Three similar rods of length and mass are welded to form a structure similar to the positive sides of 3D coordinate axes, as shown in figure above. Now it is rested on a very sharp pin about the intersection of the rods so that they remain in equilibrium facing downwards. The system is in equilibrium. Now the system is shaken a bit horizontally so that it performs SHM. Find the time period of its SHM.
The answer is of the form where and are coprime positive integers and and are square-free.
Find the value of
Details and Assumptions:
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Neglect air resistance.