EE200_hw1_solutions

EE200_hw1_solutions - EE 200L Foundations of Electrical...

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Unformatted text preview: EE 200L - Foundations of Electrical Engineering Systems Homework 1 - Solutions 1. Systems with memory: Heating a container of water - The input is the amount of heat via the stove burner. The output is the temperature of water. The instantaneous heat is not the only factor affecting the temperature of water. The amount of time is it applied also affects the temperature. Another example is a vending machine. The machine ‘remembers’ the value of coins put in for a until it dispenses the product and change then resets itself. 2. Non linear systems: A car engine - the input is the amount of fuel-air mixture regulated via the gas pedal. The response is the acceleration of the car. Depressing the pedal by a factor k more does not increase the acceleration by a factor of k. The phenomenon is non-uniform. In particular, the property of homogeneity or superposition has to be violated for a system to be non-linear. Non-linear systems are ubiquitous in nature! Typically, at the very least, they all exhibit a dead-zone or saturation effect. 1 3. (a) Gram-Schimdt algorithm for v 1 , v 2 , v 3 : u 1 = 1- 1 2- 2 u 2 = v 2- h u 1 , v 2 i h u 1 , u 1 i u 1 = 1 1- 1 - 1 + 0 + 0- 2 + 0 1 + 1 + 0 + 4 + 4 1- 1 2- 2 = 1 . 1- . 1 1- . 8- . 2 u 3 = v 3- h u 1 , v 3 i h u 1 , u 1 i u 1- h u 2 , v 3 i h u 2 , u 2 i u 2 = 5- 3 2 4- 6 - 5 + 3 + 0 + 8 + 12 10 1- 1 2- 2 - 5 . 5 + 0 . 3 + 2- 3 . 2 + 1 . 2 2 . 9 1 . 1- . 1 1- . 8- . 2 = 5- 3 2 4- 6 - 2 . 8- 2 . 8 5 . 6- 5 . 6 -...
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EE200_hw1_solutions - EE 200L Foundations of Electrical...

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