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 this equation are real, then the system will be
Over-damped
Under damped
Critically damped
Without vibrations
Correct Answer :
A. Over-damped
Related Questions
It is required to connect two parallel shafts, the distance between whose axes is small and variable. The shafts are coupled by
Universal joint
Knuckle joint
Oldham's coupling
Flexible coupling
The static balancing is satisfactory for low speed rotors but with increasing speeds, dynamic balancing becomes necessary. This is because, the
Unbalanced couples are caused only at higher speeds
Unbalanced forces are not dangerous at higher speeds
Effects of unbalances are proportional to the square of the speed
Effects of unbalances are directly proportional to the speed
ABCD is a four bar mechanism in which AB = 310 mm and CD = 450 mm. AB and CD are both perpendicular to the fixed link AD, as shown in the below figure. If the velocity of B at this condition is v. Then the velocity of C is 
v
(2/3). v
(3/2). v
(9/4). v
The relation l = (2/3).(j + 2) apply only to kinematic chains in which lower pairs are used. This may be used to kinematic chains in which higher pairs are used, but each higher pair may be taken as equivalent to
One lower pair and two additional links
Two lower pairs and one additional link
Two lower pairs and two additional links
Any one of these
The relative velocity of B with respect to A in a rigid link AB is
Parallel to AB
Perpendicular to AB
Along AB
At 45° to AB
With usual notations for different parameters involved, the maximum fluctuations of energy for a flywheel is given by
2ECS
ECS/2
2ECS²
2E²CS
Ackermann steering gear consists of
Sliding pairs
Turning pairs
Rolling pairs
Higher pairs
When the crank is at the outer dead centre, in a reciprocating steam engine, then the acceleration of the piston will be
ω² r {(n + 1)/n}
ω² r {(n - 1)/n}
ω² r {n/(n + 1)}
ω² r {n/(n - 1)}
A friction circle is a circle drawn when a journal rotates in a bearing. Its radius depends upon the coefficient of friction and the
Magnitude of the forces on journal
Angular velocity of journal
Clearance between journal and bearing
Radius of journal
In a kinematic chain, a quaternary joint is equivalent to
One binary joint
Two binary joints
Three binary joints
Four binary joints
The main disadvantage of the sliding pair is that it is
Bulky
Wears rapidly
Difficult to manufacture
Both (A) and (B) above
The motion between a pair which takes place in __________ is known as incompletely constrained motion.
One direction only
Two directions only
More than one direction
None of these
A pantograph is a mechanism with
Lower pairs
Higher pairs
Rolling pairs
Turning pairs
A disc is a spinning with an angular velocity ω rad/s about the axis of spin. The couple applied to the disc causing precession will be (where I = Mass moment of inertia of the disc, and ωP = Angular velocity of precession of the axis of spin)
(1/2).Iω²
Iω²
(1/2). I ω ωP
I ω ωP
The height of a Watt's governor (in metres) is equal to (where N = Speed of the arm and ball about the spindle axis)
8.95/N²
89.5/N²
895/N²
8950/N²
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
Elements of pairs held together mechanically is known as
Closed pair
Open pair
Mechanical pair
Rolling pair
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 the pitching of a ship is upward, the effect of gyroscopic couple acting on it will be
To move the ship towards starboard
To move the ship towards port side
To raise the bow and lower the stern
To raise the stern and lower the bow
For dynamic balancing of a shaft
The net dynamic force acting on the shaft is equal to zero
The net couple due to the dynamic forces acting on the shaft is equal to zero
Both (A) and (B)
None of the above
A body of weight W is required to move up the rough inclined plane whose angle of inclination with the horizontal is α. The effort applied parallel to the plane is given by (where μ = tan φ = Coefficient of friction between the plane and the body)
P = W tan α
P = W tan (α + φ)
P = W (sin α + μ cos α)
P = W (cos α + μ sin α)
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 coriolis component of acceleration exists whenever a point moves along a path that has
Linear displacement
Rotational motion
Gravitational acceleration
Tangential acceleration
Pulley in a belt drive acts as
Cylindrical pair
Turning pair
Rolling pair
Sliding pair
In S.H.M., acceleration is proportional to
Velocity
Displacement
Rate of change of velocity
All of the above
Hart mechanism has
Eight links
Six links
Four links
Twelve links
In the below figure, PC is the connecting rod and OC is the crank making an angle θ with the line of stroke PO and rotates with uniform angular velocity at ω rad/s. The Klien's acceleration diagram for determining the acceleration of the piston P is shown by quadrilateral CQNO, if N coincides with O, then 
Acceleration and velocity of the piston P is zero
Acceleration and velocity of the piston P is maximum
Acceleration of the piston P is zero and its velocity is maximum
Acceleration of the piston P is maximum and its velocity is zero
In a multiple V-belt drive, when a single belt is damaged, it is preferable to change the complete set to
Reduce vibration
Reduce slip
Ensure uniform loading
Ensure proper alignment
A circular bar moving in a round hole is an example of
Incompletely constrained motion
Partially constrained motion
Completely constrained motion
Successfully constrained motion
The two links OA and OB are connected by a pin joint at O. If the link OA turns with angular velocity ω₁ rad/s in the clockwise direction and the link OB turns with angular velocity ω₂ rad/s in the anticlockwise direction, then the rubbing velocity at the pin joint O is (where r = Radius of the pin at O)
ω₁.ω₂.r
(ω₁ - ω₂) r
(ω₁ + ω₂) r
(ω₁ - ω₂) 2r