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Unformatted text preview: Suggested homework questions: Section 6.5; Impulse Functions In each of the following find the solution of the initial value problem: • # 1. y 00 + 2 y + 2 y = δ ( t- π ) , y (0) = 1 ,y (0) = 0 . • # 7. y 00 + y = δ ( t- 2 π ) cos( t ) , y (0) = 0 ,y (0) = 1 . • # 9. y 00 + y = u π 2 ( t ) + 3 δ ( t- 3 π 2 )- u 2 π ( t ) with y (0) = y (0) = 0. REMARK: Make sure you are quick with the Laplace transform table and also are familiar with partial fractions . If not then do more of the same type of questions above. Section 6.6; The convolution integral • Show that f * g = g * f . Hint: Use a change of variables t- τ = z . In each of the following find the Laplace transform of h ( t ): • # 4. h ( t ) = Z t ( t- τ ) 2 cos(2 τ ) dτ. • # 5. h ( t ) = Z t sin( τ ) e τ- t dτ. # 7. h ( t ) = Z t cos( τ ) sin( τ- t ) dτ. (questions 4,5,6 have been slightly modified from book)....
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This note was uploaded on 12/29/2010 for the course MATH 263 taught by Professor Coombs during the Spring '08 term at UBC.
- Spring '08