# 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 $$A+B+C+D.$$


Details and Assumptions:

• $$g=10\text{ m/s}^2$$.

• Neglect air resistance.

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