Answer Happy

Question 1 Suppose we are given a system described by the differential equation. y" - y = sin(wt), where y(0) = 1 and y'(0) = 1, for a small w. Here t is the independent variable and y the dependent variable. 1.1 Solve the problem using Laplace transforms. That is, 1.1.1 first apply the Laplace transform to the equation, with L(y) = Y, 1.1.2 then determine the transfer function G(p), and use partial fractions to simplify it. 1.1.3 Solve for Y from the transfer function G(p). 1.1.4 Determine L-(Y) and obtain y. The latter should be the solution. 1.2 Solve the same problem using the reduction of order method. Details on this method can be found in chapter three of your textbook(Duffy). 1.3 You now have to compare the two methods: The popular belief is that the Laplace method has advantages. If you agree, then state the advantages you noticed. Otherwise, if you think the opposite is true, then state your reasons. [25]