This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 +...
View
Full
Document
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).
 Spring '07
 TERRELL,R
 Math

Click to edit the document details