33bmidterm2

# 33bmidterm2 - Midterm 2 Math 33B Daniel Murfet May 13, 2011...

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Midterm 2 Math 33B Daniel Murfet May 13, 2011 Name: Student ID: Discussion section: Signature: Q1: /3 Q2: /4 Q3: /4 Q4: /3 Q5: /4 Q6: /4 Total: /22 There are six problems and you have 50 minutes. There is some extra working paper at the end (if you use it, indicate this on the page with the question you are answering). You must show all work. 1

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Variation of parameters: Given a second order linear diﬀerential equation with forcing term f ( t ) and a fundamental set of solutions y 1 ( t ) ,y 2 ( t ) of the associ- ated homogeneous equation, a particular solution to the inhomogeneous equation is given by v 1 y 1 + v 2 y 2 where v 1 = Z - y 2 f W , v 2 = Z y 1 f W , W = Wronskian of y 1 ,y 2 . Q1 (3 points). Explain why the functions y 1 ( t ) = sin t and y 2 ( t ) = | sin t | are linearly independent on ( -∞ , ). 2
Q2 (4 points). The equation for an undamped forced spring-mass system is y 00 + ω 2 0 y = A sin ωt, (assume ω 0 6 = ω ) where y is the displacement from the spring-mass equilibrium,

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## This note was uploaded on 09/20/2011 for the course MATH 33B 262223202 taught by Professor Dai during the Spring '09 term at UCLA.

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33bmidterm2 - Midterm 2 Math 33B Daniel Murfet May 13, 2011...

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