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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