Answer
821 kg
Work Step by Step
We set the angular frequencies equal to each other to obtain:
$.79\sqrt{\frac{k}{\frac{1}{12}ML^2}}=\sqrt{\frac{k}{\frac{1}{12}ML^2+ 2m(L/2)^2}}$
$.79\sqrt{\frac{k}{\frac{1}{12}ML^2}}=\sqrt{\frac{k}{\frac{1}{12}ML^2+ .5mL^2}}$
$M=821 \ kg$
