1. 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

2. Reading: Main 5.1, 6.1 Taylor 5.5, 5.6 THE DRIVEN, DAMPED HARMONIC OSCILLATOR 2 WE’LL DO EXPERIMENT TODAY, & THE THEORY TOMORROW!

3. Natural motion of damped, driven harmonic oscillator x m m k k viscous medium F 0 cos  t Note  and  0 are not the same thing!  is driving frequency   is natural frequency 3

4. Natural motion of damped, driven harmonic oscillator L R C I V o cos  t Apply Kirchoff’s laws http://www.sciencejoywagon.com/physicszone/lesson/otherpub/wfendt/accircuit.htm 4

5. LCR circuit obeys precisely the same equation as the damped mass/spring. LRC circuit L R C I Natural (resonance) frequency determined by the inductor and capacitor Damping determined by the resistor & inductor Typical numbers: L≈500µH; C≈100pF; R≈50     ≈10 6 s -1 (f   ≈700 kHz)  =1/  ≈2µs; (your lab has different parameters)

6. STEP #1: Build a LRC Circuit -V in should be a ~1 kHz sinusoid to start -V out is measured across the resistor V out (mv) V in V out tune the frequency knob Function generator, drives circuit AC

7. 7 Measure the frequency! “ctrl-alt-del” for osc Put cursor in track mode, one to track ch1, one for ch2 Menu off button “push”=enter save to usb drive measure V out across R V in to func gen STEP #2: Figure out the oscilloscope V t

8.  x (t) V out (mv) AC frequency of V in V in V in (mV) STEP #3: get your data!!! “crest to crest”

9. 9 STEP #4: Record your data (in an Excel table or software of your choice) + save a representative data trace Upload to CANVAS before class tomorrow for 5 points fill out a table like 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!