# CU-Boulder MCEN 3037 - 11 (13 pages)

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- Pages:
- 13
- School:
- University of Colorado at Boulder
- Course:
- Mcen 3037 - Data Analysis

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Determine all sources of error divide into bias and precision Find an equation for the variable of interest in terms of given quantities Differentiate the equation to find standard random uncertainty systematic general equation plug in to find these Almostuncertainty the same asinthe previous example Why quantities Determine degrees of freedom t value Systematic uncertainty given at any confidence level tv P b Generally assume Bias error have high degrees of freedom n large t 2 At 95 confidence Bias errors typically listed at 95 confidence B We can convert this to a standard systematic uncertainly b b Here t z 1 B 2 Giving about a 68 confidence interval P Sx Now the standard random uncertainty is Sx P N Now we have standard b and P and combine them with the RSS with the result multiplied by the t value u x tv p b 2 P 2 Alternative book ux B 2 tv P P These are different 1 2 2 b P 2 2 Called combined standard uncertainty Our approach 2 Pk v k K1 4 Pk K n k 1 Alternate approach 2 2 2 2 Pk bk v Kk 1 4 K 4 Pk bk K k 1 2 2 ux B 2 tv P P k 1 nk k 1 nk ux tv p b2 P 2 0 A graduate student decides to measure the elastic modulus E of an aluminum sample by measuring the longitudinal wave velocity using an ultrasound transducer and using the relationship Longitudinal wave speed vl E density In order to measure the velocity the travel time of an ultrasound pulse through a specimen of thickness d is measured 10 measurements of the travel time give a mean value of 60 0 ms with a standard deviation of 5 0 ms These values are measured on an oscilloscope with a time resolution of 0 5 ms The thickness of the sample is measured with an optical gauge that outputs a voltage proportional to the thickness with a sensitivity of 10 mV mm The output is fed into an 8 bit A D board with a FSO range of 4V A set of 12 measurements are read into the computer and have a mean of 3 60 V and a standard deviation of 0 02 V The density of aluminum is taken to be 2700 kg m3 with a listed accuracy of 1 vl

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