186
DOC. 14 PROOF OF
AMPERE'S
CURRENTS
709
on
the
horizontal1)
axis
give
the
frequencies
of
the
alternating
current,
those
on
the vertical
axis
10 times
the
double deviation
in
centimeters.
For the calculation
we
each
time used two
points
at
the
same
height
combined
with the ordinate of the
highest point
of
the
curve.
If
for shortness'
sake
we put
4X7,
-77
=u
.t
Q
it follows from
(15)
that
m
=
|/[«iE5v
+~
|o|
CO1
Now,
if
w1(w0)
and
w2(w0)
are
the two
values
of
W corre-
sponding
to
the
same
amplitude |a|
we
have the
equations
"
=
+
4".
and
=
+
4,
\a\
V
o,#
\a\
V
o,
By
elimination of
w0
and
x
from these and from
we
find
(A*
fl1
(CO,--tf
,)*.
[15]
Let
v
be the difference in
frequency
of the
two chosen
points,
so
that
to1
-
w2 =
4nv
and
let
us
put
4=6.|«L
Then
we
find,
after
introducing
the value of
u
*
=
*'
jJ®!-*"
|/l5'
(17)
When
the
resonance
curve
has
been
drawn,
(17)
gives
a
value
of
X
for each
ordinate
\a\.
If
this value
or
what
amounts to the
1/b2/1-b2
same
v
\b2
is constant,
this
proves
that the influence of
the
damping can
really
be
represented
by a
linear term in the
equation
of
motion.
The
following
table
contains the
values of
v
and
b,
taken
from
the
diagram
and
those
of
v
1-b2
we have deduced
from them.
1)
If
the figure
is
brought into the
right
position by
a
rotation of
90°.
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