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Mechanical Vibration
Quiz 1
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Q.1
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
km\sqrt{\frac{k}{m}}mk
km+ω\sqrt{\frac{k}{m}}+\omegamk+ω
ω\omegaω
Data insufficient
Q.2
3d2xdy2+9dxdy+27x=03\frac{\text{d}^2x}{\text{d}y^2}+9\frac{\text{d}x}{\text{d}y}+27x=03dy2d2x+9dydx+27x=is the equation of motion for a damped viscous vibration. The damping factor is
0.25
0.5
0.75
1.0
Q.3
d2xdt2+36x=0\frac{\text{d}^2x}{\text{d}t^2}+36\text{x=0}dt2d2x+36x=is the equation of free vibrations of a system. Its natural frequency is (Rad/s)
36
6
9
0
Q.4
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
more than 2\sqrt{2}2
less than 2\sqrt{2}2
equal to one
less than one
Q.5
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
Q.6
Transmissibility is unity at two points. Which one of the following is true for these two points? r=\frac{\omega}{\omega_n}r=ωnω
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
Q.7
For steady-state forced vibrations, the phase lag at resonance is
0°0\degree0°
45°45\degree45°
90°90\degree90°
180°180\degree180°
Q.8
A viscous damping system with free vibrations will be critically damped if the damping factor is
Zero
Less than one
Equal to one
Greater than one
Q.9
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
0.25
0.5
1
2\sqrt{2}2
Q.10
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 isNs/m. If the mass iskg, then the damping factor and damped natural frequency (in Hz), respectively, are
0.471 and 1.19 Hz
0.471 and 7.48 Hz
0.666 and 1.35 Hz
0.666 and 8.5 Hz
Q.11
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.then transmissibility of ratio of isolation is
1/2
3/4
4/3
2
Q.12
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 =N/m. The natural frequency ( in rad/s) is
10
20
30
40
Q.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
1
1.6
2
2.4
Q.14
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}}2N
NNN
2N2N2N
Q.15
The critical speed of a rotating shaft depends upon
Mass
stiffness
mass and stiffness
mass, stiffness and eccentricity
Q.16
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
Q.17
A shaft ofmm diameter and 1 m length carries a disc which has mass eccentricity equal tomicrons. The displacement of the shaft at a speed which isof critical speed in microns is
810
900
800
820
Q.18
An automotive engine weighingkg is supported on four springs with linear characteristics. Each of the front two springs have a stiffness ofMN/m while the stiffness of each rear spring isMN/m. The engine speed (in rpm), at which resonance is likely to occur, is
6040
3020
1424
955
Q.19
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
Q.20
A shaft has two heavy rotors mounted on it. The transverse natural frequencies, considering each of the rotors separately, arecycles/sec andcycles/sec respectively. The lowest critical speed is
5367 rpm
6000 rpm
9360 rpm
12000rpm
0 h : 0 m : 1 s
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