Homework1_mae143b

Homework1_mae143b - Question 3 Solve the following ordinary...

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MAE143B Homework Set 1 - due in class Thursday October 15 Question 1 Find the time functions corresponding to each of the following Laplace transforms using partial fraction expansions. Show your work and show your verification using the residue and impulse commands in matlab. FPE-N Question 3.7 (d) 3 s 2 +9 s +12 ( s +2)( s 2 +5 s +11) , (f) 2( s +2) ( s +1)( s 2 +4) , (j) e - s s 2 . FPE-N Question 3.8 (d) s 3 +2 s +4 s 4 - 16 , (f) s 2 - 1 ( s 2 +1) 2 . Question 2 Explain why the impulse command can be used to calculate the inverse Laplace transform of F ( s ), when the inverse Laplace transform is a time function and impulse is a calculation for a system, whose inputs and outputs are time functions but which is described by a transfer function.
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Unformatted text preview: Question 3 Solve the following ordinary dierential equations using Laplace transforms. Show your work and verication using the initial function in matlab. FPE-N Question 3.9 (b) y ( t )-2 y ( t ) + 4 y ( t ) = 0; y (0) = 1 , y (0) = 2 . (d) y ( t ) + 3 y ( t ) = sin t ; y (0) = 1 , y (0) = 2 . Question 4 FPE-N Question 3.16. For a second-order system with transfer function 3 s 2 + 2 s-3 , determine (a) the DC gain; (b) the nal value to a step input. Explain your answers well....
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Homework1_mae143b - Question 3 Solve the following ordinary...

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