Oscillating wire

The arrangement shown is kept in an insulating liquid of density twice that of the identical wires making angle \(\theta\) with each other and carrying current \(I\) each, such that the tilted wire is free to rotate about the smooth hinge. The vertical wire is very long and is kept fixed. It is observed that the smaller wire of length \(L\) is in equilibrium at \(\theta = 60^{\circ}\).

Now, the smaller wire is turned through a small angle in the vertical plane and released. Find the time period of its oscillations.

Details and assumptions :
- \(L = 1m\)
- \(g = 9.8 m/s^2\)


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