PHY293 Oscillations Lecture #6
September 22, 2009
1. Second problem set now assigned (http://www.physics.utoronto.ca/ phy293h1f/waves/phy293
ps2.pdf)
2. Lecture outline will be “groomed” this week
•
Third problem set pushed back one week
•
Some additional lectures added
⇒
textbook reading pushed back
Start of material
1. Examples of Resonance in and LRC Circuit
•
Have already seen that an LC resonant circuit is another example of an oscillator
•
The natural frequency is
ω
0
= 1
/
√
LC
•
Can now add damping (a resistor) and driving (a signal generator)
◦
NB:
V
is voltage here (not velocity)
•
Use Kirchoff’s laws going around a circuit to find:
V
0
cos(
ωt
)

q/C

IR

L
dI
dt
= 0
•
Now make the association
˙
q
=
I
and divide through by
L
to get
¨
q
+
R
L
˙
q
+
q/
(
LC
) =
V
0
/L
cos(
ωt
)
•
This is just our forced/damped/SHO equation with
γ
=
R/L
;
ω
2
0
= 1
/LC
;
a
0
ω
2
0
=
V
0
/L
(
a
0
=
CV
0
)
•
Look at the circuit analogy of the velocity resonance (NB current is the circuit analog of velocity in the mechanical system)
I
(
ω
) =
I
max
γ
p
(
ω
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 Fall '07
 PierreSavaria
 Physics, mechanics, Statistical Mechanics, LRC Circuit, LC resonant circuit, http://www.physics.utoronto.ca/ phy293h1f/waves/phy293 ps2.pdf

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