MIT6_003S10_assn01

MIT6_003S10_assn01 - 6.003 Homework 1 Due at the beginning...

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6.003 Homework 1 Due at the beginning of recitation on Wednesday, February 10, 2010 . Problems 1. Independent and Dependent Variables Assume that the height of a water wave is given by g ( x vt ) where x is distance, v is velocity, and t is time. Assume that the height of the wave is a sinusoidal function of distance at each instant of time. Also assume that the positive peaks have a height of 1 meter (relative to the average water level) and that they occur at integer multiples of 2 meters when the time t = 3 seconds. a. Determine an expression for the height of the wave h ( x,t ) as a function of distance x and time t if the wave is traveling in the positive x direction at 5 meters/second. What is the function g ( ) for this case? · b. Determine an expression for the height of the wave h ( x,t ) as a function of distance x and time t if the wave is traveling in the negative x direction at 4 meters/second. What is the function g ( ) for this case? · c. Determine the speed of the wave if successive positive peaks at x = 1 . 3 meters are separated by 0 . 75 seconds. 2. Even and Odd The even and odd parts of a signal x [ n ] are defined by the following: x e [ n ] = x e [ n ] (i.e., x e is an even function of n ) x o [ n ] = x o [ n ] (i.e., x o is an odd function of n ) x [ n ] = x e [ n ] + [ n ] x o Let x represent the signal whose samples are given by x [ n ] = ± ( 2 1 ) n n 0 . 0
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MIT6_003S10_assn01 - 6.003 Homework 1 Due at the beginning...

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