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1
ME 375
HOMEWORK #7 SOLUTION
6SULQJ
PROBLEM 1
:
(30%)
GIVEN
:
An industrial sewing machine (having mass
m
) is mounted on springs (with stiffness
k
) and
dampers (with damping coefficient
b
) to decrease the force transmitted to the floor.
The input
force acting on the sewing machine during operation is denoted by
F
(
t
), while the vertical motion
of the machine is denoted by
y
(
t
).
The sewing machine mass is 150 kg.
Suitable spring and
damper values must be selected so that the vertical motion of the machine is sufficiently small.
FIND
:
(a)
Draw a schematic diagram that describes this system.
(b)
Generate the transfer function between input force
F
(
t
) and vertical displacement
y
(
t
).
(c)
The excitation force is given by
() 5s
in
(30)
Ft
t
=
N and the following springs and dampers
are available:
55
1.35 10 , 5.4 10
k
=×
×
N/m, and
2250,12000
b
=
N/(m/s), select the best
combination of one spring and one damper so that the steadystate amplitude of
y
is
5
1.0 10
−
×
m or less.
Please explain how you arrived at your answer.
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 Fall '10
 Meckle
 Damper

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