3354_f05_st3

3354_f05_st3 - y ( t ) y ( t ) = e-2 t-3 Z t y ( t-τ ) e 3...

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Math 3354, Sample Test # 3, Name 1. Find the Laplace transform of each: (a) f ( t ) = t 2 h ( t - 2), (b) f ( t ) = e 2 t sin(3 t ) , (c) f ( t ) = h ( t - 1) e - t ANSWER: (a) 2 e - 2 s ( 2 s 2 + 2 s + 1 ) s 3 , (b) 3 ( s 2 - 4 s + 13) , (c) e - s - 1 s + 1 2. Find the inverse Laplace transform of F ( s ) = 2 e - s ( s + 2) 3 + e - πs s 2 + 2 s + 2 . ANSWER: f ( t ) = h ( t - 1)( t - 1) 2 e - 2( t - 1) - h ( t - π ) e - ( t - π ) sin( t ) 3. Find the partial fraction expansion for 11 s - 23 ( s - 3) ( s - 1) ( s + 2) . ANSWER: 1 ( s - 3) + 2 ( s - 1) - 3 ( s + 2) 4. Find the inverse Laplace transform F ( s ) = 10 s 2 ( s 2 - 1)( s 2 + 4) . ANSWER: (a) 8 ( s 2 + 4) - 1 ( s + 1) + 1 ( s - 1) , (b) f ( t ) = 4 sin(2 t ) - e - t + e t 5. Use Laplace transforms to solve the integral equation for
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Unformatted text preview: y ( t ) y ( t ) = e-2 t-3 Z t y ( t-τ ) e 3 τ dτ . ANSWER: y p =-3 / 2 + 5 / 2 e-2 t 6. Use Laplace transforms to solve the initial value problem y 00-y = e t , y (0) = 1, y (0) = 0. ANSWER: y ( t ) = 2 + ( t-1) e t 7. Use Laplace transforms to solve the initial value problem y 00 + 4 y = 2 δ ( t-π/ 2), y (0) = 1, y (0) = 0. ANSWER: y ( t ) = cos(2 t )-u ( t-π/ 2) sin(2 t )...
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This note was uploaded on 10/19/2011 for the course MATH 2254 taught by Professor Gilliam during the Fall '05 term at Texas Tech.

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