Mechanics Challenge 1

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

1. Neglect oscillations in the horizontal direction.

2. Oscillations are very small.

3. Take $g = 10 m{s}^{-2}$ .