ME 375 – Spring 2011
Homework
No. 6
Due: Friday, March 4
th
Problem No. 1
(40%)
A piece of industrial equipment A (with mass m) is connected to ground with a pair of parallel
spring and dashpot components (having stiffness k and damping coefficient c, respectively) as
shown above.
A force of
0
()
f
tf
u
t
=
is applied to the equipment.
As seen earlier in the
course, the transfer function between the input
ut
and the response
y t
is given by
00
22
2
/
2
nn
ff
m
Ys
Us
m
s c
s k s
s
ζ
ωω
==
++
+
+
Where
/
n
km
ω
=
and
/(2
)
ck
m
=
. The force transmitted to the wall by the spring and
dashpot can be written as:
T
f
cy
ky
=
+
±
and the transfer function between the transmitted force
T
f
and the response y becomes:
2
(2
)
T
Fs
cs
k
m
s
=+=
+
It is desired to choose a spring stiffness to make the amplitude of the steadystate transmitted
force
( )
T
f
t
to be as small as possible for an input of
() s
in
t
=
.
(a)
Determine the transfer function
( )
( ) /
( )
T
Gs
F s Us
=
relating the transmitted force
T
f
t
for an input
.
Write your result in terms
,
0
f
, and
/
n
s
.
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 Fall '10
 Meckle
 Steady State, Attractor

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