ma330f05test2

# ma330f05test2 - MA330 Fall 2005 Test 2 2 November 2005...

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MA330 Fall 2005 Test 2 2 November 2005 Name:

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2 1. Consider the initial value problem y ±± +5 y ± +6 y =12 ,y (0) = 0 ± (0) = 0 . (a) Find the Laplace transform of the left hand side (LHS) of the above equation. (b) Find the equilibrium solution? (c) Solve the IVP using Laplace Transforms.
3 2. (a) When using Fourierr series, we assume that a function f ( x ) that is periodic with period p =2 L can be represented as an in±nite series of the form f ( x )= a 0 + (Add the necessary math symbols to complete the above expression so that it shows the standard form for the fourier series.) (b) f ( x ) , is given graphically over one period, [ - 3 , 3] , by -2 0 2 0 0.5 1 . A good estimate for a 0 would be . (c) Because f ( x ) is an even / odd (circle one) function, we expect that the coeﬃcients for the sine / cosine (circle one) terms should be 0 . (d) Find the formula for the non-zero Fourier coeﬃcients

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4 3. Consider the one-dimensional wave equation, u tt = c 2 u xx , where we assume that u ( x, t ) describes the vertical displacement from equilibrium for an elastic string of length L, with x
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## This note was uploaded on 11/29/2010 for the course MATH ME 330 taught by Professor Skufca during the Fall '10 term at Clarkson University .

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ma330f05test2 - MA330 Fall 2005 Test 2 2 November 2005...

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