Problem source

Three light elastic strings $AB,BC$ and $CD$, each of natural length
$a$ and modulus of elasticity $\lambda,$ are joined together as
shown in the diagram. 

\noindent \begin{center}
\psset{xunit=1.0cm,yunit=1.0cm,algebraic=true,dimen=middle,dotstyle=o,dotsize=3pt 0,linewidth=0.5pt,arrowsize=3pt 2,arrowinset=0.25} \begin{pspicture*}(-2.46,-1.7)(5.55,2.55) \psline(-2,2)(-2,-1) \psline(-2,-1)(4,-1) \psline(4,-1)(4,2) \psline(4,2)(-2,2) \psline[linestyle=dashed,dash=2pt 2pt](1,2)(1,-1) \psline{<->}(5,2)(5,-1)  \rput[tl](5.15,0.77){$3d$} \rput[tl](1.08,2.35){$A$} \rput[tl](1.14,0.63){$B$} \rput[tl](1.17,-0.32){$C$} \rput[tl](1.14,-1.1){$D$} \begin{scriptsize} \psdots[dotstyle=*](1,2) \psdots[dotstyle=*](1,-1) \psdots[dotstyle=*](1,0.5) \psdots[dotstyle=*](1,-0.37) \end{scriptsize} \end{pspicture*}
\par\end{center}

$A$ is attached to the ceiling and $D$ to the floor of a room of
height $3d$ in such a way that $A,B,C$ and $D$ are in a vertical
line. Particles of mass $m$ are attached at $B$ and $C$. Find the
heights of $B$ and $C$ above the floor. 

Find the set of values of $d$ for which it is possible, by choosing
$m$ suitably, to have $CD=a$?