Here is some data (time, voltage) from a Cavendish Balance

data = {  {20, 1.236}, {40, 1.181}, {60, 1.111}, {80,1.053}, {100,0.981}, {120, 0.889}, {140, 0.800},{160,0.726}, {180,0.654}, {200, 0.580}, {220,0.527}, {240, 0.491}, {260, 0.473}, {280,0.436}, {300, 0.436},{320,0.455}, {340, 0.473}, {360, 0.509}, {380, 0.563}, {400, 0.636},  {440,0.726}, {460, 0.790}, {480, 0.854}, {500, 0.905}, {520, 0.944}, {540, 0.999}, {560, 1.035}, {580, 1.053}, {600, 1.072}, {620, 1.072}, {640, 1.072}, {660, 1.053}, {680, 1.016}, {700, 0.999}, {720, 0.963}, {740, 0.926}, {760, 0.870}, {780, 0.832}, {800, 0.781}, {820, 0.726}, {840, 0.690}, {860, 0.654}, {880, 0.636}, {900, 0.580}, {920, 0.580}, {940, 0.563}, {960, 0.563}, {980, 0.563}, {1000, 0.580}, {1020, 0.599}, {1040, 0.617}, {1060, 0.653}, {1080, 0.672}, {1100, 0.726}, {1120,0.745}, {1140,0.799}, {1160, 0.817}, {1180, 0.854}, {1200, 0.875}, {1220, 0.908}, {1240, 0.926}, {1260, 0.926}, {1280, 0.944}, {1300, 0.944}, {1320, 0.926}, {1340, 0.926}, {1360, 0.890}, {1380, 0.871}, {1400, 0.853}, {1420, 0.818}, {1440, 0.799}, {1460, 0.772}, {1480, 0.726}, {1500, 0.709}, {1520, 0.690}, {1540, 0.672}, {1560, 0.654}, {1580, 0.636}, {1600, 0.636}, {1620, 0.636}, {1640, 0.636}, {1660, 0.636}, {1680, 0.654}, {1700, 0.672}, {1720, 0.672}, {1740, 0.690}, {1760, 0.708}, {1780, 0.726}, {1800, 0.745}, {1820, 0.781}, {1840, 0.799}, {1860, 0.799}, {1880, 0.817}, {1900, 0.835}, {1920, 0.853}, {1940, 0.853} ,{1960, 0.854}, {1980, 0.853}, {2000, 0.835}, {2020, 0.817}, {2040, 0.799}, {2060, 0.799}, {2080, 0.781}, {2100, 0.763}};

Length[data]

gr1 = ListPlot[data,PlotRange->{0.,2.},PlotStyle->{PointSize[0.011]}]

Fit to a damped cosine wave

ff = FindFit[data,amp (E^(-γ t)) Cos[((2 π)/per) t+ϕ] +const,{{amp,0.5},{const,0.75},{γ,1./1320.},{per, 660},{ϕ,0.01}},t]

f[t_]:=amp (E^(-γ t)) Cos[((2 π)/per) t+ϕ] +const/.ff

gr2 = Plot[f[t],{t,0.,2100.}, PlotRange->{0., 2.0}]

Show[{gr1,gr2}]

Calculate the (χ^2)

chisqmin=(∑_(i=1)^104)(1/(((0.018))^2))(((data[[i,2]]-(amp (E^(-γ data[[i,1]])) Cos[((2 π)/per) data[[i,1]]+ϕ] +const/.ff)))^2)

chisqPer[perf_]=(∑_(i=1)^104)(1/(((0.018))^2))(((data[[i,2]]-(amp (E^(-γ data[[i,1]])) Cos[((2 π)/perf) data[[i,1]]+ϕ] +const/.ff)))^2);

Find the uncertainty in the period

Plot[chisqPer[perf],{perf,645,670},PlotRange->{170,350}]

fper=FindRoot[chisqPer[perf]==chisqmin+1.,{perf,per/.ff}]
errorPer=Abs[(perf/.fper)-per/.ff]

Print["period = ",per/.ff  ," +/- ", errorPer];