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# Phys Lab PHYS 2CL

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This 18 page Class Notes was uploaded by Mrs. Taryn Treutel on Thursday October 22, 2015. The Class Notes belongs to PHYS 2CL at University of California - San Diego taught by Staff in Fall. Since its upload, it has received 83 views. For similar materials see /class/226820/phys-2cl-university-of-california-san-diego in Physics 2 at University of California - San Diego.

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Date Created: 10/22/15

Lecture 5 Physics 20L 20 August 2007 Experiment4 Filters BandPass HighPass Rejection of DataTheory Chauvenet Criterion x2 Test Quiz 4 Summer I 2007 5 X 1015 inflation Experiment 3 Filters BandPass passes frequencies within a specific range and attenuates those outside of that range HighPass passes frequencies as high as a speci c threshold frequency and attenuates any signal of lesser frequency 1 Cum Frequ may BandPass LowPass High Pass N rmallzed Output PUWEI hig39lpaysl39llter Experiment 3 Resonance Definition Tendency of system to oscillate with a maximum amplitude at a specific frequency Other Examples Acoustical Mechanical eg mass on a spring pendulum Tidal Orbital Electrical Resonance Occurs in an electric circuit when impedance between the input and the output is minimum Impedance Resistance in AC with phase Experiment 3 Electrical Resonance Timedependent signal Vt 2 V0 sinal Resistor V IR IR 2 V0 sinat gt I sinat Inductor V Z L d L 2 V0 sinat gt I a cosat dt dt L Voltage leads current by 752 1dr I 2 V0 smat gt I VOC cosat Current leads voltage by 752 Capacitor V Q C C Experiment 3 Impedance Revisited V Voem em cosat i sinat VR IRRgtIR Experiment 3 Electrical Resonance Impedance Series lZzl l21 Zzl ZR R Parallel1 1 1 ZL iwL ZE Zl Zz ZCCwCw ij we iCa iCa i2Ca2 Ca Maximize parallel impedanceMinimize series impedance In RLC electric energy oscillz field L to electrical field C vm L C R Experiment 3 Resonance Frequency Domain VR RIM smagtt p L 1 Loop rule 0 vm R Vc mcoswt VVRVCVL wC all have different VL lem coswt p phases V2 1ng ImXL ImXC 2 XL 1m Z Z XC Z R2XL7XC 1 Impedance Z R2 mLi aJC Courtesy of Professor Basov Experiment 3 Resonance Frequency Domain Resistance of Inductor G Vout a V R In I llM In In 4 M 0 39E 1 Q 390 ll I R WER 3 Plot Gain vs Frequency r quot Ierfical I hnri7nnfal I Irinnar mhlrmnm quot39M 1 39 inquot I I I I I I I I I I I I I GTn 3 frequency a a g y 1quot13 quot3 E23 Bandwidth difference between frequencies at which amplitude is Kb 60 Au 0 Experiment 3 Resonance BandPass Plot Phase vs Frequency Fit to expression p tanquot vm ax IJbe I 3 RHCoJl R17qu3 C 00 K Hi1 a RCm Experiment 3 High Pass Plot Gain vs Frequency Fit the data to an appropriate form of Rejection Of Data Chauvenet s Criterion 9393 4 suspicious x xmpm t0 x x 216220 suspect PX 20gtan20ltx1 PX 20ltxltX20 PX 20gtan20ltx1 095 nNgtltPX 20gtan20ltx 1 n lt E p SUSpICIOUS value can be rejected n 03 p 18 Is Improbable and rejectable The Probability that a measurement If the methodtechnique is suspicious will be as deviant as the suspect value must data are disposable Without comparison be scaled by the total number of measurements to other data in order to determine the expected fraction of such deviants in the relevant sample size x2 Test 30 20 YX 10 III How good is the agreement between theory and data 10 15 20 25 Courtesy of Professor Basov x2 Test continued 2 yj fxj2 N02 962 1 2 2 2 7y 7y 2 NZ 9 1 3 39 d gt of degrees of freedom 3 i q N 39 c 10 of data points of parameters 0lllllllllllllllllllllll 0 5 computed from data of constraints Courtesy of Professor Basov x2 TEST for HT 22 distribution HOW GXG 00 10M2 20 30 40 960 Prob outside to from data Courtesy of Professor Basov Probability of 952 11 2 Quantitative measure of agreement between 562 95 observed data and their expected distribution quotdef Probability of obtaining W e a P N u o avalueofj greateror 075 10 125 15 175 2 3 A 5 6 2 1 100 oz 41 39 32 26 22 19 16 s s 3 1 equal to 950 vassum39ng 2 1011 71 51 A7 37 29 22 17 14 5 2 07 02 the measurements are 3 100 86 68 52 39 29 21 15 11 3 07 02 governed b the 5 100 94 78 50 42 28 19 12 s 1 01 10 100 99 119 as 44 15 13 o 3 01 7 7 expeCted d39Str39bUtlon 15 100 mo 94 73 45 23 1o 4 1 N2 N2 Probability that for d degrees of freedom reduced 36 is as PrObd I 2 Zn large as the reduced observed x1 disagreement is significant if Probe2 10 lt 5 reject the expected disagreement is highly significant if Probe2 102 lt 1 diStribUtion Courtesy of Professor Avi Yagil Example Application of x2 Test Die is tossed 600 x Expectation each face has equivalent likelihood of showing up V 1 2 3 4 5 6 n 91 137 111 87 80 94 exp 100 100 100 100 100 100 A2 81 1369 121 169 400 36 6 10101010 1010 This term is the squared difference xzi 081 137 121 169 40 036 between observation and expectation Verification of expectation by computing the X2 Total x2 2176 In computation of x2 the A2 term is divided by ndof 2 5 expectation G is square root of expectation reduced X 435 2 Ey 6y Adapted from presentation by Professor Avi Yagil

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