deqns={m x''[t]==(((λ[t])/l)) x[t],m y''[t]==(((λ[t])/l)) y[t]-m g};

aeqns={((x[t])^2)+((y[t])^2)==(l^2)};

ics={x[0]==1,y[0]==0,x'[0]==0,y'[0]==1};

params={g->9.81,m->1,l->1};

pendulumSol=First[NDSolve[{deqns,aeqns,ics}/.params,{x,y,λ},{t,0,15},Method->{"IndexReduction"->{"Pantelides", "ConstraintMethod"->"Projection"}}]];

Show[{ParametricPlot[Evaluate[{x[t],y[t]}/.pendulumSol],{t,0,15}, PlotStyle->{DotDashed}],
Graphics[{{Red,Line[{{0,0},{0.5,-Sqrt[3]/2}}]},
{Blue,Disk[{0.5,-Sqrt[3]/2},0.1]}
}]},ImageSize->400]