Plot[{Tanh[100Sin[x]]*Exp[-0.2x]},{x,-6,6},PlotStyle->{Thickness[0.004],Blue},AxesLabel->{"x","Tanh[x]"}]

f0=1000;
T=(1/f0);
uz[t_]:=Tanh[100*Sin[2*Pi*f0*t]]*Exp[-0.5*(t/T)];
tmax=5T;
Plot[uz[t],{t,0,tmax},PlotStyle->{Thickness[0.004],Blue},AxesLabel->{"t[s]","uz[V]"}]

eqnsOfCurrs={0==i1[t]+i7[t],i1[t]==i2[t]+i4[t]+i6[t],i2[t]==i3[t],i4[t]==i5[t]};
eqnsOfParts={u1[t]-u2[t]==R1*i1[t],u2[t]-u3[t]==L*i2'[t],u3[t]-0==R2*i3[t],u2[t]-u4[t]==R3*i4[t],i5[t]==c*u4'[t],u2[t]==R4*i6[t]};
eqnsOfInitials={u4[0]==0,i2[0]==0};
eqns=Union[eqnsOfCurrs,eqnsOfParts]/.u1[t]->uz[t];
Print["number of eqns is ",Length[eqns]]

vars=Union[Cases[eqns,_Symbol[t],{0,∞}]];
Print["number of unknown vars ",Length[vars]]

values={R1->100,R2->10,R3->10,R4->1000,L->0.005,c->100*(10^(-9))};

together=Union[eqnsOfInitials,eqns]/.values;
sol=NDSolve[together,vars,{t,0,tmax},StartingStepSize->(10^(-9))];

Plot[vars/.sol[[1]],{t,0,tmax},PlotRange->All]

vars