f[t_,a_,ω_,γ_]:=a Exp[-γ t]Cos[ω t]

NotebookDirectory[]

t=Range[0,5,0.25]

y0=Table[ f[t[[i]],10.,1.5,0.1],{i,Length[t] }]

s= Round[ Sqrt[ 0.003y0^2+0.2^2],0.01]

d=Table[{t[[i]], Round[ RandomVariate[ NormalDistribution[ f[t[[i]],10.,1.5,0.1],s[[i]] ] ],0.01],s[[i]]},{i,Length[t]}]

Export[FileNameJoin[{NotebookDirectory[],"OHamortecido.dat"}],d]