Transcript Lab Slides 3

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
THE DRIVEN, DAMPED HARMONIC
OSCILLATOR
Reading:
Main 5.1, 6.1
Taylor 5.5, 5.6
WE’LL DO EXPERIMENT TODAY,
& THE THEORY TOMORROW!
2
Natural motion of damped, driven harmonic oscillator
Force = m˙x˙
restoring + resistive + driving force = mx˙˙
w0 =
w1 = w 0
k
k
m
b2
1- 2
w0
k
F0coswt
m
viscous medium
m
x
-kx - bx + F0 cos (w t ) = mx
mx + w 02 x + 2b x+ = F0 cos (w t )
Note w and w0 are not
the same thing!
w is driving frequency
w0 is natural frequency
3
Natural motion of damped, driven harmonic oscillator
Apply Kirchoff’s laws
L
I
Vocoswt
C
R
q
V0 cos (w t ) - Lq - - Rq = 0
C
V0 iw t
2
q + 2b q + w 0 q = e
L
4
http://www.sciencejoywagon.com/physicszone/lesson/otherpub/wfendt/accircuit.htm
LRC circuit
L
I
C
R
LCR circuit obeys precisely the
same equation as the damped
mass/spring.
Natural (resonance)
frequency determined by
the inductor and capacitor
1
LC
w0 =
Typical numbers:
L≈500µH; C≈100pF; R≈50W
Damping determined by
w0 ≈106s-1 (f0 ≈700 kHz)
the resistor & inductor
t=1/b≈2µs;
R
(your lab has different parameters)
b=
2L
Vout(mv)
STEP #1: Build a LRC
Circuit
- Vin should be a ~1 kHz
sinusoid to start
- Vout is measured across
the resistor
Function generator,
drives circuit AC
Vout V
in
tune the
frequency knob
Vin
Vout(mv)
STEP #2: Figure out the oscilloscope
Menu off button
“push”=enter
Measure the frequency!
“ctrl-alt-del” for osc
V
save to usb drive
t
7
Put cursor in track mode, one
measure Vout across R Vin to func gen to track ch1, one for ch2
STEP #3: get your data!!!
“crest to crest”
V
in
(mV)
Vout(mv)
Dx (t)
Vin
AC frequency of Vin
STEP #4: Record your data (in an Excel table or
software of your choice)
+ save a representative data trace
fill out a table like
Upload to CANVAS before class tomorrow for 5 points
this with data form
the oscilloscope
Choose your
frequencies
intelligently!
(~8 well placed
measurements is
enough)
Step #5: Upload your data to
CANVAS before class tomorrow
for 5 lab points.
You’re now DONE!
Congrats! 9