How bout some switch draining oscillations.

A cylindrical tank of horizontal section ares \(S=25cm^{2} \) has a hole in its bottom. The hole is closed by a thin metal plate A of area \(S_{A}=5cm^{2} \) connected with a thin rod of length \(l=10cm \) to a cylindrical float B of horizantal cross section area \(S_{B}=10cm^{2}\)The plate rod float assembly works as a special valve . This plate rod float assembly works as a special valve. Now a tap is opened and water starts entering at a constant rate \(r=10\frac{cc}{s} \) When the water level in the container reaches a particular height, The assembly lifts opening the hole through which water drains out at a rate\(\eta=1.5r \) This operation operates periodically denoting mass of the assembly by \(m=100g \) and density of water by \(\rho_{o}=1g/cm^{3} \) .Find the time interval \(\tau \) in minutes between closing and subsequent opening of the hole. Neglect the force created by water flow and the atmospheric pressure.

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