review problems for 1st midterm

# review problems for 1st midterm - REVIEW PROBLEMS FOR THE...

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Unformatted text preview: REVIEW PROBLEMS FOR THE FIRST MIDTERM 1. (a) Find the inverse transform of ( s- 2) e- s s 2- 4 s + 3 . (b) Compute the Laplace transform of δ ( t- 5) + g ( t ), where g ( t ) = sin t for ≤ t < 2, g ( t ) = 0, for t ≥ 2. (Note: it may be helpful to use sin( θ + ψ ) = sin( θ )cos( ψ ) + sin( ψ )cos( θ ). (c) Find the Laplace transform of R t f ( τ ) dτ , where L{ f } ( s ) = 1 / ( s 2 + 1) 3 / 2 . 2. (a) Find the Laplace transform of y if y 00 + 2 y + y = f ( t ), y (0) = 1, y (0) = 0, where f ( t ) = 1 if 0 ≤ t < 1 and f ( t ) = 0, if t ≥ 1. (b) Without inverting the transform explicitly, which of the following terms might appear in the solution y ( t )? Which terms could not possibly appear in the solution y ( t )? Justify your answer. (Hint: To invert the Laplace transform of y , you might need to set up some partial fraction decompositions. But to answer this question you do not need to compute the numerical values of the coefficients in these decompos- tions.) (i) ce...
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review problems for 1st midterm - REVIEW PROBLEMS FOR THE...

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