Plot[1/Sqrt[(w0^2-1)^2+4*.05],{w0,0,5}, PlotStyle -> Thick]

Plot[1/(1+Exp[-2*(t-1)]),{t,0,5}, PlotStyle -> Thick, PlotRange -> {0,1}]

Plot[1-1/(1+Exp[-3*(t-1)]),{t,0,5}, PlotStyle -> Thick, PlotRange -> {0,1}]

Plot[Exp[-t],{t,0,5}, PlotStyle -> Thick, PlotRange -> {0,1}]

Plot[w0/Sqrt[(w0^2-1)^2+4*.05],{w0,0,5}, PlotStyle -> Thick]