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Unformatted text preview: ) = 8 2 k =0 (1) k (2 k + 1) 2 sin((2 k + 1) x ) cos(4(2 k + 1) t ) . (b) Here is the initial shape of the string. Note the new Mathematica command that we used to dene piecewise a function. (Previously, we used the If command.) Clear f f x_ : 2 x ; 0 x 1 2 f x_ : 2 1 x ; 1 2 x 1 Plot f x , x, 0, 1 Because the period of cos(4(2 k + 1) t ) is 1 / 2, the motion is periodic in t with period 1 / 2. This is illustrated by the following graphs. We use two dierent ways to plot the graphs: The rst uses simple Mathematica commands; the second one is more involved and is intended to display the graphs in a convenient array....
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 Fall '11
 StuartChalk

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