The equation of motion for a single degree of freedom system with viscous damping is 4(dx²/dt²) + 9(dx/dt) + 16x. The damping ratio of the system is
9/8
9/82
9/16
9/128
Correct Answer :
C. 9/16
Related Questions
The natural frequency of free transverse vibrations due to a point load acting over a simply supported shaft is equal to (where δ = Static deflection of a simply supported shaft due to the point load)
0.4985/√δ
0.5615/√δ
0.571/√δ
0.6253/√δ
The axis of precession is __________ to the plane in which the axis of spin is going to rotate.
Parallel
Perpendicular
Both A and B
None of these
The length of a simple pendulum which gives the same frequency as the compound pendulum, is
kG + l₁
kG² + l₁
(kG² + l₁²)/ l₁
(kG + l₁²)/ l₁
The minimum force required to slide a body of weight W on a rough horizontal plane is
W sinθ
W cosθ
W tanθ
W cosecθ
Which of the following is an inversion of Single slider crank chain?
Beam engine
Rotary engine
Oldhams coupling
Elliptical trammel
Two heavy rotating masses are connected by shafts of lengths l₁, l₂ and l₃ and the corresponding diameters are d₁, d₂ and d₃. This system is reduced to a torsionally equivalent system having uniform diameter d = d₁ of the shaft. The equivalent length of the shaft is
(l₁ + l₂ + l₃)/3
l = l₁ + l₂.(d₁/d₂)³ + l₂.(d₁/d₃)³
l = l₁ + l₂.(d₁/d₂)⁴ + l₃.(d₁/d₃)⁴
l₁ + l₂ + l₃
In steady state forced vibrations, the amplitude of vibrations at resonance is __________ damping coefficient.
Equal to
Directly proportional to
Inversely proportional to
Independent of
Two pulleys of radii r₁ and r₂ and at distance x apart are connected by means of an open belt drive. The length of the belt is
π (r₁ + r₂) + (r₁ + r₂)²/x + 2x
π (r₁ + r₂) + (r₁ - r₂)²/x + 2x
π (r₁ - r₂) + (r₁ - r₂)²/x + 2x
π (r₁ - r₂) + (r₁ + r₂)²/x + 2x
In a shaper mechanism, the Coriolis component of acceleration will
Not exist
Exist
Depend on position of crank
None of the above
The Bifilar suspension method is used to determine
Natural frequency of vibration
Position of balancing weights
Moment of inertia
Centripetal acceleration
A fixed gear having 200 teeth is in mesh with another gear having 50 teeth. The two gears are connected by an arm. The number of turns made by the smaller gear for one revolution of arm about the centre of bigger gear is
2
3
4
5
In its simplest form, a cam mechanism consists of following number of links
1
2
3
4
The primary unbalanced force is maximum when the angle of inclination of the crank with the line of stroke is
0° and 90°
0° and 180°
90° and 180°
180° and 360°
Which of the following is an example of sliding pair?
Piston and cylinder of a reciprocating steam engine
Shaft with collars at both ends fitted into a circular hole
Lead screw of a lathe with nut
Ball and a socket joint
In a four stroke I.C. engine, the turning moment during the compression stroke is
Positive throughout
Negative throughout
Positive during major portion of the stroke
Negative during major portion of the stroke
A body in motion will be subjected to coriolis acceleration when that body is
In plane rotation with variable velocity
In plane translation with variable velocity
In plane motion which is a resultant of plane translation and rotation
Restrained to rotate while sliding over another body
The component of the acceleration, parallel to the velocity of the particle, at the given instant is called
Radial component
Tangential component
Coriolis component
None of these
The lead screw of a lathe with nut forms a
Rolling pair
Sliding pair
Screw pair
Turning pair
In a mechanism, the fixed instantaneous centres are those centres which
Remain in the same place for all configurations of the mechanism
Vary with the configuration of the mechanism
Moves as the mechanism moves, but joints are of permanent nature
None of the above
The example of lower pair is
Shaft revolving in a bearing
Straight line motion mechanisms
Automobile steering gear
All of the above
The maximum fluctuation of speed is the
Difference of minimum fluctuation of speed and the mean speed
Difference of the maximum and minimum speeds
Sum of maximum and minimum speeds
Variations of speed above and below the mean resisting torque line
Governor is used in automobile to
Decrease the variation of speed
Maximize the fuel economy
Limit the vehicle speed
Maintain constant engine speed
The sense of coriolis component 2 ωv is same as that of the relative velocity vector v rotated at
45° in the direction of rotation of the link containing the path
45° in the direction opposite to the rotation of the link containing the path
90° in the direction of rotation of the link containing the path
180° in the direction opposite to the rotation of the link containing the path
A Porter governor is a
Pendulum type governor
Dead weight governor
Spring loaded governor
Inertia governor
A spring controlled governor is said to be isochronous when the controlling force
Increases as the radius of rotation decreases
Increases as the radius of rotation increases
Decreases as the radius of rotation increases
Remain constant for all radii of rotation
A mechanism consisting of four links is called a __________ mechanism.
Simple
Compound
Binary
None of these
A shaft carrying three rotors will have
No node
One node
Two nodes
Three nodes
In the two rotor system as shown in the below figure (I₁ < I₂), a node of vibration is situated 
Between I₁, and I₂ but nearer I₁
Between I₁, and I₂ but nearer to I₂
Exactly in the middle of the shaft
Nearer to I₁ but outside
When the two elements of a pair have __________ when in motion, it is said to a lower pair.
Line or point contact
Surface contact
Body contact
None of these
The frequency of damped vibrations with viscous damping is ________ the frequency of undamped vibrations.
More than
Less than
Same as
None of these