ME 375 – Fall 2010
Homework No. 6
Due: Friday, October 15
Problem No. 1 (40%)
A system is made up of connector A (of negligible mass), movable support D, three
springs and a dashpot, connected as shown in the figure above. Support D is given a
PRESCRIBED
displacement
of
y
D
t
( )
=
du t
( )
, where
u t
( )
is the input to the system. All
springs are unstretched when
y
D
=
y
=
0
. For this problem:
a)
Draw an appropriate free body diagram (FBD) of the massless connector A. From
this FBD, derive the equation of motion (EOM) of the system with the displacement
of block A,
y
, being the output.
b)
Based on your EOM from a), determine the transfer function
G s
( )
=
Y s
( )
/
U s
( )
.
c)
For
u t
( )
=
sin
!
t
, we know that the steadystate response of the system can be
written as:
y
ss
t
( )
=
G j
!
(
)
sin
!
t
+
"
G j
!
(
)
(
)
. Develop expressions for the
amplitude
G j
!
(
)
and phase of the response
!
G j
"
(
)
in terms of
c
,
k
and
d
.
d)
A time history of the steadystate response of this system for
u t
( )
=
sin
2
t
is shown
in the figure on the following page for
k
=
10
N
/
m
. From this plot, estimate values
of
c
and
d
for this system.
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 Fall '10
 Meckle
 Mass

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