Be Careful with Liquid

A rectangular tank having base $$15\text{ cm} \times 20\text{ cm}$$ is filled with water (density $$\rho = 1000 \text{ kg/m}^3$$) up to $$20\text{ cm}$$ height. One end of an ideal spring of natural length $${h_0 = 20\text{ cm}$$ and force constant $$K = 280\text{ N/m}$$ is fixed to the bottom of the tank so that the spring remains vertical. This system is in an elevator moving downwards with acceleration $$a = 2\text{ m/s}^2$$. A cubical block of side $$l = 10\text{ cm}$$ and mass $$m = 2\text{ kg}$$ is gently placed over the spring and released gradually.

1. Find the compression $$a$$ (in $$\text{cm}$$) in the spring in the equilibrium position.
2. If the block is slightly pushed down from the equilibrium position and released, find the frequency of oscillation about the equilibrium position $$f = \dfrac {b\sqrt c}\pi$$ (in $$\text{Hz}$$), where $$b$$ and $$c$$ are positive integers with $$c$$ being square-free.

Enter your answer as $$abc$$.

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