Unformatted text preview: Let y [ n ] be the amount of water on the ground at hour n. Let x [ n ] be the amount of rain that enters the city hour n . Let p [ n ] be the amount of water pumped out of the city in hour n . In theory, the pumping system can pump out 2 inches of rain every hour. Let’s assume that the pumps can pump out 2 inches the first hour, but the capacity to pump decreases by 2 % each hour due to the pumps heating and wearing down. In other words p [ n ] = .98 p [ n-1] a. Write a difference equation to describe how much water is on the ground at hour n . b. A fictitious hurricane “Tom” begins (at hour 0) to bring 3.5 inches of rain every hour, and also pushes 1 inch of flood water over the levy into the city every hour. An individual goes to bed at 10pm, and the hurricane hits at 11pm. His job is closed due to the expecting hurricane, so he sleeps in until 8am. How much water is on the ground when he wakes up?...
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- Fall '08
- LTI system theory, Pump, difference equation, following Input Output