This is another simple way. The idea is to plot a $cos$ function, by changing its frequency and amplitude, you can adjust the twisting needed

f1[x_]:=Sqrt[x^2+1] data=Table[z0= 1/10 Cos[50 x];z1=f1[x];{x,z0+z1},{x,-2,2,.02}]; Show[Plot[f1[x],{x,-2,2},AxesOrigin->{0,.7}], ListLinePlot[data,PlotStyle->Red]] 

This one has smaller frequency

data=Table[z0=1/10 Cos[20 x];z1=f1[x];{x,z0+z1},{x,-2,2,.02}]; 

Manipulate[ data = Table[z0 = h Cos[w x]; z1 = f1[x]; {x, z0 + z1}, {x, -2, 2, .02}]; Show[Plot[f1[x], {x, -2, 2}, AxesOrigin -> {0, .7}], ListLinePlot[data, PlotStyle -> Red]], {{h, .1, "amplitude"}, 0, .5, .01, Appearance -> "Labeled"}, {{w, 20, "frequency"}, 1, 100, 1, Appearance -> "Labeled"}, TrackedSymbols :> {h, w}, Initialization :> ( f1[x_] := Sqrt[x^2 + 1]; ) ] 

This is another simple way. The idea is to plot a $\cos$ function, by changing its frequency and amplitude, you can adjust the twisting needed

f1[x_]:=Sqrt[x^2+1] data=Table[z0= 1/10 Cos[50 x];z1=f1[x];{x,z0+z1},{x,-2,2,.02}]; Show[Plot[f1[x],{x,-2,2},AxesOrigin->{0,.7}], ListLinePlot[data,PlotStyle->Red]] 

This one has smaller frequency

data=Table[z0=1/10 Cos[20 x];z1=f1[x];{x,z0+z1},{x,-2,2,.02}]; 

Manipulate[ data = Table[z0 = h Cos[w x]; z1 = f1[x]; {x, z0 + z1}, {x, -2, 2, .02}]; Show[Plot[f1[x], {x, -2, 2}, AxesOrigin -> {0, .7}], ListLinePlot[data, PlotStyle -> Red]], {{h, .1, "amplitude"}, 0, .5, .01, Appearance -> "Labeled"}, {{w, 20, "frequency"}, 1, 100, 1, Appearance -> "Labeled"}, TrackedSymbols :> {h, w}, Initialization :> ( f1[x_] := Sqrt[x^2 + 1]; ) ] 

This is another simple way. The idea is to plot a $cos$ function, by changing its frequency and amplitude, you can adjust the twisting needed

f1[x_]:=Sqrt[x^2+1] data=Table[z0= 1/10 Cos[50 x];z1=f1[x];{x,z0+z1},{x,-2,2,.02}]; Show[Plot[f1[x],{x,-2,2},AxesOrigin->{0,.7}], ListLinePlot[data,PlotStyle->Red]] 

This one has smaller frequency

data=Table[z0=1/10 Cos[20 x];z1=f1[x];{x,z0+z1},{x,-2,2,.02}]; 

Time for a Manipulate !

This is another simple way. The idea is to plot a $cos$ function, by changing its frequency and amplitude, you can adjust the twisting needed

f1[x_]:=Sqrt[x^2+1] data=Table[z0= 1/10 Cos[50 x];z1=f1[x];{x,z0+z1},{x,-2,2,.02}]; Show[Plot[f1[x],{x,-2,2},AxesOrigin->{0,.7}], ListLinePlot[data,PlotStyle->Red]] 

This one has smaller frequency

data=Table[z0=1/10 Cos[20 x];z1=f1[x];{x,z0+z1},{x,-2,2,.02}]; 

Manipulate[ data = Table[z0 = h Cos[w x]; z1 = f1[x]; {x, z0 + z1}, {x, -2, 2, .02}]; Show[Plot[f1[x], {x, -2, 2}, AxesOrigin -> {0, .7}], ListLinePlot[data, PlotStyle -> Red]], {{h, .1, "amplitude"}, 0, .5, .01, Appearance -> "Labeled"}, {{w, 20, "frequency"}, 1, 100, 1, Appearance -> "Labeled"}, TrackedSymbols :> {h, w}, Initialization :> ( f1[x_] := Sqrt[x^2 + 1]; ) ]