exactx[t_,ε_] :=
E^(-ε*t)Sin[Sqrt[1-ε^2]t]/Sqrt[1-ε^2];

approx[t_,ε_] :=
(1-ε*t)Sin[t];

ε = 0.1;
tmax = 10;

exactplot =
Plot[
exactx[t,ε],{t,0,tmax},
PlotStyle->{Thick,Red}
];

approxplot =
Plot[
approx[t,ε],{t,0,tmax},
PlotStyle->{Thick,Blue}
];

Show[exactplot,approxplot,PlotRange->All]