Empyrical Analysis of a ring pendulum lab equations

Empyrical Analysis of a ring pendulum lab equations - Ring...

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Empirical Analysis of a Ring Pendulum Part 1: Table I Ring T1 T2 T3 T4 T5 Average T standard error of T Fractional error of T m1= 99.4 g m1 0.259 0.258 0.260 0.258 0.259 0.259 0.0004 0.145 m2= 104.8 g m2 0.260 0.259 0.259 0.258 0.258 0.259 0.0004 0.145 m3= 35.0 g m3 0.261 0.254 0.254 0.254 0.254 0.255 0.0014 0.548 Part 2: Inner Diameter (mm) Outer Diameter (mm) Ring T1 T2 T3 Ut Ring 1 36.7 42.5 m1 0.398 0.398 0.398 0.000 36 42.5 m2 0.804 0.803 0.803 0.001 36.1 42 m3 0.624 0.625 0.625 0.001 Ring 2 153.1 164 m4 0.522 0.523 0.523 0.001 152.2 165 152.9 165 Ring 3 89.9 99.5 89.1 100 88.1 99.5 Ring 4 63.5 73.5 63.2 74 63.7 73.7 Table II d Ud Ring 1 36.267 0.219 42.333 0.167 39.300 0.137 Ring 2 152.733 0.273 164.667 0.333 158.700 0.215 d (mean diaT (average Ut (standard uncertainty) log (d) log (T) Ring 3 89.033 0.521 99.667 0.167 94.350 0.273 Ring 1 39.3 0.398 1.5943926 -0.400117 Ring 4 63.467 0.145 73.733 0.333 68.600 0.182 Ring 4 68.6 0.5226667 1.8363241 -0.281775 Ring 3 94.35 0.6246667 1.9747419 -0.204352 Table III--Average period fo the set of rings
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Unformatted text preview: Ring 2 158.7 0.8033333 2.2005769 -0.095104 d (mean diameter) T (average period) Ut (standard uncertainty) Ring 1 39.300 0.398 0.000 Ring 2 158.700 0.803 0.001 Ring 3 94.350 0.625 0.001 Ring 4 68.600 0.523 0.001 log (T) and log(d) log (d) log (T) 1.594-0.400 2.201-0.095 1.975-0.204 1.836-0.282 n= Slope = 0.0992 y-intercept = 0.4935 log(T) = log(A) + nlog(d) log(T) = -0.4935 + 0.0992 log(d) log(A) = -0.4935 A = 0.321 n = 0.0992 d in Ud in d out Ud out U A = 0.001 U n = 0.001 39.3 68.6 94.35 158.7 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 f(x) = 0.3868622087 x^0.4842930901 Average Period (T) vs. Mean Diameter (d) d (mm) T (sec) 1.5943925504 1.8363241157 1.9747419045 2.2005769268-0.45-0.4-0.35-0.3-0.25-0.2-0.15-0.1-0.05 f(x) = 0.0992461676x - 0.49345242 log(T) vs. log (d) log (d) log (T)...
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