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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