Is it S.H.M?

A weightless rigid rod with a load at the end is hinged at point \(A\) to the walls so that it can rotate in all directions. The rod is kept in the horizontal position by a vertical in-extensible thread of length \(l\), fixed at its midpoint. The load receives a momentum in the direction perpendicular to the plane of the figure (which is shown below).

If the period \(T\) of small oscillations of the system can be described as
\(2\pi\)\(\dfrac{\sqrt{kl}}{\sqrt{g}}\) Find the value of \(k\)

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