Answer
$k=\frac{12Mg}{h}$
Work Step by Step
$E_P=mgh$
$E_{Pi}=E_{Sf}$
$E_{Pi}=Mg(x+h)$
$E_{Sf}=\frac{kx_f^2}{2}$
$Mg(x+h)=\frac{kx_f^2}{2}$
$\sum F=Ma$
$Ma=kx-Mg$
$x=\frac{Ma+Mg}{k}=\frac{6Mg}{k}$
$Mg\Big(\frac{6Mg}{k}+h\Big)=\frac{k\big(\frac{6Mg}{k}\big)^2}{2}$
$\frac{6M^2g^2}{k}+Mgh=\frac{18M^2g^2}{k}$
$Mgh=\frac{12M^2g^2}{k}$
$k=\frac{12Mg}{h}$
