In[]:=
Clear[t,dosc,gR,hR,N0,Pf,Pk,k1,k2,c1,c2];
In[]:=
dosc[N0_,Pf_,Pk_,k1_,k2_,c1_,c2_]:=N0+(Pf×((Exp[-(k1×t)])×((c1×Cos[k2×(t-Pk)])+(c2×Sin[k2×(t-Pk)]))));
In[]:=
gR[t_,r_,N0_,Pf_,Pk_,k1_,k2_,c1_,c2_]:=t×Cos[r]-(dosc[N0,Pf,Pk,k1,k2,c1,c2])×Sin[r];hR[t_,r_,N0_,Pf_,Pk_,k1_,k2_,c1_,c2_]:=t×Sin[r]+(dosc[N0,Pf,Pk,k1,k2,c1,c2])×Cos[r];Manipulate[ParametricPlot[{gR[t,r,N0,Pf,Pk,k1,k2,c1,c2],hR[t,r,N0,Pf,Pk,k1,k2,c1,c2]},{t,0,75},PlotRange->{{-10,100},{-100,50}}],{{N0,5},0,10},{{Pf,1},1,10},{{Pk,0},-5,+5},{{k1,0.02},0,0.1},{{k2,0.3},0.01,2},{{c1,4.0},1.0,10},{{c2,4.0},1.0,10},{{r,0},-1.5,1.5},ControlPlacement->Top,SaveDefinitions->True]
Out[]=

