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Unformatted text preview: b) If 26 e3 t + 8 ( t2 ) represents an external force applied to a mechanical system, briey describe the action of this force. 4. Dene the function f ( x ) by f ( x ) = (x3 x 3 < x < 3 , f ( x + 6) = f ( x ) . (a) (6 points) Sketch an accurate graph of f ( x ) for three periods. Be sure to put scales on your xand yaxes. (b) (18 points) Find and simplify formulas for the coecients of the Fourier series for the function f ( x ). Do NOT use a calculator! Write out the rst ve nonzero terms of this Fourier series. You may nd the following integrals helpful. Z x sin( ax ) dx = sin ax a 2x cos ax a + C ; Z x cos( ax ) dx = cos ax a 2 + x sin ax a + C...
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This note was uploaded on 10/19/2010 for the course M 427K taught by Professor Fonken during the Spring '08 term at University of Texas at Austin.
 Spring '08
 Fonken

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