- A 45 kg machine is placed at the end of a 1.6 m cantilever beam with a modulus of 200x109 N/m2 and cross-sectional moment of inertia of 1.6x10-5 m4.
- The machine produces a harmonic force of 125 N.
- The question asks to find the stiffness of the system.
1. A 45 kg machine is place at the end of a 1.6 m cantilever beam of elastic modulus of
9 2
200×10 N/m and cross-sectional Moment of Inertia of 5 4
1.6×10 m
. The machine produces
a harmonic force of magnitude 125 N. Find
Assignment 3
The due date for submitting this assignmenthas passed.
Due on 2020-02-19, 23:59 IST.
Assignment submitted on 2020-02-18, 18:02 IST
A 45 kg machine is place at the end ofa 1.6 m cantileverbeamofelastic modulus of200x109
N/m2
and cross-sectional
Moment ofInertia of 1.6X10-5
m4
. The machine produces a harmonic force ofmagnitude 125N. Find
1 point
The stiffnessofthe systemis
(3-4) x 106
N/m
(2-3) x 106
N/m
(5-6) x 106
N/m
(4-5) x 106
N/m
Yes, the answeris correct.
Score: 1
AcceptedAnswers:
(2-3) x 106
N/m
1 point
Allowable value ofmagnification factorin orderto restrict the steady-state amplitudeto 0.2mm is
3-4
1-2
4-5
5-6
Yes, the answeris correct.
Score: 1
AcceptedAnswers:
3-4
1 point
Allowable ranges offrequenciesforan undamped systemare
110-150 rad/sec
190-300 rad/sec
300-400 rad/sec
400-500 rad/sec
2. Yes, the answeris correct.
Score: 1
AcceptedAnswers:
190-300rad/sec
1 point
A 45 kg machine is placed on fourparallelsprings ofstiffness 2x105
N/m. when the machine operates at 32Hz, the
machines steady state
amplitude is measured as 1.5mm. What is the magnitude ofexcitation provided to the machine at this
speed?
1-2 kN
4-5 N
7-8 N
4-5 kN
Yes, the answeris correct.
Score: 1
AcceptedAnswers:
1-2 kN
1 point
An SDOF systemis subjectedto sinusoidalforce.At resonance,the displacement amplitude is 70mm. At an exciting
frequency of1/5th
ofthe
naturalfrequency ofthe system,the displacementamplitude was measured to be 10mm. The damping ratio
of the systemis
6-7 %
7-8 %
8-9%
9-10%
Yes, the answeris correct.
Score: 1
AcceptedAnswers:
6-7 %
A portalframe supportsa machine that exerts a sinusoidalforce of8.5 kN at a frequency of1.75 Hz. The mass of the
machine
is 4000 kg and is added to that ofthe frame.The mass ofthe frame at the floorlevel is 5000 kg and lateralstiffness of
the frame
is 4x106
N/m.
1 point
The applied force is
8500
8500 sin (1.75t)
8500 cos (1.75t)
8500 sin (11t)
No, the answeris incorrect.
Score: 0
AcceptedAnswers:
8500 sin (11t)
3. 1 point
Naturalfrequency ofthe systemis
3-4 Hz
4-5 Hz
5-6 Hz
6-7 Hz
Yes, the answeris correct.
Score: 1
AcceptedAnswers:
3-4 Hz
1 point
Forcing frequencyis
0.5-1
1-1.5
1.5-2
2-2.5
No, the answeris incorrect.
Score: 0
AcceptedAnswers:
0.5-1
1 point
Maximum static deflection ofthe systemis
2-3 mm
3-4 mm
4-5 mm
5-6 mm
Yes, the answeris correct.
Score: 1
AcceptedAnswers:
2-3 mm
1 point
For 4% damping,the steady state amplitude ofvibration is
2-2.3 mm
2.3-2.6 mm
2.6-2.9 mm
2.9-3.2 mm
Yes, the answeris correct.
Score: 1
AcceptedAnswers:
2.9-3.2 mm
4. 1 point
At Resonance,the steadystate amplitude ofvibrationis
20-30mm
30-50mm
50-70mm
70-90mm
Yes, the answeris correct.
Score: 1
AcceptedAnswers:
20-30mm
A delicate instrument weighing 0.45kNis to be mounted on a rubberpad to the floorofa test laboratory where the
verticalacceleration
is 0.1g at a frequency of10Hz. It has been determined experimentally that the ratio ofthe stiffness,k,to the damping
coefficient,
c, is equalto 100 (1/sec)for the type ofrubberpad materialused in the isolation.Ifthe acceleration transmitted to the
instrument is 0.01g, for 10% damping
1 point
Frequency ratio is
4-5
5-6
3-4
6-7
Yes, the answeris correct.
Score: 1
AcceptedAnswers:
3-4
1 point
Naturalfrequency ofthe systemis
90-105 rad/sec
15-20 rad/sec
105-120 rad/sec
35-40 rad/sec
Yes, the answeris correct.
Score: 1
AcceptedAnswers:
15-20 rad/sec
1 point
Stiffness ofthe systemis
13500-13700 N/m
13250-13500 N/m
13750-14000 N/m
5. 14000-14250 N/m
No, the answeris incorrect.
Score: 0
AcceptedAnswers:
13500-13700 N/m
1 point
Damping of the systemis
180-200 N-s/m
140-160 N-s/m
160-180 N-s/m
130-140 N-s/m
No, the answeris incorrect.
Score: 0
AcceptedAnswers:
130-140N-s/m
A bumpy roadway is modelled as sinusoidalcurve having a verticaldisplacement frompeakto peakof12.7cm at a
distance of
L = 7.62m, between peaks.An automobile idealized as a single degree offreedomsystem,appropriatefora first
approximation,
weighs 15.57kN fully loaded.The stiffnessofthe suspension systemofthe automobile is 175.13kN/m and its viscous
damping systemprovides40% ofthe critical damping.Automobile is travelling at a velocity of50 mph. Assume the
vehicle remains
in contact with the road andthatthe tires are rigid in comparison with the suspensionsystemofthe automobile.
1 point
The verticaldisplacement ofthe tyreswill be
y(t)=10.78 sinωt
y(t)=4.38sinωt
y(t)=20.9sinωt
y(t)=17.5sinωt
Yes, the answeris correct.
Score: 1
AcceptedAnswers:
y(t)=4.38sinωt
1 point
Forcing period ofthe automobile with velocity v to travelthe distance Lis
0.3-0.5 sec
0.5-0.7 sec
0.7-0.9 sec
0.9-1 sec
Yes, the answeris correct.
Score: 1
AcceptedAnswers:
0.3-0.5 sec
6. 1 point
Forcing frequencyofthe automobile is
69-90 rad/sec
17-20 rad/sec
91-100 rad/sec
45-65 rad/sec
Yes, the answeris correct.
Score: 1
AcceptedAnswers:
17-20 rad/sec
1 point
Transmissibility ratio ofthe systemis
0.4.-0.5
0.6 -0.75
0.9-1
0.77- 0.85
Yes, the answeris correct.
Score: 1
AcceptedAnswers:
0.6 -0.75
1 point
Maximum displacement ofthe systemwhen the automobile is at maximum speed is
70-80 cm
20-40 mm
10-15 cm
80-90 mm
Yes, the answeris correct.
Score: 1
AcceptedAnswers:
10-15 cm
1 point
During a vibration test undera harmonic force it was observed that thefrequencyis 10% higherthan the resonant
frequency,the displacement
amplitude was exactly one-halfofthe resonant amplitude,the damping in the systemis
5-7%
7-9%
8-9%
9-10%
No, the answeris incorrect.
Score: 0
AcceptedAnswers:
