Summary so far:

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Summary so far Free, undamped, linear
(harmonic) oscillator Free, undamped,
non-linear oscillator Free, damped linear
oscillator Starting today Driven, damped
linear oscillator Laboratory to investigate LRC
circuit as example of driven, damped oscillator
Time and frequency representations Fourier
series
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THE DRIVEN, DAMPED HARMONIC OSCILLATOR
Reading Main 5.1, 6.1 Taylor 5.5, 5.6
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Natural motion of damped, driven harmonic
oscillator

• Note w and w0 are not the same thing!
• is driving frequency
• w0 is natural frequency

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Natural motion of damped, driven harmonic
oscillator
Apply Kirchoffs laws
http//www.sciencejoywagon.com/physicszone/lesson/
otherpub/wfendt/accircuit.htm
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underdamped
Damping time or "1/e" time is t 1/b gt 1/w0 (gtgt
1/w0 if b is very small)
How many T0 periods elapse in the damping time?
This number (times p) is the Quality factor or Q
of the system.
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LRC circuit
LCR circuit obeys precisely the same equation as
the damped mass/spring.
Typical numbers L500µH C100pF R50W w0
106s-1 (f0 700 kHz) t1/b2µs (your lab has
different parameters)
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Measure the frequency!
Menu off button
pushenter
ctrl-alt-del for osc
save to usb drive
Put cursor in track mode, one to track ch1, one
for ch2
measure Vout across R
Vin to func gen
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V0 real, constant, and known
Let's assume this form for q(t)
But now q0 is complex
This solution makes sure q(t) is oscillatory (and
at the same frequency as Fext), but may not be in
phase with the driving force.
Task 1 Substitute this assumed form into the
equation of motion, and find the values of q0
and fq in terms of the known quantities. Note
that these constants depend on driving frequency
w (but not on t that's why they're
"constants"). How does the shape vary with w?
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Assume V0 real, and constant
Task 2 In the lab, you'll actually measure I
(current) or dq/dt. So let's look at that
Having found q(t), find I(t) and think about how
the shape of the amplitude and phase of I change
with frequency.
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Assume V0 real, and constant
Task 1 Substitute this assumed form into the
equation of motion, and find the values of q0
and f in terms of the known quantities. Note
that these constants depend on w (but not on t
that's why they're constants). How does the
shape vary with w?
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"Resonance"
Charge Amplitude q0
Driving Frequency------gt
Charge Phase fq
0
-p/2
-p
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Task 2 In the lab, youll actually measure I
(current) or dq/dt. So let's look at that
Having found q(t), find I(t) and think about how
the shape of the amplitude and phase of I change
with frequency.
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Resonance
Current Amplitude I0
Driving Frequency------gt
p/2
Current Phase
0
-p/2
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Resonance
Charge Amplitude q0
w0
Driving Frequency------gt
Current Amplitude I0
w0
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Charge Phase fq
0
-p/2
-p
w0
Driving Frequency------gt
p/2
Current Phase
0
-p/2
w0