Physical Pendulum - II

A rod AB of length \(l=12\sqrt 2\)m whose linear density \(\lambda =\frac { { \lambda }_{ 0 }x }{ l } \) where \({ \lambda }_{ 0 }\) is a positive constant and \(x\) is distance from end A is pivoted at distance \(d\) from the center of mass of the rod such that end A is above the the point where it is pivoted. Find the value of \(d\) so that the time period of oscillation is minimum.

This problem is originally part of set Mechanics problems by Abhishek Sharma.
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