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Δt=0.01;δ=1;l=5;g=9.8;m=1;k=10;x0=0.1;f[t_]:=Module[{θ,ω,α,x,v,a},θ[0]=δ;ω[0]=0;x[0]=x0;α[0]=0;v[0]=0;a[0]=0;a[i_]:=a[i]=(l+x[i-1])(ω[i-1])^2-(k/m)x[i-1]+gCos[θ[i-1]];α[j_]:=α[j]=-(Sin[θ[j-1]]+2v[j-1]*ω[j-1])/(l+x[j-1]);ω[m_]:=ω[m]=ω[m-1]+α[m-1]Δt;v[p_]:=v[p]=v[p-1]+a[p-1]Δt;θ[n_]:=θ[n]=θ[n-1]+ω[n-1]Δt;x[q_]:=x[q]=x[q-1]+v[q-1]Δt;Return[{θ[t],ω[t],α[t]}]]Manipulate[{f[IntegerPart[t/Δt]],IntegerPart[t/Δt]},{t,0,50,Δt}]
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