Aditya's challenges in Mechanics 1

Three similar rods of length l=1 ml=1\text{ m} and mass m=1 kgm=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 AπB2CD,\dfrac {A\pi} {B} \sqrt { \dfrac {2 \sqrt { C } }{ D } }, whereAA and BB are coprime positive integers and CC and DD are square-free.

Find the value of A+B+C+D.A+B+C+D.


Details and Assumptions:

  • g=10 m/s2g=10\text{ m/s}^2.

  • Neglect air resistance.

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