1. A vehicle suspension system consists of a spring and a damper. The stiffness of the spring is 3.6 kN/m and the damping constant of the damper is 400 Ns/m. If the mass is 50 kg, then the damping factor (d ) and damped natural frequency (fn), respectively, are
a) 0.471 and 1.19 Hz
b) 0.471 and 7.48 Hz
c) 0.666 and 1.35 Hz
d) 0.666 and 8.50 Hz
Explanation: Given k = 3.6 kN/m, c = 400 Ns/m, m = 50 kg
We know that, Natural Frequency
ωn = √k/m = 8.485 rad/ sec
And damping factor is given by,
d or ε = c/cc
= 0.471
Damping Natural frequency,
ωd = √1 – ε2ωn
2πfd = √1 – ε2ωn
fd = 1.19 Hz.
2. For an under damped harmonic oscillator, resonance
a) occurs when excitation frequency is greater than undamped natural frequency
b) occurs when excitation frequency is less than undamped natural frequency
c) occurs when excitation frequency is equal to undamped natural frequency
d) never occurs
Explanation: For an under damped harmonic oscillator resonance occurs when excitation frequency is equal to the undamped natural frequency
ωd = ωn.
3. A vibratory system consists of a mass 12.5 kg, a spring of stiffness 1000N/m , and a dash-pot with damping coefficient of 15 Ns/m.The value of critical damping of the system is
a) 0.223 Ns/m
b) 17.88 Ns/m
c) 71.4 Ns/m
d) 223.6 Ns/m
Explanation: Given m= 12.5 kg, k= 1000N/m, c= 15 Ns/m
Critical Damping,
cc = 2m√k/m = 2√km
On substituting the values, we get
cc = 223.6 Ns/m.
4. In a reciprocating steam engine, which of the following forms a kinematic link ?
a) cylinder and piston
b) piston rod and connecting rod
c) crank shaft and flywheel
d) flywheel and engine frame
Explanation: in a reciprocating steam engine, piston, piston rod and crosshead constitute one link ; connecting rod with big and small end bearings constitute a second link ; crank, crank shaft and flywheel a third link and the cylinder, engine frame and main bearings a fourth link.
5. The motion of a piston in the cylinder of a steam engine is an example of
a) completely constrained motion
b) incompletely constrained motion
c) successfully constrained motion
d) none of the mentioned
Explanation: The piston and cylinder in a steam engine form a pair and the motion of the piston is limited to a definite direction (i.e. it will only reciprocate) relative to the cylinder irrespective of the direction of motion of the crank.
6. The motion transmitted between the teeth of gears in mesh is
a) sliding
b) rolling
c) may be rolling or sliding depending upon the shape of teeth
d) partly sliding and partly rolling
Explanation: When the two elements of a pair have a line or point contact when relative motion takes place and the motion between the two elements is partly turning and partly sliding, and in mesh the gears have a point contact.
7. The cam and follower without a spring forms a
a) lower pair
b) higher pair
c) self closed pair
d) force closed pair
Explanation: When the two elements of a pair are connected together mechanically in such a way that only required kind of relative motion occurs, it is then known as self closed pair. The lower pairs are self closed pair and the motion of cam and follower is relative to each other.
8. A ball and a socket joint forms a
a) turning pair
b) rolling pair
c) sliding pair
d) spherical pair
Explanation: When the two elements of a pair are connected in such a way that one element (with spherical shape) turns or swivels about the other fixed element, the pair formed is called a spherical pair, and ball and socket joint are such pairs.
9. The lead screw of a lathe with nut forms a
a) sliding pair
b) rolling pair
c) screw pair
d) turning pair
Explanation: When the two elements of a pair are connected in such a way that one element can turn about the other by screw threads, the pair is known as screw pair. The lead screw of a lathe with nut, and bolt with a nut are examples of a screw pair.
10. When the elements of the pair are kept in contact by the action of external forces, the pair is said to be a
a) lower pair
b) higher pair
c) self closed pair
d) force closed pair
Explanation: When the two elements of a pair are not connected mechanically but are kept in contact by the action of external forces, the pair is said to be a force-closed pair. The cam and follower is an example of force closed pair, as it is kept in contact by the forces exerted by spring and gravity.