Biomedical Engineering Reference
In-Depth Information
If the object is isolated from the base and decelerated to a complete stop
by a constant force
−
mw
,where
w
is the deceleration magnitude (
w >
0),
the peak magnitude of this force is
F
2
=
mw
.For
F
2
<F
1
, it is necessary
that
w<a
. The deceleration pulse of the object then has the form
⎨
⎩
V
w
,
−
w
if 0
≤
t
≤
u(t)
m
=
(2.30)
0 f
t >
V
w
,
and the object's absolute motion is defined by
⎧
⎨
⎧
⎨
wt
2
2
V
w
,
V
w
,
−
≤
−
≤
V
wt
if
t
Vt
if
t
x
˙
=
x
=
(2.31)
⎩
if
t >
V
⎩
V
2
2
w
if
t >
V
0
w
,
w
.
The deceleration time of the object is
V/w
and the deceleration path is
V
2
2
w
.
P
o
=
(2.32)
Since
w<a
, the deceleration path of the object is longer than the deceleration
path of the base. By subtracting
P
b
from
P
o
we find the rattlespace
a
w
−
1
P
b
a
1
.
V
2
2
a
R
=
=
w
−
(2.33)
Equation (2.33) is valid also for a system which is in a state of rest until
the shock pulse is applied to the base and accelerates it with a constant
acceleration
a
to a velocity
V
. In this case, the system of Eq. (2.24) is
subjected to the initial conditions
=
=
˙
=
˙
=
x(
0
)
0
,
z(
0
)
0
,
x(
0
)
0
,
z(
0
)
0
(2.34)
and the shock pulse has the form
⎧
⎨
⎩
V
a
,
a
if 0
≤
t
≤
v(t)
=
(2.35)
0 f
t >
V
a
.
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