, having mass 10 kg and length L = 5 m, is attached to a viscous damper having damping coefficient c. Use acceleration due to gravity g = 10 m/s². The least value of c (in N-s/m) such that small motions of the pendulum rod decay without oscillations is ______

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20

2020 · Engineering Sciences · Vibrations · Free and Forced Vibration with Damping

Engineering Sciences (XE) 2020

A rigid bar ABC of mass m and length L is hinged at A and has a point mass M attached at C. An elastic spring with linear stiffness k is attached at B as shown. Ignore the effect of gravity and damping. The natural frequency of small oscillations of this system is ______________.

A

\(\sqrt{\frac{k}{4M + m}}\)

B

\(\sqrt{\frac{k}{2(M + 2m)}}\)

C

\(\sqrt{\frac{3k}{3M + m}}\)

D

\(\sqrt{\frac{3k}{4(3M + m)}}\)

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