p2spring10 - Prelim 2 Math 2930 Spring 2010 show work, 6...

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Unformatted text preview: Prelim 2 Math 2930 Spring 2010 show work, 6 pages, no calculators 1a) (4 points) Write your name and section number at the top of this page. 1b) (8 points) A frictionless spring and mass system is forced at two angular frequencies 0 < a < 1 < b and the mass position y ( t ) is described by y 00 =- y + cos( at ) + 2 sin( bt ). Find the solutions. 1c) (4 points) In class we discussed the geometric series 1 + x + x 2 + x 3 + which converges to 1 / (1- x ) when | x | < 1. To what does the series 1 + x 2 3 + x 4 9 + x 6 27 + x 8 81 + converge, and for what numbers x ? 1d) (4 points) Estimate the error in the common approximation sin( x ) . = x , when 0 < x < 1 10 . (Remember sin( x ) = x- x 3 3! + x 5 5!- for all x .) 1 2a) (4 points) Prove that R - cos(2 t ) cos(3 t ) dt = 0 using whatever you know about trig functions. b) (6 points) Show that the functions e it , e- it and sin( t ) are linearly de- pendent. You are allowed to use complex coefficients. (You must say what linearly dependent means. No credit for any statement about Wronskian.) c) (6 points) Find (only) the coefficient a 3 in the Fourier series f ( t ) = a 2 +...
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This note was uploaded on 01/21/2011 for the course MATH 2930 taught by Professor Terrell,r during the Spring '07 term at Cornell University (Engineering School).

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p2spring10 - Prelim 2 Math 2930 Spring 2010 show work, 6...

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