EML 6267 Assignment #1 Spring 2009
Please remember to put your name on your assignment.
Due: 1/21/09
1.
(25 pts.) For a given single degreeoffreedom (SDOF) lumped parameter system
(undamped), the free vibration,
x
(
t
), is shown below.
a)
(20 pts.) If the motion was initiated with a velocity of 2
π
mm/s and zero initial displacement,
express the motion in the forms show below (use units of mm):
i)
(5 pts.)
x
(
t
) =
A
cos(
ω
n
t
) +
B
sin(
ω
n
t
)
ii)
(5 pts.)
x
(
t
) =
C
cos(
ω
n
t
+
Φ
c
)
iii)
(5 pts.)
x
(
t
) =
C
sin(
ω
n
t
+
Φ
s
)
iv)
(5 pts.)
x
(
t
) =
De
Ee
i
t
i
t
n
n
(
)
(
)
ω
ω
+
−
.
b)
(5 pts.) Given your expression for
x
(
t
) in part ai), write an expression for the velocity,
dx
(
t
)/
dt
, (mm/s). Plot your result over the same time interval (0 to 0.5 s) shown above. Verify
that the peak velocity is
ω
n
B
. Please include the computer code used to generate the plot.
2.
(20 pts.) For a SDOF lumped parameter system under free vibration with the following
values for the mass, stiffness and damping:
m = 1.0 kg
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.1
0.08
0.06
0.04
0.02
0
0.02
0.04
0.06
0.08
0.1
Time (s)
x (mm)
HW 1, problem 1
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c = 10.0 Ns/m
k = 4.0e4 N/m
a)
(5 pts.) Find
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 Spring '08
 Schmitz
 Complex number, Microphone, Damping ratio

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