1. PH 421: Oscillations - do not distribute
5/11/2019
DRIVEN, DAMPED OSCILLATOR L R C I
Vocoswt
Lecture 6 - Driven oscillations

2. PH 421: Oscillations - do not distribute
5/11/2019
CHARGE
"Resonance"
Charge
Amplitude
|q0| w0
Driving Frequency w------>
Charge
Phase fq
-π/2 -π w0
Lecture 6 - Driven oscillations

3. PH 421: Oscillations - do not distribute
5/11/2019
CURRENT
“Resonance”
Current
Amplitude
|I0| w0
Driving Frequency w------>
π/2
Current
Phase fI
-π/2 w0
Lecture 6 - Driven oscillations

4. PH 421: Oscillations - do not distribute
5/11/2019
ADMITTANCE
“Resonance”
Admittance
Amplitude
|Y0| w0
Driving Frequency w------>
π/2
Addmittance
Phase fI
-π/2 w0
Lecture 6 - Driven oscillations

5. PH 421: Oscillations - do not distribute
5/11/2019
DRIVEN, DAMPED OSCILLATOR
• can also rewrite diff eq in terms of I and solve directly (same result of course) L R C I
Vocoswt
Lecture 6 - Driven oscillations

6. QUESTION: FM radio stations have broadcast frequencies of approximately 100 MHz. Most radios use a series LRC circuit similar to the one you used in the lab as part of the receiver electronics.
Estimate minimum spacing of the broadcast frequencies of FM stations if typical receivers have a Q of 500 or better. Explain your reasoning.
station 1
station 2 Dw Dw

7. QUESTION: FM radio stations have broadcast frequencies of approximately 100 MHz. Most radios use a series LRC circuit similar to the one you used in the lab as part of the receiver electronics.
Estimate minimum spacing of the broadcast frequencies of FM stations if typical receivers have a Q of 500 or better. Explain your reasoning.
station 1
station 2 Dw
Therefore, stations 99.3 and 99.5 FM are allowed, but 99.3 and 99.4 FM are not! They have cross-talk!

8. Example: Designing a Radio Receiver
An AM radio antenna picks up a 1000 kHz signal with a peak voltage of 5.0 mV. The tuning circuit consists of a 60 mH inductor in series with a variable capacitor. The inductor coil has a resistance of 0.25 W, and the resistance of the rest of the circuit is negligible.
To what capacitance should the capacitor be tuned to listen to this radio station?
(b)What is the peak current through the circuit at resonance?
(c) A stronger station at 1050 kHz produces a 10 mV antenna signal. What is the current in the radio at this frequency when the station is tuned to 1000 kHz?

9. Example: Designing a Radio Receiver
An AM radio antenna picks up a 1000 kHz signal with a peak voltage of 5.0 mV. The tuning circuit consists of a 60 mH inductor in series with a variable capacitor. The inductor coil has a resistance of 0.25 W, and the resistance of the rest of the circuit is negligible.
To what capacitance should the capacitor be tuned to listen to this radio station?
(b)What is the peak current through the circuit at resonance?
(c) A stronger station at 1050 kHz produces a 10 mV antenna signal. What is the current in the radio at this frequency when the station is tuned to 1000 kHz?

11. PH421: Oscillations; do not distribute
Free, damped oscillators
11/12/07 x m k
friction q mg m T
Common notation for all
Lecture 5/6 - damped oscllations

12. Resonating Tug of War
Case #1: above resonance
|xo(w,t)|
driver
mass

13. Resonating Tug of War
Case #2: below resonance
|xo(w,t)|
driver
mass

14. Resonating Tug of War
Case #3: at resonance
|xo(w,t)|
driver
mass

15. wo2=g/l
Fortunately, the Q-Factor of swings is generally terrible.
So … you can get away fpush < p/2 !

16. LAB WORKSHOP II

17. MULTIPLE DRIVNG FREQUENCIES

18. Day 9 LRC/Fourier
11/17/05
I = YV
w w w0
PH421 F04

19. Vext

20. I ≠ Y Vext

21. Day 11 - Impulse response of LRC circuit
11/21/05
DRIVING AN OCILLATOR WITH A PERIODIC FORCING FUNCTION THAT IS NOT A PURE SINE
PH 421 F05; do not distribute