Solutions to Assignment No. 2
Solution 2.2
(a)
Physically, w n is the natural frequency o f the system, and f is the phase ( lead )
angle of the response.
&
x = Aw n cos(w n t + f )
or
&
x = Aw n sin(
MECH 364: MECHANICAL VIBRATIONS
Solution Guidelines for the Mid-Term Examination, March 2010
Problem 1
(a)
(i)
Undamped Natural Frequency ( n)
This is the frequency at which the system will oscillate
VIBRATION ENGINEERING
Solution 1.1
Mechanical vibration deals with the oscillatory response of mechanical systems to some
form of an excitation (initial-condition or forcing excitation). Since the per
MECH 364 Mechanical Vibrations
SOLUTION GUIDELINES TO MID -TERM EXAMINATION
November 06, 2008
Problem 1
(a) Since the springs are uniform and one end of them is assumed fixed, the distributed
spring m
MECHANICAL VIBRATIONS
Solutions to the Final Examination 2
Problem 1.
(a)
Natural vibrations are oscillatory responses. Hence, both displacement and velocity
of the mass elements of the system will un
Mechanical Vibrations
Solution to Final Examination 1
Problem 1:
a) (i) Modal analysis decouples a coupled, complex, dynamic system. The uncoupled
equations are easier to analyze, and standard procedu
MECHANICAL VIBRATIONS
SOLUTIONS TO FINAL EXAM 3
Problem 1
(a)
(i)
Piezoelectric Accelerometer:
Produces an electric charge that is proportional to the inertia force in the
mass element of the accelero
MECHANICAL VIBRATIONS:
SOLUTIONS TO MID-TERM EXAM 1
Problem 1:
F
48EI
=
ym
l3
(i)
ke =
(ii)
For the beam,
l
1m
2
KE =
[ ym q(t )] sin 2 px dx
2l
l
0
l
But sin 2
0
px
l
dx =
l
2
Hence,
1m
KE =
[ ym q(t
Mechanical Vibrations
SOLUTIONS TO MID -TERM EXAMINATION 3
Problem 1
(a)
Assume a suitable velocity profile (typically linear) and, through
integration, determine the kinetic energy of the distributed
MECHANICAL VIBRATIONS
Solutions to the Mid-Term Examination 2
Problem 1
i)
Figure 1.
Shapes of the test responses
(a) Hammer test, (b) Shaker test.
-1-
Note that the response from the Hammer test is o