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Unformatted text preview: b) If 39 e3 t + 8 δ ( t2 π ) represents an external force applied to a mechanical systsem, brieﬂy describe the action of this force. 4. Deﬁne the function f ( x ) by f ( x ) = (x4 ≤ x ≤ 4 < x < 4 , f ( x + 8) = 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 coeﬃcients of the Fourier series for the function f ( x ). Do NOT use a calculator! Write out the ﬁrst ﬁve nonzero terms of this Fourier series. You may ﬁnd 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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