In[]:=
dosc=20.0+(1.0*((Exp[-(0.02*t)])*((4.0*Cos[0.3*(t-0.0)])+(4.0*Sin[0.3*(t-0.0)]))));
In[]:=
gR[t_,r_]:=t*Cos[r]-(dosc)*Sin[r];​​hR[t_,r_]:=t*Sin[r]+(dosc)*Cos[r];​​Manipulate[ParametricPlot[{gR[t,r],hR[t,r]},{t,0,75},PlotRange->{{-10,100},{-100,50}}],{r,0,-1.5}]
Out[]=
​
r
20
40
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-100
-80
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-40
-20
20
40