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Physics I Lab Manual 2011 23

# Physics I Lab Manual 2011 23 - f a,b = a b or f a,b = a-b...

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EXPERIMENT 2. MEASUREMENT AND PRECISION Figure 2.1: Example of correlated and uncorrelated measurements The randomness of the values of the dice ensure that, on average, the spread in values you get with multiple rolls is less than when you only roll once and count the values multiple times. The same principle applies to measurement uncertainty, as the equations above show that uncorrelated uncertainties produce less spread in a measurement than correlated uncertainties. When the above two premises are applied to functions that involve the sum or difference of two or more quantities, such as
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Unformatted text preview: f ( a,b,. .. ) = a + b + ... or f ( a,b,. .. ) = a-b-... the resulting uncertainty in f due to each term is found from f a = df da a f b = df db b where for f ( a,b,. .. ) = a b + ... and df da = df db = 1 with the sign depending on if b is being added or subtracted. This gives f a = a and f b = b . When adding these uncorrelated uncertainties using ( f ) 2 = ( f a ) 2 + ( f b ) 2 + ... we get the general expression ( f ) 2 = ( a ) 2 + ( b ) 2 + ... (2.1) Sum and dierence formula for uncertainty 13...
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