A pencil of hexagonal cross-section of side a
is placed on a rough surface as shown.
The platform starts performing S.H.M. perpendicular to length of the pencil in horizontal plane with angular frequency ω
. Considering there is sufficient friction between pencil and platform such that there is no slipping between them, the maximum amplitude of oscillation such the pencil does not topple is g√αω2.
Then the value of α
(Answer upto two digits after the decimal point)