Import["ErrorBarPlots`"]

data = {{0,630},{2,560},{4,520},{6,480},{8,440},{10,405},{12,380}}

plot2=ErrorListPlot[Table[{data[[i]],ErrorBar[5]},{i,1,7}],PlotRange->{{0,13},{0,700}}];

fit=NonlinearModelFit[data,630*Exp[-k*x],{k},x]

{k,Δk}=Quantity[fit["ParameterTableEntries"][[1,1;;2]],1/"Minutes"]

Show[plot2,Plot[fit[x],{x,0,13}]]

Solve[Exp[-k x]==(1/2),x]

{((Log[2])/(0.0443911837976932`)),((Log[2])/((0.0443911837976932`)^2))0.0010842692881395599`}

ωavg[ω_,Tp_]:=(1/2)ω(1+Exp[-k Tp])

Δωavg[ω_,Δω_,Tp_,ΔTp_]:=Sqrt[((((1/2)Δω(1+Exp[-k Tp])))^2)+((((1/2)ω Δk Tp Exp[-k Tp]))^2)+((((1/2)ω k ΔTp Exp[-k Tp]))^2)]

(Subscript[ω, 1])=Quantity[{700,620,550,400},1/"Minutes"]

(Subscript[Δω, 1])=Quantity[5,1/"Minutes"]

(Subscript[T, 1])=Quantity[{128,112,103,90},"Seconds"]

(Subscript[ΔT, 1])=Quantity[2,"Seconds"]

(Subscript[ω, 1,avg])=UnitConvert[ωavg[(Subscript[ω, 1]),(Subscript[T, 1])]]

(Subscript[Δω, 1,avg])=UnitConvert[Δωavg[(Subscript[ω, 1]),(Subscript[Δω, 1]),(Subscript[T, 1]),(Subscript[ΔT, 1])]]

Iz[s_,m_,l_]:=((Quantity[s,("Seconds"*"Seconds")])/(((2π))^2)) Quantity[m*9.85,"Grams"]Quantity["StandardAccelerationOfGravity"]Quantity[l,"Centimeters"]//UnitConvert

(Subscript[plot3b, 1,15])=ErrorListPlot[Table[{QuantityMagnitude[Transpose[{(Subscript[ω, 1,avg]),(Subscript[T, 1])}][[i]]],ErrorBar[QuantityMagnitude[(Subscript[Δω, 1,avg])[[i]]],QuantityMagnitude[(Subscript[ΔT, 1])]]},{i,1,Length[(Subscript[ω, 1,avg])]}],PlotRange->{{0,20},{0,130}}];

(Subscript[fit3b, 1,15])=LinearModelFit[QuantityMagnitude[Transpose[{(Subscript[ω, 1,avg]),(Subscript[T, 1])}]],x,x,IncludeConstantBasis->False]

(Subscript[fit3b, 1,15])["ParameterTable"]

Show[(Subscript[plot3b, 1,15]),Plot[(Subscript[fit3b, 1,15])[x],{x,0,700}]]

Iz[{11.7,0.5},1,15]

(Subscript[ω, rest])=UnitConvert[Quantity[{540,440,350,250,600,500,400,300,1200,1000,800,600},1/"Minutes"]]

(Subscript[Δω, rest])=UnitConvert[Quantity[5,1/"Minutes"]]

(Subscript[T, rest])=Quantity[{209,62,50,35,106,51,38,28,81,69,55,40},"Seconds"]

(Subscript[ΔT, rest])=Quantity[2,"Seconds"]

(Subscript[ω, rest,avg])=UnitConvert[ωavg[(Subscript[ω, rest]),(Subscript[T, rest])]]

UnitConvert[(Subscript[ω, rest,avg]),1/"Minutes"]

(Subscript[Δω, rest,avg])=UnitConvert[Δωavg[(Subscript[ω, rest]),(Subscript[Δω, rest]),(Subscript[T, rest]),(Subscript[ΔT, rest])]]

UnitConvert[(Subscript[Δω, rest,avg]),1/"Minutes"]

(Subscript[plot3b, 1,20])=ErrorListPlot[Table[{QuantityMagnitude[Transpose[{(Subscript[ω, rest,avg]),(Subscript[T, rest])}]][[i]],ErrorBar[QuantityMagnitude[(Subscript[Δω, rest,avg])[[i]]],QuantityMagnitude[(Subscript[ΔT, rest])]]},{i,1,4}],PlotRange->{{0,30},{0,300}}];

(Subscript[fit3b, 1,20])=LinearModelFit[QuantityMagnitude[Transpose[{(Subscript[ω, rest,avg]),(Subscript[T, rest])}]][[2;;4]],x,x,IncludeConstantBasis->False]

(Subscript[fit3b, 1,20])["ParameterTable"]

Show[(Subscript[plot3b, 1,20]),Plot[(Subscript[fit3b, 1,20])[x],{x,0,1200}]]

Iz[{8.65,0.05},1,20]

(Subscript[plot3b, 2,15])=ErrorListPlot[Table[{QuantityMagnitude[Transpose[{(Subscript[ω, rest,avg]),(Subscript[T, rest])}]][[i]],ErrorBar[QuantityMagnitude[(Subscript[Δω, rest,avg])[[i]]],QuantityMagnitude[(Subscript[ΔT, rest])]]},{i,5,8}],PlotRange->{{0,30},{0,300}}];

(Subscript[fit3b, 2,15])=LinearModelFit[QuantityMagnitude[Transpose[{(Subscript[ω, rest,avg]),(Subscript[T, rest])}]][[6;;8]],x,x,IncludeConstantBasis->False]

(Subscript[fit3b, 2,15])["ParameterTable"]

Show[(Subscript[plot3b, 2,15]),Plot[(Subscript[fit3b, 2,15])[x],{x,0,1200}]]

Iz[{6.0,0.2},2,15]

(Subscript[plot3b, 2,20])=ErrorListPlot[Table[{QuantityMagnitude[Transpose[{(Subscript[ω, rest,avg]),(Subscript[T, rest])}]][[i]],ErrorBar[QuantityMagnitude[(Subscript[Δω, rest,avg])[[i]]],QuantityMagnitude[(Subscript[ΔT, rest])]]},{i,9,12}],PlotRange->{{0,30},{0,300}}];

(Subscript[fit3b, 2,20])=LinearModelFit[QuantityMagnitude[Transpose[{(Subscript[ω, rest,avg]),(Subscript[T, rest])}]][[9;;12]],x,x,IncludeConstantBasis->False,Weights->1/(((QuantityMagnitude[(Subscript[Δω, rest,avg])[[9;;12]]]))^2),VarianceEstimatorFunction->(1&)]

(Subscript[fit3b, 2,20])["ParameterTable"]

Show[(Subscript[plot3b, 2,20]),Plot[(Subscript[fit3b, 2,20])[x],{x,0,1200}]]

Iz[{4.18,0.03},2,20]

Iz[2*{4.18,0.03},2,20]

Mean[{0.0043,0.00423,0.0044,0.00409}]

StandardDeviation[{0.0043,0.00423,0.0044,0.00409}]

(2/5)Quantity[4.164,"Kilograms"]((Quantity[5.08,"Centimeters"])^2)//UnitConvert

(Subscript[ω, F])=UnitConvert[Quantity[2π*{600,570,540,510,480,450,420,390,360,330},1/"Minutes"]]//N

(Subscript[Δω, F])=UnitConvert[Quantity[2π*5,1/"Minutes"]]//N

Ω=UnitConvert[Quantity[20π/{17.0,18.4,19.0,20.8,21.2,23.2,25.4,27.2,28.3,30.9},1/"Seconds"]]//N

ΔΩ=UnitConvert[Quantity[20π/{17.0,18.4,19.0,20.8,21.2,23.2,25.4,27.2,28.3,30.9}^2*0.5,1/"Seconds"]]//N

Transpose[{Ω,ΔΩ}]

plot4b=ErrorListPlot[Table[{QuantityMagnitude[{(Subscript[ω, F])[[i]],Ω[[i]]}],ErrorBar[QuantityMagnitude[(Subscript[Δω, F])],QuantityMagnitude[ΔΩ[[i]]]]},{i,1,Length[Ω]}],PlotRange->{{0,66},{0,4}}];

fit4b=LinearModelFit[QuantityMagnitude[Transpose[{(Subscript[ω, F]),Ω}]],x,x,IncludeConstantBasis->False,Weights->1/(((QuantityMagnitude[ΔΩ]))^2),VarianceEstimatorFunction->(1&)]

Show[plot4b,Plot[fit4b[x],{x,0,65}]]

fit4b["ParameterTable"]

D[c/(x-d),x]

{(Subscript[J, z]),(Subscript[ΔJ, z])}=Quantity[{0.00426,0.00013},"Kilograms" (("Meters")^2)]

(Subscript[J, z])+((Subscript[J, z])/(17.3-1))

(Sqrt[((((Sqrt[(((((Subscript[ΔJ, z])/(17.3-1))))^2)+(((((Subscript[J, z])/(((17.3-1))^2))0.1))^2)])))^2)+((Subscript[ΔJ, z])^2)])

list=Transpose[UnitConvert[Quantity[{{690,660,610,550,530,510,480,450,400,350},{650,620,570,515,500,480,450,425,380,330}},1/"Minutes"]*(2π)]]//N//QuantityMagnitude

UnitConvert[Quantity[5*(2π),1/"Minutes"]]//N

listplot=ErrorListPlot[Table[{list[[i]],ErrorBar[0.5,0.5]},{i,1,Length[list]}],PlotRange->{{0,75},{0,75}}];

listfit=LinearModelFit[list,x,x,IncludeConstantBasis->False]

Show[listplot,Plot[listfit[x],{x,0,75}]]

listfit["ParameterTable"]

((Subscript[J, z])/(.94))

(Sqrt[(((((Subscript[ΔJ, z])/(.94))))^2)+(((((Subscript[J, z])/((.94)^2))0.001))^2)])

UnitConvert[Quantity[{0.044,0.001},1/"Minutes"]]

UnitConvert[Quantity[{15.6,0.4},"Minutes"]]