Aditya's challenges in Mechanics 1

Three similar rods of length \(l=1\text{ m}\) and mass \(m=1\text{ kg}\) 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 \(\dfrac {A\pi} {B} \sqrt { \dfrac {2 \sqrt { C } }{ D } },\) where\(A\) and \(B\) are coprime positive integers and \(C\) and \(D\) are square-free.

Find the value of \(A+B+C+D.\)

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Details and Assumptions:

• \(g=10\text{ m/s}^2\).

• Neglect air resistance.