Problem source

A small lamp of mass $m$ is at the end $A$ of a light rod $AB$
of length $2a$ attached at $B$ to a vertical wall in such a way
that the rod can rotate freely about $B$ in a vertical plane perpendicular
to the wall. A spring $CD$ of natural length $a$ and modulus of
elasticity $\lambda$ is joined to the rod at its mid-point $C$ and
to the wall at a point $D$ a distance $a$ vertically above $B$.
The arrangement is sketched below. 

\noindent \begin{center}
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 \rput[tl](-0.56,0.41){$B$} \rput[tl](1.59,1.89){$C$} \rput[tl](3.41,4.28){$A$} \rput[tl](-0.56,2.84){$D$} \parametricplot{0.7583777142101807}{3.8999703677999737}{1*0.16*cos(t)+0*0.16*sin(t)+3.22|0*0.16*cos(t)+1*0.16*sin(t)+3.77} \psline(3.1,3.66)(3.33,3.88) \begin{scriptsize} \psdots[dotsize=5pt 0](0,0) \psdots[dotstyle=*](3.11,3.89) \psdots[dotstyle=*](0,2.53) \end{scriptsize} \end{pspicture*}
\par\end{center}

Show that if $\lambda>4mg$ the lamp can hang in equilibrium away
from the wall and calculate the angle $\angle DBA$.