# Exam3 - Math 427K Exam 3 Name UT EID Instructions Please...

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Math 427K Exam 3 Name: UT EID: Instructions Please put your name and UT EID in the space provided. There are 4 questions each worth 10 points. You have 50 minutes to complete the test. Please write your working and solutions on the test paper. You may use the back of the pages. Calculators are not allowed. For Instructor’s Use Question 1 Question 2 Question 3 Question 4 Total

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M427K Exam 3 May 4th, 2005 Question 1 [10 Points] Solve the initial value problem y ( t ) + 4 y ( t ) + 4 y ( t ) = h ( t ) , y (0) = 0 , y (0) = 1 for the discontinuous forcing function h ( t ) = 0 0 t < 2 e - 3 t 2 t using the Laplace transform. 2
M427K Exam 3 May 4th, 2005 Question 2 (a) [5 points] Find the inverse Laplace transform of 2 s ( s 2 + 1) 2 . (b) [5 points] Solve the initial value problem y ( t ) + y ( t ) = δ ( t - π ) - δ ( t - 3 π ) , y (0) = 0 , y (0) = 0 using the Laplace transform. Sketch the solution y ( t ). 3

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M427K Exam 3 May 4th, 2005 Question 3 Consider the conduction of heat in a 50 cm iron rod ( α 2 = 0 . 12 cm 2 / sec 2 ). Suppose
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