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

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

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

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

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

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

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!

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?

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?

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

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

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

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

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

LAB WORKSHOP II

MULTIPLE DRIVNG FREQUENCIES

Day 9 LRC/Fourier 11/17/05 I = YV w0 2w0 3w0 PH421 F04

Vext

I ≠ Y Vext

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