There is a teeter toy with base stick of length \(L = 1 m\) and from the top end, 2 balls of masses \(m = 2 kg\) are suspended with a string of length \(l = 3 m\) which makes an angle \(\theta = 60^{\circ}\) with the base stick. Find the time period of small oscillations of the system in the vertical direction.

If the time period can be written as \(p^a q^b\) where \(p,q\) are prime numbers and \(a,b\) are real numbers, give your answer as \(p + a + q + b\).

**Details and Assumptions**

Neglect oscillations in the horizontal direction.

Oscillations are very small.

Take \(g = 10 m{s}^{-2}\).

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