l=1.387; g=9.81;

τ= Sqrt[(2l)/(3g)];

lϕpp[ϕ_]=(3Sin[ϕ])/2*g


Plot[{lϕpp[ϕ],y[ϕ]=9.81},{ϕ,0,1.56},AxesLabel-> {"Auslenkwinkel ϕ in rad","Winkelbeschleunigung*Stablänge in m/s^2"}]

Solve[lϕpp[ϕ]==g,ϕ]