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

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