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Solution to textbook problems

# Solution to textbook problems - c Considering that U(s is a...

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3.5 – 1 Laplace transform: Extra homework problems 1) Assume that the following system of two differential equations is given: u x x dt dx u x dt dx 1170 . 1 2381 . 2 8333 . 0 7 4048 . 2 2 1 2 1 1 - - = + - = Furthermore y = x 2 . The initial conditions are x 1 (0) = x 2 (0) = 0. a) Demonstrate that the two equations can be rearranged to one second-order differential equation. Hint: First solve the second equation for x 1 , then take the derivative and substitute in the first equation. b) Apply the Laplace transform to the second-order differential equation obtained in a), and solve for Y(s). The initial conditions are: y(0) = dy(0)/dt = 0 and u(0) = 0.
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Unformatted text preview: c) Considering that U(s) is a unit step input – i.e. U(s) = 1/s – find the correct expression for y(t). d) Calculate the value of y(t) for ∞ → t by applying the final value theorem. 2) Exercise 3.4 in Seborg et al. (2004). 3) Exercise 3.7 (c) in Seborg et al. (2004) 4) Exercise 3.13 (a) in Seborg et al. (2004) Solutions (on paper) to these problems can be submitted in the mailbox of Krist V. Gernaey (building 227, second floor)!...
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