The equation of free vibrations of a system is (d²x/dt²) +36 π²x, its natural frequency is
3 Hz
3π Hz
6 Hz
6π Hz
Correct Answer :
A. 3 Hz
Related Questions
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 vibration isolation system, if ω/ωn > 1, then the phase difference between the transmitted force and the disturbing force is
0°
90°
180°
270°
A foot step bearing and rotor of a vertical turbine form examples of
Incompletely constrained motion
Partially constrained motion
Completely constrained motion
Successfully constrained motion
Which of the following governor is used to drive a gramophone?
Watt governor
Porter governor
Pickering governor
Hartnell governor
When the sleeve of a Porter governor moves upwards, the governor speed
Increases
Decreases
Remain unaffected
First increases and then decreases
Klein's construction can be used when
Crank has a uniform angular velocity
Crank has non-uniform velocity
Crank has uniform angular acceleration
Crank has uniform angular velocity and angular acceleration
The rotor of a ship rotates in clockwise direction when viewed from stern and the ship takes a left turn. The effect of gyroscopic couple acting on it will be
To raise the bow and stern
To lower the bow and stern
To raise the bow and lower the stern
To raise the stern and lower the bow
The frictional torque transmitted in a flat pivot bearing with assumption of uniform pressure is _________ as compared to uniform wear.
Less
More
Same
None of these
Kinematic pairs are those which have two elements that
Have line contact
Have surface contact
Permit relative motion
Are held together
Which of the following statement is correct for gears?
The addendum is less than the dedendum
The pitch circle diameter is the product of module and number of teeth
The contact ratio means the number of pairs of teeth in contact
All of the above
The velocity of a body moving with simple harmonic motion is __________ at the mean position.
Zero
Minimum
Maximum
None of these
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
Which type of gearing is used in steering system of an automobile?
Rack and pinion
Worm and wheel
Spiral gears
None of the above
A rotary internal combustion engine has __________ cylinders.
Four
Five
Six
Seven
A chain comprises of 5 links having 5 joints. Is it kinematic chain?
Yes
No
It is a marginal case
Data are insufficient to determine it
A typewriter mechanism has 7 numbers of binary joints, six links and none of higher pairs. The mechanism is
Kinematically sound
Not sound
Soundness would depend upon which link is kept fixed
Data is not sufficient to determine same
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)}
Which of the following disciplines provides study of relative motion between the parts of a machine?
Theory of machines
Applied mechanics
Mechanisms
Kinematics
The cam and follower is an example of
Sliding pair
Rolling pair
Lower pair
Higher pair
When the elements of a pair are kept in contact by the action of external forces, the pair is said to be a
Lower pair
Higher pair
Self-closed pair
Force-closed pair
If the pressure angle is __________, a reciprocating follower will jam in its bearings.
Small
Too small
Large
Too large
If ω/ωn = 2, where co is the frequency of excitation and ωn is the natural frequency of vibrations, then the transmissibility of vibration will the
0.5
1
1.5
2
If there are L number of links in a mechanism, then number of possible inversions is equal to
L + 1
L - 1
L
L + 2
The instantaneous centres which vary with the configuration of mechanism are called
Permanent instantaneous centres
Fixed instantaneous centres
Neither fixed nor permanent instantaneous centres
None of the above
The frictional torque transmitted in a flat collar bearing, considering uniform pressure, is (where r₁ and r₂ = External and internal radii of collar respectively)
(1/2). μ W (r₁ + r₂)
(2/3). μ W (r₁ + r₂)
(1/2). μ W [(r₁³ - r₂³)/(r₁² - r₂²)]
(2/3). μ W [(r₁³ - r₂³)/(r₁² - r₂²)]
The example of spherical pair is
Bolt and nut
Lead screw of a lathe
Ball and socket joint
Ball bearing and roller bearing
If the controlling force line for a spring controlled governor when produced intersects the Y-axis at the origin, then the governor is said to be
Stable
Unstable
Isochronous
None of these
The size of a gear is usually specified by
Pressure angle
Circular pitch
Diametral pitch
Pitch circle diameter
Which of the following is a lower pair?
Ball and socket i
Piston and cylinder
Cam and follower
Both (A) and (B) above
When a rigid body is suspended vertically and it oscillates with a small amplitude under the action of the force of gravity, the body is known as
Simple pendulum
Compound pendulum
Torsional pendulum
Second's pendulum