∝ 
V
R

2
then “half power” occurs when

V
R
 → 
V
R
√
2

. Label these
ω

and
ω
+
respectively.
•
You will now collect data about the resonant peak to get a better idea of how

V
R

and
φ
depend on
ω
.
At each point, record the frequency, amplitude, and phase of the sine
wave. The phase can be found by comparing the time of the peaks to those in the Output
voltage. Be sure to take approximately 5 data points below
ω

, 5 above
ω
+
and at least
10 between the two (being sure to include
ω

,
ω
0
and
ω
+
).
•
Now you will fit to the amplitude data the following expression, with A, B, C as fitting
parameters:

V
R
(
ω
)

=
A
q
1 +
B
2
(
ω
C

C
ω
)
2
(3)
•
What physical meaning do A, B and C have? What are their units? Verify their theoretical
values using your knowledge of the fitting parameters.
•
You will also fit the phase data with the following model function:

φ
(
ω
)

= arctan
D
ω

F
ω
(4)
•
What physical meaning do D and F have? What are their units? Verify their theoretical
values using your knowledge of the fitting parameters.
2
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 Spring '11
 shpyrko
 Resistance, parameters, critical damping resistance

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