The equation of motion for a vibrating system with viscous damping is (d²x/dt²) + (c/m).(dx/dt) + (s/m).x = 0, if the roots of the equation are __________ then the system will be under damped.
Equal
Real
Complex conjugate
None of these
Correct Answer :
C. Complex conjugate
Related Questions
According to Kennedy's theorem, if three bodies have plane motions, their instantaneous centers lie on
A triangle
A point
Two lines
A straight line
Which of the following statement is correct?
For constant velocity ratio transmission between two gears, the common normal at the point of contact must always pass through a fixed point on the line joining the centres of rotation of gears.
For involute gears, the pressure angle changes with the change in centre distance between gears.
The epicyclic gear trains involve rotation of atleast one gear axis about some other gear axis.
All of the above
In a hydrodynamic journal bearing, there is
A very thin film of lubricant between the journal and the bearing such that there is contact between the journal and the bearing
A thick film of lubricant between the journal and the bearing
No lubricant between the journal and the bearing
A forced lubricant between the journal and the bearing
Which of the following is an inversion of a double slider crank chain?
Oldham's coupling
Elliptical trammel
Scotch yoke mechanism
All of these
The gears are termed as medium velocity gears, if their peripheral velocity is
1-3 m/s
3-15 m/s
15-30 m/s
30-50 m/s
In vibration isolation system, if ω/ωn < 2, then for all values of damping factor, the transmissibility will be (where ω = Angular speed of the system, ωn = Natural frequency of vibration of the system)
Less than unity
Equal to unity
Greater than unity
Zero
Which of the following is an example of a higher pair?
Toothed gearing
Belt and rope drive
Ball and roller bearing
All of these
When the relation between the controlling force (Fc) and radius of rotation (r) for a spring controlled governor is Fc = ar + b, then the governor will be
Stable
Unstable
Isochronous
None of these
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
The radial distance from the top of a tooth to the bottom of a tooth in a meshing gear, is called
Dedendum
Addendum
Clearance
Working depth
With single Hooke's joint it is possible to connect two shafts, the axes of which have an angular misalignment up to
10°
20°
30°
40°
If the number of links in a mechanism is equal to l, then the numbers of possible inversions are equal to
l - 2
l - 1
l
l + 1
Ball and a Socket forms a
Turning pair
Rolling pair
Screw pair
Spherical pair
Coriolis component acts
Perpendicular to sliding surfaces
Along sliding surfaces
Somewhere in between above two
None of the above
To obviate axial thrust, following gear drive is used
Double helical gears having opposite teeth
Double helical gears having identical teeth
Single helical gear in which one of the teeth of helix angle a is more
Mutter gears
In under damped vibrating system, the amplitude of vibration
Decreases linearly with time
Increases linearly with time
Decreases exponentially with time
Increases exponentially with time
In S.H.M., acceleration is proportional to
Velocity
Displacement
Rate of change of velocity
All of the above
A kinematic chain requires at least
2 links and 3 turning pairs
3 links and 4 turning pairs
4 links and 4 turning pairs
5 links and 4 turning pairs
The displacement of the reciprocating roller follower, when it has contact with the straight flanks of the tangent cam, is given by (where r₁ = Minimum radius of the cam, r₂ = Radius of the roller follower, and θ = Angle turned by the cam from the beginning of the follower displacement)
(r₁ - r₂) (1 - cosθ)
(r₁ + r₂) (1 + cosθ)
(r₁ - r₂) [(1 - cosθ)/cos θ]
(r₁ + r₂) [(1 - cosθ)/cos θ]
Which of the following is false statement in respect of differences between machine and structure?
Machines transmit mechanical work, whereas structures transmit forces
In machines, relative motion exists between its members, whereas same does not exist in case of structures
Machines modify movement and work, whereas structures modify forces
Efficiency of machines as well as structures is below 100%
In higher pair, the relative motion is
Purely turning
Purely sliding
Purely rotary
Combination of sliding and turning
When two links are connected by a pin joint, their instantaneous centre lies
On their point of contact
At the centre of curvature
At the centre of circle
At the pin joint
The example of spherical pair is
Bolt and nut
Lead screw of a lathe
Ball and socket joint
Ball bearing and roller bearing
3.The retardation of a flat faced follower when it has contact at the apex of the nose of a circular arc cam, is given by (where OQ = Distance between the centre of circular flank and centre of nose)
ω² × OQ
ω² × OQ sinθ
ω² × OQ cosθ
ω² × OQ tanθ
The velocity of the belt for maximum power is (where m = Mass of the belt in kg per metre length)
T/3
(T.g)/3
√(T/3m)
√(3m/T)
When a shaking force is transmitted through the springs, damping becomes detrimental when the ratio of its frequency to the natural frequency is greater than
0.25
0.5
1
2
The Kutzbach criterion for determining the number of degrees of freedom (n) is (where l = number of links, j = number of joints and h = number of higher pairs)
n = 3(l - 1) - 2j - h
n = 2(l - 1) -2j - h
n = 3(l - 1) - 3j - h
n = 2(l - 1) - 3j - h
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
Which of the following disciplines provides study of the relative motion between the parts of a machine and the forces acting on the parts?
Theory of machines
Applied mechanics
Mechanisms
Kinetics
The following is the inversion of slider crank chain mechanism
Whitworth quick return mechanism
Hand pump
Oscillating cylinder engine
All of the above